Air University

Allen G. Peck, Lt Gen, Commander

Air Force Research Institute

John A. Shaud, Gen, PhD, USAF, Retired, Director

School of Advanced Air and Space Studies

Gerald S. Gorman, Col, PhD, Commandant

James M. Tucci, PhD, Thesis Advisor
AIR UNIVERSITY

AIR FORCE RESEARCH INSTITUTE

Air Superiority at Red Flag

Mass, Technology, and

Winning the Next War

Joseph W. Locke

Lieutenant Colonel, USAF

Drew Paper No. 9

Air University Press

Maxwell Air Force Base, Alabama 36112-5962

October 2009
This Drew Paper and others in the series are available 

electronically at the Air University Research Web site 

http://research.maxwell.af.mil and the AU Press Web 

site http://aupress.au.af.mil.

ii

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distribution unlimited.

Muir S. Fairchild Research Information Center Cataloging Data

Locke, Joseph W.

Air superiority at Red Flag : mass, technology, and winning the next war / Joseph 

W. Locke. 

 p. ; cm. – (Drew paper, 1941-3785 ; no. 9)

Includes bibliographical references.

ISBN 978-1-58566-201-2.

1. Air power—United States. 2. Air warfare—Mathematical models. 3. Fighter 

pilots—Training of—United States—Statistics. 4. Eagle (Jet fighter plane). I. Title. II. 

Series.

358.4340973—dc22
iii

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v

Contents

Chapter	 Page

DISCLAIMER . . . . . . . . . . . . . . . . . . . . . . . . . . ii

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ABOUT THE AUTHOR . . . . . . . . . . . . . . . . . . . ix

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . 1

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 METHODOLOGY: RED FLAG . . . . . . . . . . . . . . 13

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 STRATEGIC IMPLICATIONS . . . . . . . . . . . . . . . 61

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . 67

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . 71

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . 207

Illustrations

Figure

1 Nevada test and training range (NTTR) size 

comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 NTTR airspace functionality . . . . . . . . . . . . . . . 15

3 Daily attrition variation . . . . . . . . . . . . . . . . . . . 24

4 Yearly attrition variation . . . . . . . . . . . . . . . . . . 25

5 2001 attrition variation . . . . . . . . . . . . . . . . . . . 26

6 Yearly average sortie variation . . . . . . . . . . . . . . 27

7 Yearly force ratios . . . . . . . . . . . . . . . . . . . . . . . 27

8 Attrition variation versus threat aircraft . . . . . . 30
vi

Figure	 Page

9 Threat weapon and aircraft comparison . . . . . . 31

10 Final data breakdown . . . . . . . . . . . . . . . . . . . . 32

11 MiG-23/29 short scatter plot . . . . . . . . . . . . . . 33

12 MiG-23/29 short attrition box plot . . . . . . . . . . 34

13 MiG-23/29 short force ratio histogram . . . . . . . 35

14 MiG-23/29 short regression results . . . . . . . . . 36

15 SU-27 long regression lines . . . . . . . . . . . . . . . . 37

16 MiG-23/29 short attrition lines log scale . . . . . . 43

17 Force ratio histogram . . . . . . . . . . . . . . . . . . . . 43

18 MiG-23/29 short kill ratio . . . . . . . . . . . . . . . . . 46

19 MiG-23/29 surviving Red Aircraft versus 

F-15C sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

20 MiG-23/29 short A-A missile 100 versus 

100 kill ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

21 MiG-23/29 short A-A missile 100 versus 

100 leakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

22 MiG-23/29 short A-A missile 100 versus 

300 kill ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

23 MiG-23/29 short A-A missile 100 versus 

300 leakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

24 MiG-23/29 short A-A missile 100 versus 

700 kill ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

25 MiG-23/29 short A-A missile 100 versus 

700 leakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

26 SU-27 long missile attrition lines log scale . . . . 56

27 SU-27 long kill ratio . . . . . . . . . . . . . . . . . . . . . 56

28 Combined attrition and kill ratio . . . . . . . . . . . . 57

Table

1 MiG-23/29 campaign plan analysis data . . . . . . 49

2 SU-27 long campaign plan analysis data . . . . . . 58

CONTENTS
vii

Foreword

Soviet premier Joseph Stalin once famously noted, “Quantity 

has a quality all its own.” Certainly the Allied victory in the 

Second World War, in which Stalin’s war machine played a vital 

role, depended on the tremendous output from Allied armaments 

factories that swamped Nazi Germany and imperial Japan. Yet 

studies of air warfare have always emphasized the important 

role of technological quality, as opposed to simple mass. Certainly Stalin’s much larger air force was overwhelmed in June 

1941 by the technologically superior and better-trained Luftwaffe. North Atlantic Treaty Organization planners in the 1970s 

and the 1980s likewise sought to check Warsaw Pact numerical 

superiority by fielding smaller numbers of superior aircraft.

Yet planners would be unwise to neglect the importance of 

“mass” even in today’s high-tech air superiority environment. 

Lt Col Joseph W. Locke’s study offers a model for understanding the relationship between technology, mass, and attrition in 

aerial warfare that is useful for shaping operational and strategic 

force decision making. The F-15C’s offensive counterair (OCA) 

sweep mission within the capstone United States Air Force exercise Red Flag highlights one potentially useful relationship 

that has value as a model for air superiority. A rigorous comparison of data from 299 Red Flag missions suggests a change 

in attrition rates that correlates with force ratios. The most significant implication of this study, however, is the predicted 

variance in changing kill ratio as the force ratio changes. The 

wide middle area of stability, identified as numerical attrition, 

is consistent with the traditional notion that kill ratio is largely 

a function of training and technology. It is also consistent with 

most of the historical record, including the early campaigns of 

World War II, that suggested that nominal changes in the relative mass of forces brought about little change in the kill ratio. 

This is also the reason evolving technology often produced the 

only observable change in the kill ratio. The rapid change in 

attrition rate at either end of the model also has great explanatory value. By indicating regions where disproportionate force 

dictates a similarly lopsided victory, the concept accounts for 

several notable historical cases, such as Operations Desert 

Storm (1991) and Allied Force (1999). With continuous devel-
viii

opment and the incorporation of additional data, these diagrams 

can aid operational planners in developing more effective air 

superiority campaigns in future conflicts.

“Air Superiority at Red Flag” was originally written as a master’s thesis for Air University’s School of Advanced Air and 

Space Studies (SAASS) at Maxwell AFB, Alabama. The thesis 

was directed by Lt Col John Terino, a member of the SAASS 

faculty. Lieutenant Colonel Locke’s thesis is thoroughly researched, analytically rigorous, and forcefully written. It was 

the recipient of the 2008 “SAASS Thesis Award in Technology, 

Space, and Cyberspace,” sponsored by the Air University Foundation. SAASS is pleased to partner with the Air Force Research 

Institute and Air University Press to publish it as a Drew Paper, 

thereby making it available to a wider audience.

RICHARD R. MULLER

Professor of Military History and Associate Dean

USAF School of Advanced Air and Space Studies

FOREWORD
ix

About the Author

Lt Col Joseph W. Locke graduated from the United States Air 

Force Academy in 1995. After completing undergraduate pilot 

training in 1997, he proceeded to fly F-16CJs at Mountain 

Home Air Force Base (AFB), Idaho. Subsequently, Colonel Locke 

served as an air liaison officer and joint terminal air controller 

from 2001 to 2003 and supported several units, including the 

10th Mountain Division, Operations Detachment Alpha 365 and 

1st Battalion 5th Special Forces Group in both Operations Enduring Freedom and Iraqi Freedom. He returned to the F-16CJ 

in 2003 and served as an instructor pilot, flight commander, 

and assistant director of operations at Spangdahlem Air Base, 

Germany. He is a senior pilot with 1,500 hours of flying. Colonel Locke graduated from the Air Command and Staff College 

and SAASS.

Colonel Locke, a native of Cedaredge, Colorado, is married to 

the former Erin M. O’Connell of Evanston, Wyoming. They have 

three children: Caron, Jessica, and Garrett.

xi

Acknowledgments

I would like to thank Col Gerald S. Gorman and the rest of 

the SAASS faculty for their dedication to the mission. I would 

also like to thank the administrative staff, including Sheila 

McKitt and Kelly Rhodes, who supported each student well beyond the requirements of their job descriptions. 

This thesis would not have been possible without the outstanding support of the Red Flag team at Nellis AFB, Nevada. 

Thanks go to Col David Stilwell, commander of the 57th Adversary Tactics Group. Col Greg Neubeck, commander of the 414th 

Combat Training Squadron, allowed me the freedom to follow a 

hunch. Additionally, Everett Clason and the entire Arcata crew 

were not only instrumental in collecting the data but also provided valuable insight into Red Flag historical trends.

The other major hurdle in this thesis was my own rudimentary understanding of computers and statistics. Capt Travis 

Herbranson personally saved me many hours of work by assembling the final database and checking it for accuracy. In 

addition, Dr. Melanie Teichert and Dr. Gary Schaub helped me 

through the doldrums of statistics to find patterns in the chaos. 

I cannot say enough about the love and support I received 

from my wife and other family members. Their enthusiasm and 

understanding made the past year a pleasure instead of a year 

of pain.

xiii

Introduction

Through nearly 2,500 years of recorded warfare, the strategic debate over the primacy of quantity versus quality remains 

undecided. Esoteric examples of highly trained and motivated 

soldiers defeating massive, yet impotent, hordes clutter history. 

Hannibal’s exploits at Cannae, Napoléon’s victory at Austerlitz, 

and Nelson’s victory at Trafalgar are only a few examples of 

great captains overcoming the odds and defeating numerically 

superior forces with skill and guile. Military historians often 

cite these victories and analyze them for insight and inspiration. With so many examples for inspiration, however, it is easy 

to forget that, in many cases, mass wins. Many skilled commanders have fallen to the weight of superior numbers despite 

heroic efforts and battlefield genius. Therefore, the essential 

issue for commanders is not about quality or quantity. Instead, 

commanders must focus on how these two factors interact and 

what combination provides the best chance for victory. 

Clausewitz understood this interaction and combined these 

complementary factors into a unifying concept of strength. 

Strength combines raw numbers with a host of other factors—

including training, tactics, skill, weapons, initiative, and commander’s genius—that routinely affect the fighting strength of 

the opposing armies and their soldiers.1 Qualitative differences 

involving these factors can create advantages that offset numerical shortcomings, especially when applied at decisive points. 

At the strategic and operational levels of war, the challenge is 

to determine the strength required for a desired effect. Attacking with insufficient strength ensures the loss of offensive 

power at the expense of achieving the desired objective. Conversely, using excessive strength squanders effort better used 

to exploit opportunities concurrent with the main attack or 

useful in influencing the attainment of other objectives. 

Operations Desert Storm and Allied Force and the opening 

gambit of Operation Iraqi Freedom are routinely invoked as 

contemporary benchmarks of American conventional military 

accomplishment. Although the skill required to execute each of 

the previously mentioned campaigns was noteworthy, the United 

States’ disproportionate strength heavily favored American military victory. In each case, the strategic environment held the 
xiv

enemy completely at risk, while at the same time ensuring 

American and allied forces were immune from attack. Col John 

Warden describes this situation as Case II-offensive operations.2 He fittingly describes this situation as a “commander’s 

dream . . . [that] provides the opportunity for decisive action—

action so decisive the war can theoretically be won from the 

air.”3 As a result, his famed five-ring model was well suited for 

the situation where United States (US) Air Force stealth platforms and precision munitions could combine to attrite enemy 

capability without a direct ground confrontation. Regrettably, 

visions of brief, pristine conflicts with only minuscule losses 

have transformed recent strategic opinion toward a belief that 

such victories were not only possible but also probable. According to some, high-technology war made victory such a foregone conclusion that visionaries were primarily concerned with 

refining the elegance of the final product. Obviously, the recent 

lessons from Iraq and Afghanistan highlight the fallacy that 

tactical capability ordains strategic victory. As America focuses 

toward winning the war against terror, the temptation is for the 

United States to rest on its laurels in the conventional arena. 

Frederick Kagan highlights the pitfalls of believing “future 

adversaries will simply cede the realm of conventional war to 

the US.”4 He suggests America’s aerial hegemony is a temporary phenomenon that will last only until other nations find 

methods of incorporating or countering its technology. America’s 

enemies will adapt for their own survival and attempt to alter 

the balance of power in their favor. The first step in the process, 

developing counter tactics, is easily identifiable in the conflicts 

since Desert Storm. Serbian surface-to-air missiles (SAM) operators successfully shot down a stealthy F-117 using an outdated SA-3, ingenuity, and patience.5 Insurgent groups in Iraq 

and Afghanistan are dispersing and blending into the terrain to 

negate the advantage of American high-technology reconnaissance and precision-strike capabilities. Other nations are actively taking the steps necessary to counter American technology 

directly by developing their own innovative, high-technology 

systems to hold American aerial hegemony at risk.

In the future, when American forces act outside of Warden’s 

Case II scenario, immaculate victory becomes less likely, and the 

stakes increase dramatically, yet victory remains the only option. 

INTRODUCTION
xv

In that case, the depth of America’s military strength becomes 

more influential than its esoteric application. This realization does 

not negate the great strides evident in such new planning methods as effects-based operations or systemic operational design.6

Understanding the enemy, the enemy’s centers of gravity, and 

potential weaknesses are always critical elements in any viable 

plan no matter the scenario. The main difference is in execution. 

Where enemy offensive strength is considerable, American offensive potential diminishes due to increases in defensive requirements. Conversely, when enemy defensive strength is significant 

enough to prevent—at least temporarily—strategic attacks on 

their centers of gravity; tactical military force-on-force confrontation is the only remaining option. 

Before the next major war begins, strategic decisions about 

military force structure will shape the feasibility of operational 

plans and preordain the costs in both dollars and lives required 

for victory. The increasing expense of next generation aerial 

weapons means that current and future inventories are shrinking at an alarming rate. Current trends suggest that 20 B-2s 

and fewer than 200 F-22s will face the responsibility of defending America’s shores and projecting power worldwide. Future 

systems, like the joint strike fighter, will similarly supplant current aircraft with increased capabilities and reduced numbers. 

These shrinking inventories of high-technology aircraft will 

likely result in a future conflict where America will fight outnumbered and be completely reliant on technology to maintain 

a preponderance of Clausewitzian strength. Therefore, efficiency is essential to maintain freedom of action. 

Efficiency is only attainable through understanding. By exploring the relationship between mass and technology in the 

broader context of aerial combat, commanders can increase 

the quality of their operational and strategic decisions before 

placing forces in harm’s way. How much mass is needed to accomplish the objective? Will more aircraft increase the chances 

of success? If more aircraft will help, how much of an advantage will accrue? What are the potential effects of a new technology on the battlefield? Bounding these operational questions 

are strategic decisions about numbers and types of aircraft 

made years or even decades before a confrontation erupts. 

INTRODUCTION
xvi

Finding a method for understanding these relationships is essential for enhancing the decision process.

Purpose and Objectives

This study proposes a model for understanding the relationship between technology, mass, and attrition in aerial warfare 

that is useful for shaping operational and strategic-force decision processes. Red Flag serves as the data set used to highlight and explain one potentially useful relationship. This 

daunting task, if taken as a whole, could lead to an unusable 

mess confused by the limits of training and result in sweeping 

generalities irrelevant to strategic and operational users. Additionally, like most exploratory studies attempting to use observed data from events designed for another purpose, this 

complex scenario contains numerous unaccounted for variables that hamper pristine scientific correlation.7 Instead, by 

focusing the analysis on a narrow piece of the larger whole, 

relationships become less ambiguous, trends become clearer, 

and correlation more direct. The ideal subject for analysis includes as few training limitations as possible, maintains the 

greatest possible interaction with the adversary forces, shows a 

consistent level of participation and performance over time, 

and represents one of the emphasized mission areas exercised 

during Red Flag. Therefore, the air-to-air mission area, and 

specifically the F-15C and the offensive counterair-sweep mission, provides an ideal center of attention.8

Air superiority is the “pivotal prerequisite for success” that 

enables every other airpower function from strategic attack to 

airlift.9 As such, it is a critical capability with grave strategic 

implications for failure. Once air superiority is established, the 

US Air Force can directly focus on attacking the enemy’s ability 

and will to fight. Without it, however, every mission becomes a 

fight for the air itself and results in little pressure applied to the 

enemy. While air superiority in and of itself does not guarantee 

victory, it helps to ensure a joint force commander’s freedom of 

maneuver and initiative within his operational area. This lesson, reinforced in every major operation since World War I, requires constant focus and is easy to take for granted.

INTRODUCTION
xvii

Chapter 1 highlights the quest for a more complete understanding about the character of aerial combat and explains the 

limitations of the major approaches applied in this quest. Chapter 2 examines Red Flag and statistically explores the Red Flag 

data to create an attrition model relating mass and technology. 

This section helps those uninitiated with the Red Flag exercise 

and those interested in the underlying explanation of the final 

relationships. Readers familiar with Red Flag or uninterested 

in the statistical data analysis can skip to chapter 3 to enter 

directly into the exploration of the results of the analysis and 

its implications.

Chapter 3 develops and recommends a method of attrition 

modeling designed to help commanders make informed decisions about air strategy at the operational level of war. It attempts to account for the character of modern aerial combat, is 

flexible enough to adjust to the realities of different scenarios, 

and is simple enough for timely results to shape campaign 

plans. Chapter 4 analyzes the strategic implications of the data 

and makes recommendations for additional research.

Notes

(Notes for this chapter and the following chapters appear in shortened form. 

For full details, see appropriate entries in the bibliography.)

1. Clausewitz, On War, 194–97.

2. Warden, Air Campaign, 17. Warden identifies five specific cases of air 

superiority characterized by the vulnerability of blue and red airfield/rear 

areas and the accessibility of the battle-lines to aircraft. Case I (the Chess 

Game) holds both sides vulnerable across all three variables. Case II (Offense) 

threatens red and holds blue immune to attack. Case III (Defense) is the 

opposite of Case II. Case IV (Limited Options) occurs when both sides are 

immune from attack on their resources but can fight over the battle area. 

Finally, Case V is a scenario where neither the battlefield nor the adversary 

homelands are vulnerable to aircraft.

3. Ibid., 33.

4. Kagan, Finding the Target, 390.

5. Lambeth, NATO’s Air War for Kosovo, 117–18.

6. Air Force Doctrine Document (AFDD) 2.0, Operations and Organization,

13–20, 85–97; and Schmitt, “Systemic Operational Design,” unpublished 

paper.

7. Kutner, Nachtsheim, and Neter, Applied Linear Regression Models, 345–46.

8. AFDD 2–1.1, Counterair Operations, 17.

9. AFDD 1, Air Force Basic Doctrine, 41.

INTRODUCTION



Chapter 1

Review of Literature

The object of science is knowledge; the object of art is 

creative ability.

—Carl von Clausewitz

On War

Like war as a whole, airpower theory has evolved with an 

acknowledgment that strategy is both an art and a science. 

Controversy between these two diametric terms stems from the 

faulty belief that success lies in emphasizing one over the other. 

The variable character of warfare and the unique temperament 

of individual battles ensure the irrelevance of either a checklist 

methodology or blind trust in a previously successful commander. War is fickle if for no other reason than because it is a 

clash of wills between learning and evolving opponents.1 Effective strategy then must balance both the knowledge of what is 

probable with the coup d’oeil to realize what is possible. Unfortunately, extrapolating tactical science to help shape operational and strategic art is difficult. 

Such land warfare maxims as successful attacks needing a 

three-to-one advantage provide commanders with a baseline for 

gauging the strengths of their plan. The rule, however, remains 

open for interpretation within the specific context of the situation. Environmental factors like terrain and vegetation present 

unique challenges and opportunities that focus on a commander’s perception of the possible.2 Similarly, the human element 

is an overriding force in land warfare that greatly influences a 

commander’s options.3 The machines used to augment human 

power often magnify the effects of the human will. Mechanized 

troops that are out of fuel can regress to a role as infantry to 

continue the fight. Admittedly, their effectiveness will decrease, 

but as long as their will remains, resistance will continue.

Unlike ground combat, however, aerial warfare exists in a 

different environment and follows a different set of rules. The 

aerial environment is largely uniform and unpredictable. When 

Airmen confront each other in the sky, few geographic benefits 
REVIEW OF LITERATURE

provide an initial edge. There is no terrain to supply an advantage or vegetation to offer concealment. Weather can obviously 

play a role, but its effects are often equally restrictive for both 

sides. The sun may offer a fleeting advantage in the visual engagement, but only for an instant. Admittedly, geography exerts an 

influence on basing and determines flight routes and proximity to 

the battle. However, global reach technology makes virtually any 

location accessible with the right equipment. As a result, the 

balance of technology between the opposing forces defines the 

realm of the possible in aerial warfare. Lt Col William Sherman 

eloquently explains this relationship in his 1926 book, Air Warfare, by suggesting, “The man in the air is peculiarly at the 

mercy of material things. No matter how great his determination nor how high his courage, he is helpless against an enemy 

with a machine that can out-run, out-climb, and out-maneuver 

him.”4 Additionally, an aircraft out of fuel or weapons must either retreat to safety or perish. The Airman in combat is completely reliant on his machine for relevance on the battlefield. 

Technology, like terrain, however, can only go so far in determining the outcome of conflict. Pilot training, tactics, numbers 

of aircraft, and chance all play into the relationship to determine the outcome. This is true historically and will continue to 

be true into the near future.

The Combined Bomber Offensive

One germane historical example is the combined bomber offensive of World War II, since it provides an excellent case to 

highlight the aforementioned interaction of factors. Changes in 

relative levels of technology and mass between the Allied and 

Axis powers resulted in vastly different outcomes in the skies 

over Germany. Largely understood as a war of attrition, the air 

war’s character and levels of losses evolved greatly between 

when the US Army Air Forces (AAF) entered the war in 1942 

and final victory in 1945. Early air-to-air combat against the 

Germans in 1942 resulted in an even kill ratio of approximately 

1:1.

5 Given the high level of German experience in the air-to-air 

arena compared to the green American pilots, it is fortunate 

that results were not worse. Additionally, with the stress on 

unescorted bombing in 1942, the AAF put little emphasis on 
REVIEW OF LITERATURE

the air superiority role. By 1943, however, the need for fighter 

escort was obvious, and fighter sortie counts began to rise. For 

the first several months, force ratios between the fighters remained about even, but by early 1944, the Allies had nearly a 

three-to-one advantage in fighters over the intercepting German aircraft.6 Initially, this had little effect on the kill ratio. 

Between 6 April and 5 June 1944, the Allies flew nearly three 

times as many air-to-air sorties as the Germans but accounted 

for a kill ratio of only 1.2:1.

7 The following three-month period, 

however, saw a twofold increase in Allied forces that significantly altered the balance of power. Between 6 June and 5 September 1944, Allied fighter sorties outpaced the German missions sixfold, and the fighter kill ratio jumped to 6.8:1.

8

Pilot training and new technology explain some of this dramatic jump in kill ratio. A lack of German emphasis on producing pilots early in the war resulted in a dramatic decrease in 

their pilot’s experience and training levels by 1944.9 A United 

States Strategic Bombing Survey (USSBS) document, however, 

contradicts this interpretation. While it acknowledges that 

overall bomber losses were declining, it concludes that the 

number of “bombers lost to E/A [enemy aircraft] per 100 combats with E/A” increased from 5.0 in late 1943 to a high of 17.7 

in the second quarter of 1944.10 While increases in the effectiveness of German armament account for some of this increase, it would not be possible without a high degree of pilot 

skill.11 Similarly, many sources credit the introduction of the 

P-51 Mustang in late 1943 with tipping the technological advantage toward the Allies.12 The Mustang, however, provided 24 

percent of the Allied fighter sorties between 6 April and 5 June 

1944 and 30 percent between 6 June and 5 September 1944. 

Again, this small change can account for some of the difference 

in the kill ratio, but it cannot explain the dramatic change in 

kill ratio from about even to an advantage of 6.8:1 in only three 

months. Morale could also have played a part, but the German 

war machine continued to function for more than a year after 

the Normandy invasion. Instead, the dramatic increase in the 

mass of the Allied air offensive seems to correlate most closely 

with the increase in the kill ratio. Noting this trend, Edward 

Luttwak concludes that Germany’s “qualitative military superiority had become insufficient to offset numerical inferiority.”13
REVIEW OF LITERATURE

Air Force Doctrine Document (AFDD) 1, Air Force Basic Doctrine, states, “The purpose of mass is to concentrate the effect of 

combat power at the most advantageous place and time to 

achieve decisive results . . . through effectiveness of attack, not 

just overwhelming numbers.”14 Given airpower’s inherent speed, 

range, and flexibility, this concept is potentially more valid today than ever before. Whether measuring numbers of aircraft or 

the number of targets each aircraft can attack, however, both 

are merely tactical measures, which require expansion. Endurance, sortie generation, and industrial potential are all important measures of mass at the operational and strategic level.

Unlike land warfare, where combat assets—man or material—can remain within the confines of battle from the start of 

an operation to the decision, combat aircraft effectiveness is 

fundamentally limited by time. Fuel becomes a significant problem during an engagement as fuel consumption rates increase. 

Aircraft unable to remove themselves from the fight before 

running out of fuel become unnecessary casualties aiding the 

enemy’s cause. Likewise, opportunities to press an advantage 

may slip away if fuel restricts pursuit. Similarly, weapons capacity and use rates have virtually the same effect. An aircraft 

out of munitions becomes a liability rather than an asset in 

combat. Aerial refueling goes a long way to solving part of the 

problem by allowing aircraft to extend their range from home 

base, but fuel consumption remains an issue for deciding the 

duration combat aircraft can remain engaged. Weapons consumption, however, is only resolved by returning to base. As a 

result, harmonizing the time an aircraft needs to remain in 

combat with the rate it expends fuel and munitions is a delicate 

balance. Expect too much and the operational plan begins to 

break apart with gaps in capability. Expect too little and the 

sorties are wasted through inefficiency.

Closely nested with the on-station time requirement, sortiegeneration capability is essential to keeping aircraft actively in 

the fight. Two of the most important measures of this capability 

are utilization (UTE) rates and average sortie duration (ASD). 

The UTE rate measures the average number of sorties an individual aircraft is required to fly in a specific period to accomplish the tasking.15 ASD simply averages the amount of time 

individual sorties remain airborne.16 Increasing either measure 
REVIEW OF LITERATURE

puts added strain on the aircraft and maintenance. Ground 

turn times also can affect the overall measure of mass, because 

the longer aircraft are unavailable between sorties results in 

decreasing UTE rates. Up to a point, generating more sorties 

will increase the efficiency of the operation and ensure maximum pressure on the enemy. Past that point, however, efficiency rapidly decreases as aircraft begin to break faster than 

ground crews can make repairs. Therefore, a balanced operational plan must account for these realities and attempt to use 

aircraft at, but not exceeding, their maximum efficiency. 

The last measure of mass is usually unaccounted for until it 

is too late. Manufacturing aircraft is a long process that requires specialized facilities and specially trained workers. 

Therefore, underestimating the number of aircraft required can 

have catastrophic consequences. Again, the German experience in World War II proves instructive. As German lessons 

from the Spanish Civil War indicated, “The problem of air superiority was not primarily one of numerical strength but of the 

quality of the personnel and weapons in the [air] arm.”17 After 

spectacular victories in Poland and France in 1939–40, the 

German government did not increase aircraft production to 

prepare for the larger battles ahead.18 Instead, “the Germans 

were sure that their technological expertise and military competence could master any threat.”19 By the time the Luftwaffe 

realized the error, it was too late to increase aircraft production 

enough to stem the tide of Allied numerical superiority.20

By contrast, Pres. Franklin D. Roosevelt set the goal of producing 10,000 combat aircraft a year in November 1938 and 

increased the goal to 50,000 a year in May 1940.21 Despite the 

foresight, American industry was unable to make the transition rapidly. Production rates reached the 10,000 aircraft a 

year mark in early 1942 and did not exceed 50,000 a year until 

1943.22 Given the significantly longer lead times to produce 

modern high-technology military aircraft, the timeline to increase the size of today’s Air Force would likely be significantly 

longer.23 Today’s trend toward shrinking aircraft inventories 

and long production lines accentuates this dilemma. Unlike 

the preparation for World War II, modern combat aircraft have 

virtually nothing in common with automotive or even civilian 

aircraft production. No longer can automobile factories and 
REVIEW OF LITERATURE

their workers simply transition from building Fords to building 

F-22s. Instead, special facilities and specialized workers with 

the skills to work titanium, carbon fiber, and a myriad of other 

specialized materials would have to be grown. 

Combining that production ramp-up timeline with the lethality 

of current systems means the US Air Force will likely have to 

fight and win the next war with the equipment it has on hand. 

Therefore, understanding the combat repercussions of peacetime force structure is essential to determining future American 

wartime success. With the increased lethality of forces, however, the time to wait and see what happens may be minimal. 

Generals will face a rapid succession of events where choices 

about when and where to mass forces can rapidly escalate towards inevitable victory or defeat before new aircraft production becomes a reality. Underestimating the number of aircraft 

required to gain and maintain air superiority against a wellequipped enemy may prove unrecoverable in an unexpected 

war. Overestimating, however, is no longer fiscally feasible. 

Therefore, attempting to understand the relationship between 

mass and technology is essential for intelligent force structure 

decisions. Similarly, understanding the relationship could prove 

helpful for building successful operational plans. Finding a 

method to extrapolate tactical relationships into a useful form 

for shaping operational and strategic plans, however, has 

proven elusive. The past century witnessed several different 

methods for estimating the effort and time required to establish 

air superiority. Ranging from simple historical extrapolation to 

complex computer models, these techniques attempt to inform 

a commander’s decisions with varying degrees of success. 

Mathematical Modeling

F. W. Lanchester published one of the first models for aerial 

warfare in his 1916 book, Aircraft in Warfare. One of the earliest attempts to write a coherent airpower theory, he envisioned 

the full range of missions from reconnaissance to strategic attack and argued for the necessity of an independent air arm to 

maintain air superiority over enemy forces.24 Despite his significant contributions and balanced analysis of early airpower, 

Lanchester’s standing among aviators faded in comparison to 
REVIEW OF LITERATURE

less mathematically inclined theorists such as Giulio Douhet 

and William “Billy” Mitchell in the 1920s. Despite his obscurity 

to the line Airman, he had a deep and persistent influence in 

the emerging field of operations research. 

Intertwined within Lanchester’s analysis of airpower was a 

deterministic mathematical relationship for analyzing military 

forces. Deterministic methods use equations to describe a relationship between relevant, quantifiable variables. As a result, 

they provide predictable and repeatable answers to known 

questions. They are extremely useful in the regime of pure science where an input directly correlates to a known effect. Unfortunately, if the analysis is biased or skewed in sections of 

the relationship, erroneous results can lead to poor decisions.25

Lanchester’s most prominent and controversial equation is the 

N-squared law that uses differential equations to derive a simple 

mathematical relationship to assess the strength of technologically driven military forces on the battlefield. His N-squared 

law suggests that “the fighting strengths of a force may be 

broadly defined as proportional to the square of its numerical 

strength multiplied by the fighting values of its individual 

units.”26 The derivation of the equation is unimportant in this 

analysis except to explain that Lanchester’s measure of military strength equals the force’s quality (M) times the square of 

its mass (b) as expressed by the equation:

Strength = Mb2

Assuming an accurate quality factor (M) for each side, the 

model provides a deterministic method of estimating the winning side and the timeline for the decision based on the interaction of quality and raw numbers.27 J. F. C. Fuller even used 

the N-squared law as part of the rationalization to emphasize 

battlefield technology over mass.28 Unfortunately, the appealing simplicity masks the complexity and variability of actual 

combat. By ignoring factors like morale, combined arms, and 

movement, Lanchester’s equation requires significant modification to produce acceptable levels of accuracy.29 Additionally, 

even with modification, the factors need specific “tuning of the 

equations” for the results to match historical examples.30 As a 

result, Kenneth Watman, currently the deputy chief of staff for 

strategic plans and programs at Headquarters Air Force, con-
REVIEW OF LITERATURE

cludes, “It cannot be said that the Lanchester equations have 

ever constituted a generalizable model of warfare.”31

Recognizing the deficiencies of Lanchester, Col Trevor N. Dupuy, 

US Army, attempted to predict future battlefield results through 

a rigorous quantitative analysis of military engagements throughout history. Approaching the problem from an entirely different 

direction, his quantified judgment method of analysis (QJMA) 

used 73 discrete variables, including mass, technology, the environment, surprise, morale, and other intangible factors to 

calculate a “power potential ratio.”32 All told, his methodology 

enables the deterministic calculation of a winner and the approximate number of casualties on both sides. To bolster his 

methodology, he concludes that his results are similar to 

Lanchester’s despite the differing methods.33 Dupuy’s methodology, however, never reached acceptance as a viable methodology, and the QJMA model had little lasting effect on modern modeling practice. 

Instead, other methods of predicting combat outcomes proved 

more feasible. Joshua Epstein made a substantive addition to 

the field with the creation of the adaptive dynamic model that 

accounts for some of the many shortcomings omitted by 

Lanchester, including unit maneuvers and diminishing marginal returns on increased force sizes (tactical over-crowding).34

His model gained some credibility and helped to shape the debate about force postures late in the Cold War. Unfortunately, 

as Steven Biddle has pointed out, his model shares one weakness with Lanchester’s model because it “displays unstable 

equilibrium behavior.”35 Deterministic calculation induces the 

flaw by ignoring the realm of chance. As a result, when opposing forces are closely matched, minuscule changes in a single 

input variable can result in large differences in the outcome. 

Contrasting with the exact answers of deterministic models, 

stochastic models use similar equations but use statistical 

variability to influence the model’s output.36 These models rely 

on randomness and repeated calculations to create a solution 

indicating both the needed answer and a perspective on the 

variability in the solution.37 As a result, they can account for 

problems with deterministic models and their unstable equilibrium behaviors. The drawback is they require a great deal of 

computing power. The remarkable leaps in computer tech-
REVIEW OF LITERATURE

nology over the past half century enabled the rapid growth of 

stochastic computation and modeling. In turn, these stochastic computer models are facilitating a robust analysis program 

within the Department of Defense (DOD).38

Ranging from specific tactical analysis to broad strategic 

simulation, current computer war-gaming techniques offer the 

potential for enlightening operational strategy. Several technical 

models, like the trajectory analysis program, provide detailed 

analyses of air weapon kinematics and lethality that actively 

shape the development of aerial tactics, techniques, and procedures.39 On the other end of the spectrum, strategic simulations integrate seamlessly in large-scale war games that help 

leaders refine their strategic thinking.40 Modern modeling and 

simulation techniques also have the potential to shape operational plans.

Planning Operation Desert Storm

During planning for Operation Desert Storm, staffs attempted 

to estimate aerial attrition for the upcoming campaign. The Air 

Staff’s Checkmate Doctrine Division produced an early effort, 

dated 27 August 1990. It used a combination of “quantitative 

analysis, historical experience, and sound professional judgment to derive a reasonable estimate of projected aggregate 

losses.”41 Models developed for a conflict against the Soviets 

resulted in an estimate of 2 percent attrition. Adding depth to 

the analysis, they used Operation Linebacker II as a historical 

model with an overall attrition rate of 1.4 percent. By comparing relevant technological and political factors, the division 

concluded that an overall attrition rate of between 1 to 2 percent was likely and would result in the loss of 20 to 40 aircraft 

in the first six days of aerial operations. Unfortunately, it provided no insight regarding which types of aircraft were vulnerable or the reason for their calculated vulnerability.

A later analysis, dated 12 December 1990, by the secretary 

of defense’s Program Analysis and Evaluation Division used a 

similar but more in-depth methodology that divided attrition 

rates into four combat categories: air-to-air, interdiction, close 

air support, and multirole. Using an estimation of 50,000 total 

sorties resulted in anticipated total losses of 210 fighters, in-
REVIEW OF LITERATURE

10

cluding 14 from air-to-air engagements, 71 from interdiction, 

88 from close air support, and an additional 36 losses of multirole aircraft.42 This was obviously not far from the actual Operation Desert Storm tally of 65,000 sorties but a gross overestimation of the actual 38 aircraft losses.43 Additionally, with 

an expected campaignwide combat attrition rate of 0.42 percent, this estimate appears executable. Unfortunately, it focused 

exclusively at the strategic level of war and made little effort at 

analyzing the operational implications of the prediction. 

Taking a closer look at the projected losses compared to the 

number of aircraft deployed paints a different picture. Using 

Gulf War Air Power Survey figures for the number of deployed 

aircraft, 210 losses would equal 15 percent of the coalition 

fighter and bomber force destroyed.44 A more detailed breakout 

indicates projected aircraft loss percentages would equal 7 percent of air-to-air, 27 percent of interdiction, 39 percent of close 

air support, and 9 percent of multirole aircraft.45 The estimate 

also includes 623 “additional battle damage incidents,” which 

suggests that 60 percent of coalition aircraft would either be 

destroyed or damaged in combat.46

The discrepancy may be rooted in the method of calculation, 

because nominal Air Force attrition rates calculated losses for 

a massive Soviet confrontation.47 This model was extremely different from the problem presented by Iraq. Instead of fighting 

outnumbered and on the defensive against communist hordes, 

coalition forces were attacking a numerically and qualitatively 

inferior adversary. The report acknowledged the differences 

and attempted to account for them by making corrections based 

on historical evidence. Unfortunately, its examples merely cited 

different attrition rates but did not account for any of the other 

relevant differences like the size of the forces or their technological capabilities. Perhaps adding another field of study could 

have increased their awareness of these issues and improved 

their estimate.

In The Art of Wargaming, Peter Perla suggests that adding 

exercise analysis could help. He recommends a “continuous 

cycle of research, war games, exercises, and analysis” as a 

method of augmenting our understanding of reality.48 The US 

Air Force exercise that serves as the foundation for this work, 

Red Flag, provides just such an opportunity. Unfortunately, no 
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11

attempt to extract Red Flag’s lessons beyond the tactical level 

was available. While it is improbable that this data would have 

changed the outcome of Desert Storm, equipping the planners 

with the larger lessons may have improved their prescience 

about the likely results. Chapter 2 explains the applicability of 

Red Flag to operational planning and then attempts to extract 

meaning from the collected data for future reference.

Notes

1. Clausewitz, On War, 149.

2. Army Field Manual (FM) 6-0, Command and Control of Army Forces, 

B4–B7.

3. FM 3-0, Operations, 6-5.

4. Sherman, Air Warfare, 35.

5. Reinburg, Air-to-Air Combat in World War II, 10.

6. “The Defeat of the German Air Force,” 26.

7. Reinburg, Air-to-Air Combat in World War II, 11.

8. Ibid., 15.

9. Murray, Strategy for Defeat, 254.

10. “The Defeat of the German Air Force,” 16.

11. Ibid., 21–23.

12. Jacobs, “Operation Overlord,” 277–78.

13. Luttwak, Strategy, 240–41.

14. Air Force Doctrine Document (AFDD) 1, Air Force Basic Doctrine, 22.

15. Maintenance Metrics US Air Force, 34.

16. Ibid., 33.

17. Grabmann, “USAF Historical Studies,” 79.

18. “The Defeat of the German Air Force,” 27.

19. Murray, Strategy for Defeat, 302.

20. Ibid., 302–3.

21. Sherry, Rise of American Air Power, 79, 91.

22. Lilley et al., Problems of Accelerating Aircraft Production during World 

War II, 92.

23. This statement does not suggest that America needs 50,000 combat 

aircraft in its inventory. Rather the intent is to highlight that changing the 

American aircraft industry to wartime production rates requires significant 

warning and years to bring it to fruition.

24. Lanchester, Aircraft in Warfare, 148–50.

25. Keppel and Zedeck, Data Analysis for Research Designs, 202.

26. Lanchester, Aircraft in Warfare, 55. The author used several terms to 

describe M over the course of his derivation. Fighting value is the most common, but efficiency and effectiveness are also used. 

27. Epstein, Calculus of Conventional War, 3.

28. Fuller, Foundations of the Science of War, 266–71.
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12

29. Taylor and Neta, “Explicit Analytical Expression for a Lanchester 

Attrition-Rate,” 3–4; Epstein, Calculus of Conventional War, 4–7.

30. Watman, “War Gaming and Its Role in Examining the Future,” 57.

31. Ibid.

32. Dupuy, Numbers, Predictions, and War, 33, 51.

33. Ibid., 148–50.

34. Epstein, Calculus of Conventional War, 4–13.

35. Biddle, “European Conventional Balance,” 108.

36. Thierauf and Klekamp, Decision Making through Operations Research, 

454–55.

37. Ibid.

38. Ball, Fundamentals of Aircraft Combat Survivability Analysis and Design, 143.

39. Ibid., 150.

40. E. L. Perry (Air Force War Gaming Institute/Northrop Grumman Contractor), interview by the author, 12 December 2007.

41. “Predicted Attrition for Instant Thunder Air Campaign,” 1.

42. “Desert Shield Tactical Air Force Combat Losses, Damage, and Munitions Consumption.”

43. United States General Accounting Office, Operation Desert Storm, 92.

44. Keaney and Cohen, Gulf War Air Power Survey, 44.

45. Ibid., 27–28.

46. “Desert Shield Tactical Air Force Combat Losses, Damage, and Munitions Consumption.”

47. Ibid.

48. Perla, Art of Wargaming, 287.
13

Chapter 2

Methodology

Red Flag

Quantities derive from measurements, figures from 

quantities, comparisons from figures, and victory from 

comparisons.

—Sun Tzu

The Art of War

For more than 30 years, Red Flag has existed as the premier 

aerial combat training environment in the world. During that 

time, it has evolved significantly to prepare America’s Airmen 

for war. By providing pilots with their first 10 combat missions 

insulated from the imminent threat of death, aircrews can learn 

to survive in a chaotic and lethal environment. Red Flag obviously retains a tactical focus to enhance the skills of aircrews 

from the newest wingman to the most experienced mission 

commander.1 Additionally, by assembling complete aerial force 

packages in a single location, units have the invaluable opportunity to “train the way we intend to fight” by fully integrating 

the numerous aircraft capabilities of the US Air Force, joint, and 

coalition aircraft into a single harmonious and lethal unit.2 By 

constraining the lessons of Red Flag to the tactical level, however, 

the US Air Force is missing an opportunity to gain operational 

and strategic insight into the chaotic world of aerial combat.

The combination of excellent airspace, robust threat replication, high-fidelity instrumentation, and zealous debriefs produces 

an unsurpassed training environment that approaches combat 

without actually firing live missiles, destroying equipment, and 

killing. The Nevada Test and Training Range (NTTR) at Nellis 

Air Force Base outside Las Vegas, Nevada, is an enormous 

combination of airspace and land ranges that facilitates largescale aerial training. Covering approximately 12,000 square 

nautical miles, it provides areas for aircraft to marshal, air refuel, and fight in size similar to the geographic lanes used in 

combat operations.3 In comparison to familiar recent combat 
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14

geography, figure 1 shows the NTTR over a map of Iraq. By land 

area, the NTTR is one-tenth the size of Iraq and twice the size 

of Israel. Unfortunately, the entire area is not available for use 

by Red Flag.

Figure 1. Nevada test and training range (NTTR) size comparison. 

(Reprinted with permission from National Geographic Society online maps).

Five primary areas divide the facility as depicted by figure 2. 

For Red Flag, the areas in orange, red, and blue are of major 

interest. Orange represents the area contested only by enemy 

air assets and small tactical-level SAMs. Red contains heavily 

defended terrain with the full array of enemy air and ground 

threats, houses simulated Red Air tactical regeneration airfields, and coincides with the target sets that striker assets 

plan to attack. As a result, the red area in figure 2 shows the 

scene of continuous chaos during a mission and is the location 

of most aircraft losses from a dense collection of SAMs and 

enemy aircraft. The area depicted in blue provides a location 

for such command and control assets as Airborne Warning and 

Control System and aerial refueling during the missions and is 

considered a blue safe area. Black is either a no-fly area, or it 

represents restricted areas for Red Air participants only and 

constitutes an area outside of the exercise. The green area usu-
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15

ally holds close air support training and is off limits to the main 

strike package. As a result, the red and orange areas constitute 

the actual area for Red Flag combat maneuver training and cover 

an area slightly larger than the country of Israel. While a source 

of consternation for mission planners, the restricted areas are 

essential for training administration. They also coincidentally 

introduce restraints common in war. National boundaries and 

different mission packages in adjacent sectors can all restrict 

the attack breadth and direction to suboptimal levels. 

The 57th Adversary Tactics Group (ATG) is responsible for 

adding a robust and realistic threat to the outstanding training 

airspace. As the premier training aid for US personnel, the 57th 

ATG continually refines its tactics to present an accurate representation of the full spectrum of enemy capabilities.4 The 

64th and 65th Aggressor Squadrons (AGRS) and the 507th Air 

Defense Aggressor Squadron (ADAS) are central to the accuracy of the simulation. Flying F-16 and F-15 aircraft, the 64th 

and 65th AGRS replicate the tactics, techniques, and proceFigure 2. NTTR airspace functionality. (Reprinted from Red Flag home 

page [https://www.mil.nellis.af.mil/units/redflag/do/do.asp]).
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16

dures (TTP) of existing and postulated adversaries. Their pilots 

are highly experienced and complete a rigorous training program to ensure accurate aircraft and weapons replication.5 The 

507th ADAS adds the second element of air defense by replicating adversary SAM systems within the NTTR. Using a combination of military personnel and civilian contractors, the 507th is 

continually refining its ability to provide the “best SAM simulation possible.”6 Unfortunately, due to the classification of this 

paper, the credibility of the 57th ATG cannot be discussed in 

detail. Based on the author’s experience and interviews with 

operators in all three squadrons, one thing became clear: while 

there is always room for improvement, the threat replication 

provided by the 57th ATG is at least as capable as any anticipated enemy without exceeding plausible adversary capabilities. 

Another great advantage the NTTR and Red Flag have over 

combat operations is their instrumentation through a system 

called the Nellis Air Combat Training System (NACTS). This 

system provides continuous, real-time updates on the exact 

locations of every aircraft on the NTTR. While this system is 

intentionally not used for mission execution, it provides an unparalleled capability for reconstructing the mission afterward. 

NACTS provides exact parameters and relationships to other 

aircraft that are continually available for analysis and play an 

essential role in ensuring the results are as realistic as possible. 

What used to take hours to reconstruct can be replayed in 

rapid succession or slowed down to a crawl for detailed scrutiny. As a result, outcomes become less ambiguous and more 

accurate. This accuracy leads directly to the ability to find root 

causes for errors, learn from those mistakes, and improve performance the next day. This truth data also prevents the traditionally heated debriefs from degenerating into debates about 

sequences and outcomes. In total, the synergy of excellent 

training airspace, adversary support, and accurate post-mission 

analysis adds greatly to the training environment.7

Limitations

Despite these geographically and technologically enabled 

benefits, some shortcomings in the Red Flag scenario and their 

execution ensure results will never exactly mirror combat con-
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17

ditions. First, real-world intelligence is never perfect. America’s 

next test in combat may face tactics or weapons previously unknown or unimagined. Such surprises inevitably occur in war. 

If there is a flaw in the current threat replication, that flaw relies on the precision of intelligence. Adversary crews strive for 

precise replication of tactics but are rarely free to improvise. As 

a result, a critical piece of the war is missing from the exercise. 

War is a conversation between opposing sides.8 In its current 

state, Red Flag is muting half of the dialogue by constraining 

its aggressor operators from using their systems to the best of 

their ability. On one hand, this policy makes sense because it 

provides Blue Air a consistent set of assumptions to fight. Unfortunately, it also trains crews to trust intelligence data implicitly and to solve the problem of aerial combat mechanically. 

This could lead to a catastrophic problem where units cannot 

improvise in the face of new enemy tactics not predicted by intelligence sources. 

Second, despite the chaotic, free-flowing environment presented by Red Flag, the emotional stress falls well short of combat. Undoubtedly, the capabilities of new wingmen to perceive, 

comprehend, and react to complex scenarios are greatly enhanced over the course of a two-week Red Flag. The true effects 

of combat are knowingly absent because real missiles are not 

flying and losses to enemy action only draw repercussions during debrief. Imagine the difference in a flight leader’s mentality 

launching on his third Red Flag sortie determined not to get 

another wingman “killed.” Then compare that to the emotions 

of the same pilot launching on a combat sortie back to the 

same area where his wingman ejected the day prior. Some will 

react in a highly competitive way determined to make a mark 

on the enemy, while others may face severe anxiety leading up 

to the sortie. While the courage to “press on” despite the loss of 

a wingman is required in both events, Red Flag obviously falls 

significantly short of combat emotions.9 Only placing an individual in the real scenario will reveal a true reaction. 

Third, since Red Flag is a training exercise, safety takes 

precedence over realism. In most cases, sound tactics equate 

to safe execution, and there is no effect on the flow of the mission. Sometimes, however, deconfliction takes the front seat. 

In these instances, pilots elect not to make a full defensive ef-
METHODOLOGY

18

fort against the exercise threat and instead ensure deconfliction from other flights in the area. The result is often an official 

“kill” due to lack of maneuvers when in reality the crew may 

have survived the same scenario during combat. Similarly, 

night missions often require aircraft to maintain specific altitudes for the entire duration to guarantee deconfliction from 

stealth aircraft. This measure for training safety restricts tactical effectiveness and would likely lead to decreases in attrition rates for both sides. The desire for deconfliction does not 

fade during combat operations. Similar schemes are apparent 

in combat missions, but pilots are more likely to deviate from 

planned parameters when the need for survival outweighs the 

perceived risks of safety. 

Fourth, the shot-kill criteria used to determine the outcomes 

contain known errors that preclude their use as true results. 

The 83d Fighter Weapons Squadron uses extensive testing 

through live missile launches with operational squadrons to 

verify air-to-air weapons capability. The results of the testing 

go directly toward building detailed models of missile capability 

throughout their flight to a target. Despite this accuracy, pilots 

must analyze their shots in real-time while tactically executing 

a stressful mission. As a result, simplified rules of thumb substitute for complex computer models and enable a sufficiently 

accurate kill-removal process to take place within the framework of the exercise. This simplification leads to conservative 

results and potentially fewer than expected kills.10 On the other 

end of the spectrum, probability in the exercise becomes a binary, yes-or-no solution. Missiles do not work this way. Each 

missile will have a varying chance of killing its target between 

0 and 100 percent. Actual missile probability of kill (Pk) is determined by the equation: Pk = PhPk/h.

11 Probability of hit (Ph) 

represents the probability of a missile hitting its target. This 

factor accounts for a complex sequence of events including the 

missile launch sequence, guidance phase, and fusing at the 

target. For the training scenario, Ph varies based on simplified 

understanding of the missile’s capability and is 0, 50, or 100 

percent effective depending on several factors. Oversimplification leads toward an optimistic result, since most valid shots 

result in a 100-percent training Ph. The probability that a hit 

will result in a kill (Pk/h) is a gauge of target aircraft survivability 
METHODOLOGY

19

measured against the missile. Real-world Pk/h varies by aircraft 

based on the specific element of its design in relation to the 

weapon.12 In the training simulation, Pk/h equals 100 percent 

for all fighter aircraft. Modern aircraft designs specifically attempt to reduce their vulnerability to missile impact. With numerous examples of aircraft returning with significant combat 

damage, it is obvious that Pk/h is less than 100 percent. An irreparable aircraft sitting on a friendly airbase, however, is just 

as useless as a crashed one except that a search and recovery 

mission would not be launched for the downed aircrew. Even 

reparable aircraft will remain out of the usable inventory for a 

fixed time before returning to duty. The result is optimistic by 

forecasting target destruction with every impact. Fortunately, 

the conservative simulation model and the optimistic missile Pk

tend to offset each other. The result is a usable approximation 

of missile capability, but it will skew the accuracy of the findings away from actual results.13

Despite the previously discussed limitations, the Red Flag 

exercise results in a near-combat experience usable to model 

modern aerial combat. Since the same conditions influence 

both sides, the relationships between the opposing forces 

should remain near their natural, wartime character. The final 

attrition numbers will inevitably vary from the results of a combat engagement, but they should mirror combat relationships. 

As a result, it is important to emphasize that the useful part of 

this analysis will lie in the linkages and not in the specific values of the data. While using this analysis may prove fruitful for 

anticipating the results of future Red Flag missions, attempting to use the specific results of this data for real-world planning would likely lead to erroneous conclusions and poor strategic decisions. Therefore, Red Flag can serve as a reasonable 

model for modern combat and is useful for representing combat experiences within the scope of this thesis. The patterns 

and relationships are therefore the focus of analysis. 

Assumptions

In addition to the previously discussed tactical limitations 

within the Red Flag scenario, some operational level assumptions are required to frame the applicability of the data. Pri-
METHODOLOGY

20

mary among them is that Red Flag replicates a near-peer competitor with comparable resources to the deployed US military 

force. The adversary is capable of investing in not only a robust 

military architecture but also a military force of highly trained 

professionals who are ready to fight.

Next, the Red Flag scenario does not account for the effects 

of bombing on future sortie generation for either side. This is 

most similar to Colonel Warden’s Case IV—limited options. In 

this case, airfields and rear areas are immune from attack either because of “political restraints or because of the physical 

inability to reach appropriate targets.”14 One example of this 

scenario is the fight for aerial supremacy during the Korean 

War when both sides left plans for attacking enemy airfields off 

the table due to fears of escalating the war toward open global 

conflict.15 These political limitations are an unfortunate but occasionally necessary element in warfare that affects the range 

of options available to military commanders. The Red Flag data 

may also have utility in other scenarios, but the correlation will 

be less direct.

Finally, the Red Flag tactics on both sides are high risk, and 

leaders expect losses. Red Air methodology focuses on a mentality of defending its homeland but also accounts for Blue Air 

training requirements.16 Similarly, Blue forces execute using 

a high-risk mentality where losses are acceptable for mission 

accomplishment. The result is a fight for survival mentality 

that guarantees attrition on both sides. This mentality is also 

common throughout history, with the strategic bombing campaign against Germany during World War II serving as an example of how high-risk missions can produce elevated attrition rates. Changes in acceptable levels of risk for either side 

would likely decrease the frequency of aerial confrontation 

but should not affect the attrition values for individual battles 

within the larger campaign.

Data Set

This study uses Red Flag as a quantitative model to highlight 

and explain the relationship between mass and technology in 

aerial combat to advance operational and strategic thought regarding the relationship. This daunting task, if taken as a 
METHODOLOGY

21

whole, could lead to an unusable situation confused by the limits of training and result in sweeping generalities irrelevant to 

strategic and operational users. Instead, by focusing on a single 

mission area with the fewest possible variables, trends become 

clearer and correlation more direct. 

Red Flag’s focus on offensive operations necessitates further 

focus on the role of OCA in creating air superiority. AFDD 2-1.1, 

Counterair Operations, defines OCA as “offensive operations 

aimed at destroying, disrupting, or degrading enemy air and 

missile threats.”17 OCA defines a spectrum of actions that range 

from direct kinetic attacks by dropping bombs on enemy airfields, known as OCA-surface attack, to the less invasive electronic jamming of enemy surface-to-air radars that is part of 

OCA suppression of enemy air defenses (SEAD). Within that 

continuum of aerial combat, one mission, OCA sweep, seeks to 

destroy airborne enemy assets before they engage other friendly 

aircraft. The sweep mission holds a unique place with the Red 

Flag exercise. In the interest of training, friendly strikers, SEAD 

players, and other friendly aircraft in the exercise continue on 

their mission after an enemy attack to facilitate their training. 

Sweep players, on the other hand, exist within the scenario 

and face immediate kill removal during execution. Kill removal 

is not permanent, since sweep players can regenerate after exiting the fight area, but the immediate removal ensures that the 

sweep scenario more closely replicates the lessons of combat. 

Focusing on the initial OCA-sweep missions inside the exercise provides several other advantages. First, the F-15C, the 

primary OCA-sweep aircraft of the US Air Force, has changed 

little between 2001 and 2005. Despite updated software suites 

enabling subtle new capabilities, its primary tactics and weapons have remained similar for the entire period. Critical capabilities like beyond visual range (BVR) identification, Link-16 

data sharing, and the advanced medium-range air-to-air missile (AMRAAM) have remained constant throughout the period. 

Significant additional capabilities include the joint helmet 

mounted cueing system and the AIM-9X heat-seeking missile 

in 2004–7. While these systems greatly enhance the F-15C’s 

lethality in a visual engagement, most of the engagements occur with the AMRAAM at longer ranges. Therefore, a significant 

difference between the results should not exist. By further fo-
METHODOLOGY

22

cusing the investigation on ingress results, the data remains 

less affected by the friction of the training environment. After 

the initial sweep, “killed” aircraft clutter the airspace transiting 

toward regeneration areas or returning to base. This added 

ambiguity often leads directly to artificial results from erroneous tactical decisions based on poor situational awareness and 

the inability to identify enemies as dead or alive. The ingress 

sweep phase, however, does retain the positive stresses of Red 

Flag, since both air and ground threats are present.

Arcata Associates, Inc., under contract to the US Air Force 

since 1999, collects the data used in this thesis for assessing 

the effectiveness of units during the course of each two-week 

Red Flag exercise. Each data point was collected during the 

detailed debriefs after each of 784 missions.18 Although Arcata 

employees are not involved in the analysis process, they personally record the arbitrated debrief results and consolidate 

the information into a single source database for each Red Flag. 

A macro consolidates individual Red Flag databases into a single document for analysis. Extracting additional information 

on threats from the Air Combat Command after action reports 

provided the data necessary to analyze the effects of adversary 

tactics on mission results. Unfortunately, since the reports 

were generated to summarize training and not facilitate analysis, several are missing data or lack the detail necessary to be 

useful in this study. As a result, the viable data set decreased 

by 338 missions (216 before 2001; 42 in 2001; one in 2002; 60 

in 2005; and 19 in 2006) to 446. Additionally, a major change 

in the Red Flag scenario occurred starting in 2006. Red Flag 

added several new scenarios, and the adversary threats shifted 

significantly to replicate a modernized threat scenario. While 

this is a great enhancement for US Air Force training and readiness, it represents a qualitative shift in the data for this analysis. While data collected starting in 2006 should more accurately represent a fully modernized adversary, the small number 

of available data points and additional scenarios hinders this 

analysis.19 As a result, the remaining 320 missions from 2001 

to 2005 provide a focused data set with reasonably consistent 

conditions for analysis. 

Within the 320 remaining missions, no OCA-sweep aircraft 

launched on six missions, and a single F-15C that launched 
METHODOLOGY

23

without additional OCA support accounted for another: all 

seven cases were removed. Additionally, four missions dropped 

out because they recorded zero losses on both sides for the ingress sweep. This was likely due to an in-flight emergency or 

other training-related termination of the fight. Arcata deletes 

incomplete results caused by administrative procedures.20 Finally, Red Air presented a MiG-21 threat on two missions in 2004. 

With only two missions, they represent no statistical benefit for 

the analysis and were deleted. This left 307 effective missions 

with 299 containing F-15Cs as the primary or sole element in 

the sweep. The N of 299 missions is the basis for the analysis, 

except when analysis requires the additional information. 

The data set covers the results of execution for each flight of 

aircraft regardless of mission and includes basic measures of 

effectiveness depending on the specific mission area. As a result, air-to-air engagements and air-to-ground mission success rates are available for each flight. One difference between 

air-to-air and air-to-ground data collection is the break point 

between the ingress and egress units of measure. The dividing 

line for air-to-ground missions is weapons release on target. 

Air-to-air ingress data transitions at the reset of the preliminary aggressor tactic.21 This difference in break point leads to 

an inaccurate accounting of aerial kills between strikers and 

aggressors since striker ingress can take place after the first 

presentation. As a result, it is not possible to correlate striker 

losses or air-to-air kills using this data. 

Data Analysis

The analysis used both Excel and Statistical Program for the 

Social Sciences (more commonly referred to as SPSS) version 

12.0.1 to determine the significance of results and produce the 

outputs for this paper. Statistical tests used in this analysis to 

determine significance and correlation include frequencies, 

percentages, correlations, t-tests, and analysis of variance 

(ANOVA). Correlations will use Pearson’s correlation coefficient. 

Tukey’s honestly significant difference (HSD) post-hoc analysis 

methodology will support initial ANOVA results, assuming 

Levene’s test for homogeneity proves insignificant. Regression 

analysis using the method of least squares provided the predic-
METHODOLOGY

24

tive trends of future results. Analysis relied on the 0.05 level of 

significance for evaluation.

Since Red Flag is a training environment, it is essential to 

understand when changes in attrition are due to changes in 

participant training level. Traditional lore would predict a decrease in Blue and an increase in Red attrition over the twoweek exercise due to increased aircrew proficiency. The threat, 

however, continually increases over the same time-span. Logic 

would therefore suggest an increase in Blue and a decrease in 

Red attrition over the same time span. Figure 3 shows the averages for both F-15 and Red Air ingress attrition broken out by 

week and day. 

Contrary to the expected decrease in F-15C attrition, figure 3 

indicates a trend of increasing attrition over the course of both 

weeks one and two. Additionally, attrition is nearly identical or 

greater in week two when compared to the same day in week 

one. This is exactly opposite of the expected results if training 

and pilot skill were the only factors. A T-test indicates no significant differences in the attrition between weeks one and two. 

ANOVA analysis also indicates no significant variation amongst 

the days for each week except for between Monday and Thursday on week two (p=0.045). The Red Air trends match more 

closely the expected results. Week one follows a gradual inMON TUE WED THU FRI

DAY

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000 WK

1

2

Estimated Marginal Means of F15 ING ATT

Estimated Marginal Means

MON TUE WED THU FRI

DAY

0.6300

0.6600

0.6900

0.7200

0.7500

0.7800

Estimated Marginal Means

WK

1

2

Estimated Marginal Means of RED ING ATT

Figure 3. Daily attrition variation.
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25

crease in Red losses, while week two remains relatively constant, but neither analysis indicated any statistically significant variation in the averages. As a result, the trends indicate 

that the increase in the scenario’s difficulty likely exceeds the 

increased skill over the course of the week (appendix A3). 

Between 2001 and 2005, F-15C attrition decreased, and Red 

Air attrition increased over the same period as indicated in figure 4. ANOVA analysis indicated a significant variation in both 

F-15C (F=2.993/p=0.019) and Red Air (F=12.627/p= 0.000) attrition (appendix A1). Tukey’s HSD test revealed a significant 

difference in F-15C attrition between 2001 and 2004 (p=0.012) 

only. Similarly Red Air attrition in 2001 varied significantly 

(p=0.000) between all other years.

Figure 4. Yearly attrition variation.

Further inspection of 2001 reveals insignificant variation in 

F-15C attrition but significant variation in Red Air attrition 

(F=3.015/p=0.024 in appendix A2). Tukey’s HSD test indicates 

Red Flag 2001 3-2 varied significantly from 2001 4-2 (p=0.019) 

as depicted in figure 5. The Red Flag 2001 3-2 after action report indicated weather problems that forced mission changes and 

restrictions to account for exercise safety. Interestingly, the initial suggestion is that adverse weather decreases Red Air attrition. Normal safety precautions cuff Red Air maneuvers during 

weather days and would therefore suggest an increase in Red 

2001 2002 2003 2004 2005

Year

0.5500

0.6000

0.6500

0.7000

0.7500

0.8000

Mean of RED_ING_ATT

2001 2002 2003 2004 2005

Year

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

Mean of F15_ING_ATT
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26

Air attrition due to more predictable and therefore less-effective 

maneuvers. Unfortunately, Arcata data does not track weather 

conditions or restrictions sufficiently to explore the ramifications of weather on attrition occurring on all Red Flag missions.

The counterintuitive trend, however, suggested there might 

be another source for the changes in attrition. Checking for 

variation in other factors reveals that the 2001 anomaly is more 

likely due to differences in simulation instead of weather. Using 

an ANOVA test to analyze the numbers of aircraft flown on each 

side in Red Flag 2001 3-2 indicates a significant change in the 

numbers of aircraft flown. F-15C numbers increased slightly 

from a year average by approximately one sortie per mission to 

8.53 (p=.024), while Red Air sorties increased by over three sorties per mission to 11.67 (p=0.000). 

Taking this observation and stepping back to the yearly analysis reveals a similar trend. The year 2001 boasts the highest 

number of Red Air sorties and a comparatively low number of 

F-15C sorties when compared to 2002–2005. The significantly 

higher than average F-15 attrition and lower Red Air attrition 

in figure 4 noticeably corresponds with the significantly higher 

than average (p=0.001) number of Red Air in 2001 as depicted 

in figure 6. Similarly, the Tukey HSD test confirms a significantly lower number of F-15C sorties in 2001 as compared to 

both 2002 and 2004. 

Figure 5. 2001 attrition variation.

3-1 3-2 3-3 4-1 4-2

RF

0.1000

0.1250

0.1500

0.1750

0.2000

0.2250

0.2500

Mean of F15_ING_ATT

3-1 3-2 3-3 4-1 4-2

RF

0.4000

0.4500

0.5000

0.5500

0.6000

0.6500

0.7000

Mean of RED_ING_ATT
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27

The trend becomes clearer by transforming the raw numbers 

of aircraft into a force ratio. Dividing the total number of F-15C 

aircraft on a mission by the total number of Red Air present 

provides a simple number comparing the relative strength of 

each side. Force ratios greater than one indicate F-15C numerical advantage, while quantities less than one give the advantage to the Red Air. Figure 7 clearly depicts the difference in 

force ratios between 2001 and 2002–2005, because it is the 

only year when on average 

Red Air outnumbers F-15C 

aircraft (appendix A1). ANOVA 

testing confirms the difference (F=18.539/p=.000). A 

follow-on Tukey HSD test 

confirms that 2001 is significantly different from 2002 

(p=0.008), 2003 (p=0.000), 

and 2004 (p=0.000).

By comparing figure 7 to 

figure 4, the correlation between force ratio and attrition 

becomes clearer. The year 

2001 is characterized by the 

only force ratio numerically 

Figure 6. Yearly average sortie variation.

2001 2002 2003 2004 2005

Year

6

7

8

9

Mean of RED_TOT_FTR_FL

2001 2002 2003 2004 2005

Year

7

7.5

8

8.5

9

9.5

10

Mean of OCA_F15_FL

2001 2002 2003 2004 2005

Year

1.0000

1.2500

1.5000

1.7500

Mean of F15_FLOWN_RATIO

Figure 7. Yearly force ratios.
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28

in favor of Red Air. Predictably, F-15C attrition is highest, and 

Red Air attrition is lowest in 2001. A Pearson two-tailed correlation test confirms the association (appendix A10). Using the 

logarithm of the force ratio, F-15C attrition correlates at -0.297 

(p=0.000), and Red Air attrition correlates at 0.396 (p=0.000). 

Neither correlation is strong enough, from a purely scientific 

standpoint, to suggest this is the sole cause. However, given 

the chaotic nature of combat and the other independent variables present, this is expected. Additionally, the high level of 

significance suggests utility in using force ratio for predicting 

attrition on both sides over using only the historical average. 

This common measure of relative strength, however, is not 

without shortcomings. First, it tends to mask the increasing 

complexity of large formation battles. For example, a one-versusone duel is numerically equal to an exceedingly chaotic 100-

versus-100 mêlée. Since the Red Flag scenario is built around 

eight scheduled F-15C sorties, this issue becomes less of a 

problem, but it has the potential to give false impressions if the 

data is extrapolated to very large or very small formations. Additionally, the ratio compresses Red Air numerical advantages 

into a small range between zero and one, while F-15C advantages range from one to infinity. Representing all ratios on a 

logarithmic scale easily alleviates this problem by balancing 

the presentation around the 1:1 ratio. 

The suggestion that an increase in the number of opposition 

forces will negatively influence the outcome of the engagement 

is as old as war itself and is useless without understanding 

how other variables interact with it. In addition to the number 

of aircraft on each mission, Arcata collects data on 12 other 

independent variables. As explained earlier, weather data is not 

collected, but sorties are broken down between day-and-night 

missions. Recent combat experience suggests American night 

vision goggle (NVG) tactics should represent a distinct advantage. Initial analysis of the entire data set using an independent samples T-test indicates F-15C attrition drops by 3.67 

percent (p=0.037), and Red Air attrition increases by 6.43 percent (p=0.014) during hours of darkness (appendix A4). This 

potential difference is explored with better fidelity later in this 

analysis by including such additional variables as adversary 

weapons and tactics within the final data set. For now, with a 
METHODOLOGY

29

10 percent difference in attrition favoring Blue Air, the night 

advantage needs further exploration. 

The remaining 11 variables describe the capabilities of the 

adversary and include threat aircraft, weapon, threat tactics, electronic attack, regeneration rate, reaction level, maximum number of live groups, surface-to-air missile rules of engagement, 

surface-to-air missile proficiency, communications jamming, 

and ground-based radar jamming. Attempting to analyze each 

variable independently led to insignificantly small groups that 

yielded little or no useful information. Factor analysis (appendix A11) suggests two discrete groups for examination in addition to the force ratio and day/night variables already discussed. 

The first and largest group includes nine tactical variables 

used to describe the adversary’s less-obvious technical and 

training capabilities. The first five—tactics, electronic attack, 

regeneration rate, reaction level, and maximum number of 

groups—all directly influence the OCA-sweep mission. Two 

variables, SAM readiness levels and SAM rules of engagement, deal directly with the ground threat. Although apparently extraneous to this analysis, these variables may affect 

the ability of OCA-sweep aircraft to pursue Red Air into hostile 

territory and add to the chaos of the operational environment. 

Finally, Radio Electronic Combat and Big Crow simulate 

ground-based jammers and their effects on Blue performance. 

Unfortunately, the Red Flag training environment adjusts the 

whole group of variables simultaneously to replicate an overall threat change. As a result, a Pearson Bivariate Correlation 

test reveals that the variables significantly correlate to each 

other (r≥ 0.501, p=0.000) except maximum number of live 

groups (r≥ 0.302, p=0.000) (appendix A9). This indicates the 

variables change—together within the scenario and, therefore, 

the effects of individual variables—are unfortunately beyond 

the fidelity of this data. 

The second group, consisting of adversary aircraft and weapons capabilities, is more useful. Threat aircraft simulations include MiG-23, MiG-29, and SU-27 by the 57th ATG aggressor 

aircraft. Between 2001 and 2005, F-16s replicated this significant spectrum of threat capabilities. Although aggressor threatreplication standards try to replicate enemy capability accurately, there is the potential for an undesired uniformity in 
METHODOLOGY

30

performance. This is especially apparent at the merge, where 

actual aircraft flight characteristics are most prominent. In the 

radar missile BVR engagement, however, aggressor replication 

specifically restricts the use of aircraft systems and reactions 

to match expected threat capabilities.22 A threat aircraft ANOVA 

analysis suggests a significant variation in attrition for F-15C 

(F=6.562/p=0.002), but Red Air variation is insignificant. With 

sufficient homogeneity, the Tukey HSD comparison shows significant variation between both the MiG-23 and MiG-29 when 

compared with the SU-27 simulation for the F-15C (p=0.005/

p=0.020) attrition. Variations in Red Air attrition were insignificant (fig. 8 and appendix A5).

Figure 8. Attrition variation versus threat aircraft.

MIG-23 MIG-29 SU-27

THRT AC

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

Mean of F15_ING_ATT

MIG-23 MIG-29 SU-27

THRT AC

0.7000

0.7100

0.7200

0.7300

0.7400

0.7500

0.7600

Mean of RED_ING_ATT

MIG-23 MIG-29 SU-27

THRT AC

Count

WEAPON2

SHORT

LONG

0

20

40

60

80

100

120

140

34

56

75

138

0

5
METHODOLOGY

31

Similarly, threat weapons capability follows an almost identical path (fig. 9). Aggressor threat matrices weapons categories 

included short (MiG-23/N=34, MiG-29/N=138, SU-27/N=56) 

and long (MiG-29/N=4 and SU-27/N=75) air-to-air missile 

simulations. T-test analysis identified significant variation within 

both F-15C (p=0.012) attrition with Red Air attrition being insignificant (appendix A6). This mixed combination of weapons 

and simulated aircraft makes determining differences between 

the MiG-29 and SU-27 simulation difficult. Holding one variable steady and then analyzing the other simplify this problem. 

Figure 9. Threat weapon and aircraft comparison.

MIG-23 MIG-29 SU-27

THRT AC

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000

Estimated Marginal Means

WEAPON2

SHORT

LONG

Non-estimable means are not plotted

Estimated Marginal Means

of F15 ING ATT

First, by selecting only the short weapon and second running 

an aircraft ANOVA analysis, no statistically significant difference appears in any of the three attrition categories, despite a 

mean increase in attrition proceeding from the low MiG-23, 

through MiG-29, to SU-27. Similarly, an independent sample 

T-test comparing MiG-29 and SU-27 with short weapons results in no significant difference. With the long missile MiG-29 

(N=4) small sample size, no adequate comparison is feasible. 

Looking at the SU-27 and comparing the short and long missile 

also produce an insignificant difference in any of the three attrition rates. By correlating MiG-29 aircraft with short missiles 

and SU-27 aircraft with long missiles, a significant difference 
METHODOLOGY

32

emerges for the F-15C (p=0.025). Similarly, by adding MiG-23 

short missions back into the mix with the MiG-29, the significance continues for F-15C (p=0.004) attrition (appendix A7).

This grouping of the MiG-23 and the MiG-29 with the short 

missile compared to the SU-27 with the long missile provides 

many advantages for analysis. First, both data sets provide relatively large sample sizes (N=239) as depicted in figure 10 with 

significant variations in Blue Air attrition between day and 

night (appendix A8). Additionally, the pairing presents two different categories of enemies. The short MiG-23/29 pair represents a country with an early fourth-generation fighter capability 

similar to the threats America faced in Operations Desert Storm 

and Allied Force. The long SU-27 combination represents a 

country further along the technological road attempting to compete qualitatively with the F-15C. This dialectic provides the 

metaphor for analysis in this thesis. First, the short MiG-23/29 

scenario provides sufficient data for attrition trend identification and the Blue versus Red comparison. With the relevant 

factors and decision points identified, the long SU-27 scenario 

introduces a change in enemy technology, which facilitates the 

exploration of the ramifications on Blue capabilities.

Figure 10. Final data breakdown.

DAY NIGHT

LIGHT

Count

99

72

48

20

WEAPON

SHORT

LONG

0

20

40

60

80

100
METHODOLOGY

33

With the final data set defined for study, it is time to try to 

find order in the chaos of combat. Since this thesis explores 

relationships and does not seek to gain specific values for prediction, analysis focuses on comparisons with the intent of 

highlighting relationships for future study. Before proceeding 

further, however, it is important to confirm the previous observations within the final data set. Running a Pearson two-tailed 

correlation test with the entire group (N=239) indicates continued significant correlation between the force ratio and F-15C 

(-0.304/p=0.000) and Red Air (0.368/0.000) attrition (appendix A12). Additionally, F-15C attrition correlates with the aircraft weapons pairing (0.214/p=0.001), but Red Air does not 

change significantly. Finally, day/night does not represent a 

significant correlation for either F-15C or Red Air attrition 

within the final data set. With that in mind, analysis focuses 

completely on the short MiG-23/29 and the long SU-27 relationship to infer the potential ramifications of the enemy introducing new technology on the battlefield. 

The short MiG-23/29 scenario provides the starting point 

and therefore requires a detailed explanation of the relationships and analysis. This process attempts to extract useful information from the confusion of Red Flag. Figure 11 contains 

scatter plots of both F-15C and Red Air attrition plotted against 

the logarithm of the force ratio.

-1.0 -0.5 0.0 0.5 1.0 1.5

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

F15 ING ATT

Figure 11. MiG-23/29 short scatter plot.

-1.0 -0.5 0.0 0.5 1.0 1.5

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

RED ING ATT
METHODOLOGY

34

Although neither the F-15C nor the Red Air data groups 

neatly around a central line, the general trend is clear: increasing the force ratio for a mission results in decreasing F-15C 

and increasing Red Air attrition. Another way to visualize this 

trend is by using a box plot as shown in figure 12. It helps to 

visualize trends in the data not initially evident in the scatter 

plot. Each line indicates a single force ratio and the variance of 

the data with the solid area representing the central 50 percent 

and the whisker reaching out to accommodate most of the remaining data. Points with numbers next to them indicate outliers from the main body of the data. The dark mark near the 

center of each indicates the median value.

Figure 12. MiG-23/29 short attrition box plot.

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

F15 ING ATT

295

221

298

-.8109-.5878

-.4055

-.2624

-.2231

-.1335

-.1054

.0000

.1335

.1823

.2513.3365.4055

.4520

.5108

.6931.8755

1.02961.3863

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

-.8109-.5878

-.4055

-.2624

-.2231

-.1335

-.1054

.0000

.1335

.1823

.2513.3365.4055

.4520

.5108

.6931.8755

1.0296

1.3863

RED ING ATT

219

47

302

243

This chart again supports the correlation between force ratio 

and attrition. Therefore, regression analysis may provide a useful equation to represent the data. While several non-linear regression methods may eventually prove more applicable to a 

larger data set, basic linear regression based on the logarithm 

of force ratio is most applicable in this case for two reasons. 

First, since Red Flag is a military exercise and not a scientific 

test, the data is not evenly distributed. Instead, figure 13 reveals a nearly normal distribution of data centering on an even 

1:1 force ratio (i.e., log[1] = 0), which falls in line with normal 

exercise planning factors of scheduling nearly equal numbers 
METHODOLOGY

35

of air-to-air sorties for each side. As a result, the data confidence is best in the center and becomes less reliable at both 

extremes. The second problem with the data is that the data do 

not cover the entire range of possible outcomes. While both F-15C 

and Red Air attrition appear to anchor near their extremes, approaching 0 percent and 100 percent attrition respectively, on 

the right side of figure 12, neither side approaches the opposite 

extreme. This missing data leave much doubt about the natural trends as the force ratio moves left and favors Red Air. With 

these limitations in mind, linear regression provides a baseline 

analysis. Future studies with more complete data, however, 

may suggest other, more complex relationships.

Forward stepwise regression using the tactical variables recommends eliminating the other factors from the analysis except force ratio (appendix B1). Figure 14 represents the regression results for both F-15C and Red Air with representations 

for error analysis. Taking a closer look at both the F-15C and 

the Red Air data reveals several trends common in this analysis. First, ANOVA testing indicates that the regression line accounts for only about 14 percent of the data variation but that 

the variation is not due to chance for either the F-15C (F=26.078/

p=0.000) or Red Air (29.618/p=0.000). Similarly, the model’s 

Figure 13. MiG-23/29 short force ratio histogram.

60

50

40

30

20

10

0

-1.0000 -0.5000 0.0000 0.5000 1.0000 1.5000

LOG F15/RED FORCE RATIO

Frequency

Mean = 0.102742

Std. Dev. = 0.3831581

N = 171 1 3

16

50 51

23

14

10

1 2
METHODOLOGY

36

R-squared values of 0.134 for the F-15C and 0.149 for Red Air 

corroborate the weak correlation but also suggest that using 

the model is better than using the average attrition alone. Casewise diagnostics highlight two outliers for each case highlighted 

in figure 14 (F-15C–#s 202/221, Red Air–#s 47/259). Additionally, points 185 and 186 have disproportionate influence on 

the regression for both sides. In all cases, historical data did 

not indicate any influences that would suggest any reason to 

exclude the data and inclusion did not detract from correlation. 

Therefore, their influence is noted, but they remain as part of 

the analysis.

Using the same forward stepwise multiple regression technique for the long SU-27 scenario did not work as smoothly. 

Initial ANOVA testing suggested a weaker correlation for the 

F-15C (F=3.454/p=0.068) but significant correlation (F=7.310/

p=0.009) for Red Air (appendix B2). Two points (119/228) had 

excessive influence within both data sets. Again, neither case 

suggested abnormal circumstances for the scenario, but 228 

was a Friday night mission on the second week of a Red Flag. 

Normal Red Flag protocol requires units to depart on Saturday 

to make room for follow-on units. Therefore, pilot motivation to 

shorten the debriefing process by minimizing shots and kills 

may have decreased performance, but there is no specific evidence to support this hypothesis. While this speculation is not 

Figure 14. MiG-23/29 short regression results.

-1.0 -0.5 0.0 0.5 1.0 1.5

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

F15 ING ATT

95%

90%

80%

221

202

185

186

R Sq Linear = 0.134

-1.0 -0.5 0.0 0.5 1.0 1.5

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

RED ING ATT

R Sq Linear = 0.149

95%

90%

80%

186

185

47 259
METHODOLOGY

37

sufficient in and of itself, the small data set is less tolerant of 

abnormality. By removing mission number 228 from the data 

set, the regression returns to the same pattern observed in both 

of the short MiG-23/29 and the Red Air long SU-27 analyses 

for the F-15C (F=5.778/p=0.019) and Red Air (F=7.531/p=0.008) 

as depicted in figure 15. With that in mind, mission 228 was 

removed from the analysis as an anomaly but kept in the database for future use. Other outliers were retained in the analysis. As expected with the smaller data set and large variance 

shown in figure 15, the error size is larger but still better than 

using the mean to predict attrition.

Figure 15. SU-27 long regression lines.

-0.5 -0.2 0.0 0.2 0.5 0.8 1.0

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

F15 ING ATT

210

95%

90%

85%

101

136

254

119 

R Sq Linear = 0.082

-0.5 -0.2 0.0 0.2 0.5 0.8 1.0

LOG F15/RED FORCE RATIO

0.0

0.2

0.4

0.6

0.8

1.0

RED ING ATT

95%

90%

80%

117

11

28

198

304

256

119 

R Sq Linear = 0.104

Before moving to the explanation of the results, it is important to explain one of the limitations of the linear regression 

lines. Attrition values cannot logically exceed 100 or go below 0 

percent. On the low end of the spectrum, some aircraft will inevitably fail due to mechanical problems or pilot error. Similarly, no matter how disadvantageous the scenario, a chance 

for survival always exists. As a result, a complete data set would 

logically indicate a line approaching a logistic curve with both 

extremes asymptotically approaching but never reaching either 

0 or 100 percent. To prevent the regression lines from violating 

the limits of reality, their values have arbitrarily been limited to 

between 0.5 and 99.5 percent. Future studies should adjust 
METHODOLOGY

38

these values based on observed and calculated data not available in this study.

The four regression models just discussed form the basis of 

analysis for the remainder of the study. Their wide confidence 

intervals combined with the disproportionate influence of a few 

outliers highlight the inadequacy of the data from a scientific 

standpoint. The consistency between the four models, however, 

suggests a baseline validity to the correlation between force 

ratio and attrition. Chapter 3 makes use of these models to 

suggest methods commanders and planners can use for future 

planning efforts. The inaccuracies inherent in the regression 

models caused by the training environment skew the values 

away from similar data collected for testing purposes. Therefore, the specific values calculated in the following pages attempt to explain a thought process and highlight decision 

points instead of making predictions about real world combat.

Notes

1. “Tenets of Red Flag.” 

2. Ibid.

3. Nevada Test & Training Range (NTTR) Briefing.

4. Col David R. Stilwell (Commander, 57th Adversary Tactics Group), interview by the author, 5 December 2007.

5. Lt Col Steven D. Imonti (64th Aggressor Squadron/DOO, Aggressor 

1995–2007), interview by the author, 3 December 2007.

6. Lt Col Robert J. Smith (Commander, 507th Air Defense Aggressor 

Squadron), interview by the author, 4 December 2007.

7. Lt Col Thomas A. Bouley (Deputy Commander, 414th Combat Training 

Squadron–Red Flag), interview by the author, 4 December 2007.

8. Clausewitz, On War, 77.

9. Lt Col James A. Rousseau (507th Electronic Warfare Officer), interview 

by the author, 4 December 2007.

10. Maj Jon K. Tinsley (USAF Air-Air Weapons System Evaluation Program F-16 Program Manager), e-mail interview by the author, 14 April 2008.

 11. Ball, Fundamentals of Aircraft Combat Survivability Analysis and Design, 10–12.

12. Ibid., 603.

13. Tinsley, interview.

14. Warden, Air Campaign, 66.

15. Hone, “Korea,” 467. For a more nuanced view regarding the sanctuary 

of MiG bases north of the Yalu, see Werrell, “Across the Yalu,” 451–75. Dr. 

Werrell highlights the unassigned raids American pilots took across the Yalu 

to reduce the strategic sanctuary the communists enjoyed north of the Yalu. 
METHODOLOGY

39

While tactically rewarding, these missions risked global escalation and set a 

dangerous precedent that supported tactical action over following strategic 

orders within US Air Force squadrons.

16. Capt Ryan A. Howland (64th Aggressor Squadron/DOO, Mig-29 SME), 

interview by the author, 3 December 2007

17. Air Force Doctrine Document (AFDD) 2-1.1, Counterair Operations, 11.

18. Everett L. Clason (ARCATA Associates Red Flag Analysis Program 

Manager), interview by the author, 3–5 December 2007.

19. Starting in 2006, adversary threat replication expanded to include the 

SU-30 and actively guided air-to-air missiles. Thursday scenarios changed to 

a DCA mission for F-15Cs separated from the remaining Red Flag participants. Other factors affecting the homogeneity of the simulation, such as a 

more complete and active Red Force increased the level of training “fog” in the 

scenario. Future classified analysis of the post-2006 results may be extremely 

useful but is beyond the scope and classification of this thesis. 

20. Hugh H. Lester (ARCATA Associates Night Air-Air Mission Analyst), 

interview by the author, 3–5 December 2007.

21. Don Newell (ARCATA Associates Day Air-Air Mission Analyst), interview by the author, 3–5 December 2007.

22. Imonti, interview.

41

Chapter 3

Results

We will need those extra planes because this is an aerial 

war in which one or the other of the combatants will be 

driven from the sky — and it won’t be us. This is a grim 

struggle in which anything goes. . . . The only thing that 

counts is the score. Did you kill the enemy or did he kill 

you?

—Lt Gen Henry H. Arnold

“Our Air Force after One Year at War”

The regression models built in chapter 2 are of little value 

unless they can help shape operational plans and inform strategic decisions. To be useful, the model must answer vital questions that shape an air campaign and more specifically the air 

superiority campaign against enemy aircraft. What is the enemy’s 

most dangerous course of action? How much mass is needed to 

accomplish the objective? Will more aircraft increase the chances 

of success? If more aircraft will help, how much of an advantage will they provide? These questions frame the essential elements of the initial air campaign plan. 

Once the plan is enacted, the commander also needs a 

method to inform him of the ramifications of actual events 

and to illuminate decision points for greater advantage. Are 

the plan’s assumptions valid? Is there a better plan for defeating the actual enemy course of action? How long will it 

take before we are ready to enter the next phase of execution? Do we need reinforcements, and if so, how many? What 

is the potential effect of a new enemy technology on the battlefield? Anticipating the answers to these questions can avert 

battlefield disaster by keeping operations short of a culminating point. Additionally, correctly assessing the tide of war 

and making the appropriate adjustments stands at the core 

of the operational art.

Bounding these operational questions are strategic decisions 

about numbers and types of aircraft made years or even decades before a confrontation erupts. Between the end of World 
RESULTS

42

War II and the demise of the Soviet Union, American defense 

policy focused on opposing the gigantic Soviet threat and averting global catastrophe.1 This emphasis was obviously unavoidable based on the perceived menace of Communism and the 

immense size of the Soviet military. Today’s reality, however, 

requires a different balance between both fiscal responsibility 

and a ready and capable force structured for victory against a 

robust opponent. Therefore, a better understanding of the requirements is essential to ensure an adequate strength to meet 

the nation’s grand strategy but at minimum cost. Finding a 

method for understanding the relationships is essential for enhancing the decision process. The following pages present one 

method of organizing the information and augmenting a commander’s understanding of aerial warfare before the first combat sortie launches. 

Operational Use

Taken individually, the regression lines of both the F-15C 

and Red Air provide little relevant insight. In fact, they appear 

to be both banal and a confirmation of obvious conventional 

wisdom. Insinuating that adding more aircraft to a mission decreases Blue losses and increases Red losses is common sense 

and requires no further discussion. Plotting the lines together, 

however, proves powerful in augmenting the understanding of 

aerial combat. Figure 16 plots both lines together with the scatter chart data and 95 percent confidence intervals. 

Before proceeding further, understand the importance of 

each chart element. The X-axis plots force ratio on a logarithmic scale, and the Y-axis represents expected attrition rate between 0 and 100 percent. The areas in gray indicate the regions 

not represented by Red Flag data and are therefore only extrapolations of observed trends. Future graphs will continue to include this feature to emphasize which regions of the graphs 

represent actual data. It is also essential to emphasize that although future graphs will indicate the regression line only, they 

do not represent the only possible result from any single engagement. Instead, the regression lines represent the averaged 

peaks of the individual bell curves for each force ratio. As an 
RESULTS

43

example, figure 17 represents the distribution of points at an 

even 1.0 force ratio. 

MiG-23 and MiG-29 w/ SHORT A-A Missile 

y = -0.137Ln(x) + 0.123

R2 = 0.134

y = 0.222Ln(x) + 0.708

R2 = 0.149

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1 1.0 10.0

F15/RED FORCE RATIO

ATTRITION

F15 ATTRITION RED AIR ATTRITION RED 95% CI LOW RED 95% CI HIGH

BLUE 95% CI LOW BLUE 95% CI HIGH Log. (F15 ATTRITION) Log. (RED AIR ATTRITION)

Figure 16. MiG-23/29 short attrition lines log scale.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

F15 ING ATT

0

5

10

15

20

Frequency

Mean = 0.098906

Std. Dev. = 0.1538837

N = 37

F-15C Regression

Prediction = 12.3% 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

RED ING ATT

0

2

4

6

8

10

Frequency

Mean = 0.718919

Std. Dev. = 0.2083764

N = 37

Red Air Regression

Prediction = 70.8% 

Figure 17. 1:1 (1.0) Force ratio histogram.
RESULTS

44

Therefore, remember in subsequent charts that there will be 

deviations from the regression line for individual missions. 

Over time, however, the averages of several missions will move 

closer toward the regression line. As emphasized in chapter 1 

during the discussions of Lanchester’s method, there is clarity 

with deterministic solutions that can conceptualize expectations 

for the commander. Unlike his method, however, this conceptualization adds a view of statistical variability that can further 

augment a commander’s judgment about the amount of risk 

the plan accounts for and even how the battle is progressing. 

Remember that figure 16 represents a combination of three 

different values that prove helpful in calculating most of the 

information needed for analyzing an air superiority campaign. 

Each of the attrition lines (Batt and Ratt) represents the expected 

losses for each side divided by the total number of sorties where 

the variables B and R indicate F-15C and Red Air respectively.

(1)

(2)

The force ratio (Frat) represented on the X-axis is the ratio of 

Blue sorties to Red sorties. 

(3)

With this in mind, the graph represents the interaction of the 

two competing weapon systems, all Blue losses (Bloss) represent 

Red kills (Rkill), and Red losses (Rloss) represent Blue kills (Bkill). 

Therefore, attrition equations 1 and 2 can be modified as the 

following:

(4)

Dividing Ratt by Batt results in the attrition ratio (Arat) for each 

force ratio. By simplifying the factors using the refined values 
RESULTS

45

for attrition taken from equation 4, attrition ratio equals the 

following:

(5)

Since kill ratio (Krat) is the number of Blue kills divided by Red 

kills,

(6)

further simplification of equation 5 results in the realization 

that the attrition ratio equals kill ratio (equation 6) times force 

ratio (equation 3).

(7) 

Therefore, kill ratio equals attrition ratio divided by force ratio.

(8)

As identified in chapter 1, kill ratio is an important operational 

measure of merit for assessment. Plotting kill ratio from the attrition lines results in a line with a sideways S pattern as shown 

in figure 18. The secondary axis to the right side of the graph 

indicates values for kill ratio displayed on a logarithmic scale. 

Between the force ratios of 0.1 and 0.8, the kill ratio remains 

nearly constant at approximately five blue kills to one red kill. 

At an even force ratio of 1:1, the F-15C is winning by an average 

of 5.8 to one. Once the force ratio reaches 2:1, the F-15C kill 

ratio reaches 15.4:1. The actual data confirms the predicted 

trends. In the 24 missions with a force ratio greater than or 

equal to 2.0, the average kill ratio is 18.4:1. The 22 missions 
RESULTS

46

with a force ratio less than or equal to 0.8 indicate a kill ratio 

of only 4.5:1. 

The shape of the kill ratio curve in this study suggests the 

presence of three regions of aerial combat that require different 

strategies. The first region, decisive air superiority, consists of 

the region where kill ratio is on the dramatic increase. Assuming the data used in the analysis is reasonably close to actual 

conditions, commanders could expect a high kill ratio with disproportionate enemy losses and a rapid establishment of air 

supremacy. For this scenario, force ratios greater than 1.0 are 

a good starting place, with a peak kill ratio of 73:1 at the force 

ratio of 2.47, where F-15C attrition approaches zero. After that 

point, inefficiency starts to decrease the kill ratio slightly due 

to the increased number of aircraft exposed to the risk of combat without the ability to increase the toll on enemy forces. The 

decrease in kill ratio passed the 2.47 force ratio is, however, 

insignificant compared to the benefit of overwhelming enemy 

forces. As a result, larger force ratios would likely add assurance to the outcome by increasing the probability that missions would return with zero losses. Unfortunately, larger force 

ratios would also decrease efficiency as the additional sorties 

generate little excess effect since Red attrition is already near 

100 percent. 

MiG-23 and MiG-29 w/ SHORT A-A Missile

0.01 0.1 1 10

ATTRITION

0.1

1

10

100

KILL RATIO

RED AIR BLUE AIR KILL RATIO

1

0.8

0.6

0.4

0.2

0

Figure 18. MiG-23/29 short kill ratio.
RESULTS

47

The second region, numeric attrition, is captured by the flat 

kill ratio plateau between the force ratio of 0.1 and 1.0. Incremental adjustments in the force ratio within this region will 

have little or no observable effect on the kill ratio between the 

two sides. If forced to fight in this regime, raw numbers, morale, and the industrial base to produce more aircraft become 

the deciding factor in victory. Arguably, this region describes 

most combat experiences, especially early in a campaign when 

forces are fresh. Once attrition starts, the physical realities of 

the interaction between the forces bind a commander’s options. 

Additionally, factors like tactical and technological change become significant in determining the campaign’s outcome since 

they may shift the attrition rate more significantly than small 

changes in the force ratio. The next section explores the effects 

of new technology on the battlefield in more detail, but it is important to emphasize its potential here.

The third region, desperate measures, exists on the descending curve of enemy superiority. With force ratios falling below 

0.1, this scenario would result in an exponential loss of aircraft 

with little return, besides making a show of effort. Within this 

region, commanders face gigantic strategic problems with maintaining a viable force, let alone gaining air superiority. Depending on the scenario, commanders must choose between making 

a last valiant stand, piecemealing their forces with little effect, 

and attempting to shelter their forces for future use. 

In addition to kill ratio, a measure of air superiority is also 

helpful for projecting the follow-on options for the other essential 

parts of the air campaign. If the initial sweep eliminates most 

enemy aircraft, following waves of strike aircraft can eliminate 

the remaining threat and accomplish the air campaign mission 

without undue reductions in effectiveness. As the number of 

surviving enemy aircraft increases, however, bomber crews 

must shift their attention towards survival, and when they do, 

bombing success will suffer. By anticipating the level of difficulty, planners can efficiently tailor force packages early in the 

planning process to enable mission success without significant 

losses or wasted effort. Therefore, the best way to anticipate 

the level of difficulty for these forces is by calculating the expected number of Red Air surviving the initial sweep, commonly 

referred to as leakers. The importance of the target will subse­
RESULTS

48

quently shape the follow-on strike package or even suggest delaying the strike mission until air superiority is sufficient to 

facilitate the mission without undue risk.

Making this calculation is extremely simple. Since Ratt is the 

percentage of enemy aircraft killed in the sweep, subtracting 

Ratt from 1 results in the percentage of aircraft surviving as illustrated below.2

(9)

All that is needed is to determine the number of Red aircraft 

initially launched. Since US forces cannot control enemy actions, enemy strength is estimated based on F-15C planned 

sorties and force ratios. In other words, dividing the number of 

planned F-15C sorties by the force ratio equals the number of 

enemy sorties for any point on the graph. Figure 19 displays 

the curves based on the Red Air attrition regression line. The 

solid line represents the number of leakers anticipated against 

an eight ship of F-15Cs, and the dashed line to the left represents projected leakers against a four ship. Initially this may 

seem counter intuitive, but remember the X-axis represents 

force ratio while the right side Y-axis represents actual aircraft. 

Therefore, for any force ratio, doubling the number of F-15C 

also doubles the number of Red Air fighters. To explain this 

relationship, three scenarios are instructive. First, if eight 

Red Air are opposed by four F-15Cs, a 1:2 (0.5) force ratio, we 

MiG -23 an d MiG-29 w / SH ORT A-A Missile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10

ATTRITION

0

1

2

3

4

5

6

7

8

9

10

# SURVIVING RED A/C 

AFTER SWEEP

RED AIR BLUE AIR RED LEAKERS VS 8 F-15C RED LEAKERS VS 4 F-15C

Figure 19. MiG-23/29 surviving Red Aircraft versus F-15C sweep.
RESULTS

49

would expect about four (3.567 plus or minus error) leakers. If 

the same eight Red Air are opposed by eight F-15C aircraft, a 

1:1 (1.0) force ratio, we would expect about two (2.336 plus or 

minus error) leakers. Finally, if only four Red Air confront eight 

F-15Cs, a 2:1 (2.0) force ratio, the result is less than one leaker 

(0.552 plus or minus error). 

Again, these predictions are intuitive, but by quantifying the 

trend, operational decisions about risk, pacing, force composition, and priority become better defined. Table 1 compares the 

relevant numbers for each of the three scenarios. The disproportionate difference between the third scenario and the first two 

clearly emphasizes the advantage of increasing the force ratio.

Table 1. MiG-23/29 campaign plan analysis data.

Force 

Ratio

Expected 

F-15C 

Attrition

Expected 

F-15C 

Losses

Expected 

Red 

Attrition

Expected 

Red 

Losses

Kill 

Ratio

Red 

Leakers

4:8 (0.5) 21.8% 0.872 55.4% 4.432 5.1:1 3.567

8:8 (1.0) 12.3% 0.984 70.8% 5.664 5.8:1 2.336

8:4 (2.0) 2.8% 0.224 86.2% 3.448 15.4:1 0.552

Unfortunately, it is impossible to predict the amount of enemy 

resistance on each mission. Understanding when risks outweigh the rewards, however, can help the commander predetermine specific force ratios to match the acceptable levels of 

risk (ALR) for each mission. Armed with specific guidance, mission commanders would have better fidelity on when to push to 

the target, when to proceed with the sweep but call off the strike 

package, and when to abort the entire mission against unexpected 

enemy resistance. Thus, the forces could be better prepared to 

execute in accordance with the commander’s intent. 

Combining these results also helps to build a more comprehensive picture to educate a commander’s perception about an 

impending war. To explain the application more concretely, an 

arbitrary force of 100 F-15Cs will provide the backdrop. The 

following graphs utilize the regression models calculated in appendix B1 to estimate the attrition for each side. As discussed 

in chapter 1, these calculations use deterministic processing 

with all of its inherent limitations and pitfalls. Actual results 
RESULTS

50

would vary for each mission and could potentially have significant effects on the viability of the model. Their utility for augmenting a commander’s visualization of combat effects, however, outweighs the inevitable inaccuracy of the predictions. As 

long as the lines remain a planning tool and not a blind prediction of results, they can help shape plans and suggest decision 

points that would remain ambiguous without the analysis. 

Assuming both sides can develop identical UTE rates and 

on-station times, a direct comparison of aircraft numbers is 

initially useful as a measure of mass. The following graphs assume a 2.0 UTE rate with one-hour mission (vulnerability) 

period for each combat iteration unless otherwise noted. The 

model also assumes aircraft will launch in even numbers. This 

is typical of Western tactics, but it may not represent every enemy 

course of action. Additionally, each mission results in a combat 

engagement and does not account for any effects of OCA-strike 

missions targeting enemy airfields and supply lines. 

Given those assumptions, three outcomes seem probable. 

First, against an enemy with less than 100 MiG-23 and MiG-29 

aircraft, decisive air superiority is a distinct possibility. As 

noted in figure 20, kill ratios likely would start around 6:1, 

with the ratio increasing as the enemy’s forces are rapidly de100

90

80

70

60

50

40

30

20

10

0

# Aircraft

MiG 23/29 w/ Short A-A Missile

Kill Ratio

# Vulnerability Periods

70

60

50

50

40

40

30

30

20

20

10

10

0

0

BLUE REMAINING RED REMAINING KILL RATIO

Figure 20. MiG-23/29 short A-A missile 100 versus 100 kill ratio.
RESULTS

51

stroyed. The changing number of available sorties at the 2.0 

UTE rate causes the fluctuating kill ratio. Mission 14 exhibits 

a dramatic jump in the kill ratio. Once Red Air has less than 48 

aircraft available, the aircraft generated per mission drops from 

four to two. The resulting shift in force ratio produces the sharp 

change in kill ratio.3 An enemy surge or switch to three-ship 

tactics could potentially avert this problem temporarily, but 

the results would remain similar. Figure 21 also indicates that 

fewer than two enemy aircraft should survive the initial sweep, 

so follow-on strike packages would find less resistance en route 

to their targets. Additionally, after mission 15, only occasional 

enemy resistance is probable. Even without a successful bombing campaign, gaining air superiority in this scenario would be 

rapid and complete, whether the enemy chose complete destruction or ceased aerial opposition. Assuming a maximum 

enemy effort, the enemy would run out of aircraft in 38 missions at the cost of approximately eight F-15Cs.

The second option includes an enemy with more than 100 

aircraft and fewer than 500 aircraft. In this regime, initial combat would probably be messy with about one F-15C falling per 

sweep. Three hundred enemy aircraft provide a snapshot at a 

potential conflict within this region. The expected kill ratio of 

Figure 21. MiG-23/29 short A-A missile 100 versus 100 leakers.

MiG 23/29 w/ Short A-A Missile

# Aircraft

# Leakers

120

100

80

60

40

20

0

0

0

0.5

1

1.5

2

2.5

10 20 30 40 50

# Vulnerability Periods

BLUE REMAINING RED REMAINING RED AIR LEAKERS
RESULTS

52

approximately 5:1 displayed in figure 22 would hold for approximately 40 missions. While expected enemy losses outstrip 

friendly losses and eventually would result in a Blue numerical 

advantage, the resulting losses of F-15Cs would prove significant. Additionally, as numbers fall, the peak kill ratio would 

only reach approximately 15:1 after the 44th mission. 

Figure 22. MiG-23/29 short A-A missile 100 versus 300 kill ratio.

MiG 23/29 w/ Short A-A Missile

# Vulnerability Periods

# Aircraft

Kill Ratio

BLUE REMAINING RED REMAINING KILL RATIO

350

300

250

200

150

100

50

0

0 10 20 30 40 50 60 70 80

18

16

14

12

10

8

6

4

2

0

Expected losses of 52 F-15Cs in 73 missions could prove 

catastrophic for American morale. Furthermore, if the combat 

progressed at a full pace, only three days would elapse from 

start to finish. This would offer virtually no time for reinforcements, without a sanctuary or cease-fire. Finally, figure 23 explains the limitations on air superiority during the early phases 

of the war. Leakers would only drop below four on the 30th 

mission and below two after 36 iterations. This could delay the 

follow-on bombing effort, especially if the number of available 

aircraft is limited or vulnerable to attack. More significantly, 

those follow-on missions could only proceed in safety after the 

majority of F-15C losses had already taken place. As a result, 

the strategic flexibility for supporting future combat operations 

could also decrease.
RESULTS

53

Finally, the third scenario with more than 500 enemy aircraft indicates a region of potential defeat without changes in 

technology or tactics. Figure 24 depicts the mean results of 100 

F-15Cs against an armada of 600 MiG-23/29 type fighters. 

Consistently outnumbered, the F-15Cs would face a swarm of 

other lesser aircraft to rely solely on mass to offset the F-15C’s 

technological advantage. In approximately 80 missions, the enemy 

Figure 23. MiG-23/29 short A-A missile 100 versus 300 leakers. # Aircraft

# Leakers

350

300

250

200

150

100

50

0

0 10 20 30 40 50 60 70 80

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

BLUE REMAINING RED REMAINING Red Air Leakers

MiG 23/29 w/ Short A-A Missile

Figure 24. MiG-23/29 short A-A missile 100 versus 700 kill ratio.

700

600

500

400

300

200

100

0 0

1

2

3

4

5

6

0 20 40 60 80 100

MiG 23/29 w/ Short A-A Missile

# Vulnerability Periods

# Aircraft

Kill Ratio

BLUE REMAINING RED REMAINING KILL RATIO
RESULTS

54

would own air superiority with all 100 F-15Cs destroyed and 

about 140 enemy fighters remaining. Additionally, few if any 

Blue Air bombing missions are possible in such a scenario because of the overwhelming numbers of enemy aircraft still defending the area. 

Admittedly, this is a glaring oversimplification of an operational scenario, but it is necessary to highlight the basic math. 

This scenario also provides the opportunity to discuss the 

ability of other aircraft to augment the F-15C forces during the 

sweep. Current multirole fighters from both the Air Force and 

Navy can aid in the sweep mission if necessary. Red Flag tactics often use an additional four ships of fighters for just this 

purpose. Unfortunately, due to airspace congestion, limited 

tactical integration, or technical limitations, the other conventional sweep aircraft account for an overall kill ratio of 2.1:1 

while the F-15C accounts for 5.8:1 against the MiG-23/29 

combination with the short air-to-air missile (fig. 25). At the 

same time, F-15C attrition averaged 10.1 percent, while other 

aircraft accounted for only 4.2 percent.4 Based on the author’s 

experience at Red Flag and the data, F-15Cs do the majority of 

the high-threat work and the augmenting aircraft cover other 

areas with less threat. This study’s limited focus and data fidelity 

also inhibited a positive correlation between augmentation and 

Figure 25. MiG-23/29 short A-A missile 100 versus 700 leakers.

MiG 23/29 w/ Short A-A Missile

# Vulnerability Periods

# Aircraft

# Leakers

BLUE REMAINING RED REMAINING Red Air Leakers

700

600

500

400

300

200

100

0

0 10 20 30 40 50 60 70 80 90 100

0

5

10

15

20

25

30

35

40
RESULTS

55

changes in kill ratio. Future studies are therefore needed to 

reach any conclusions about the effectiveness of this tactic.

Finally, depending on the scenario, modifying the standard 

24-hour operations pattern could prove helpful, especially when 

force ratios are close to the transition from the middle ground 

of attrition to decisive air superiority. For example, if forces on 

both sides were approximately equal, redistribution of sorties 

to favor specific missions could improve overall effects by temporarily spiking the kill ratio and providing better protection of 

bomber assets. This method could facilitate earlier bombing 

missions by massing sweep assets to defend and overwhelm 

the defense’s capabilities. Similarly, by temporarily increasing 

the UTE rates, commonly referred to as a surge, the aircraft 

sorties could boost the force ratio into the decisive air superiority 

regime, but not without risk. If the desired enemy attrition rates 

do not materialize, the gamble could prove counterproductive. 

Once aircraft cross the threshold of declining maintenance 

standards, available sorties will decrease despite planned efforts to increase the UTE rate. The result could be a chaotic 

operational effort instead of a measured plan for action.

Effects of New Enemy Technology

Some technological innovations can significantly alter the 

balance of power between two military forces. Changing the 

scenario from the MiG-23/29 to the SU-27 represents more 

than a new tactical problem. The added capability of the new 

aircraft and missile also makes the operational problem of defeating the better-equipped enemy more challenging, especially 

if the goal is decisive air superiority. Figure 26 initially looks 

similar to the previously explained figure 16, but closer inspection reveals a few differences. First, the 95 percent confidence 

intervals are farther apart. This is likely due to the smaller data 

set rather than any correlation with the new technology. Second, the data set contains less diversity in the force ratio than 

the previous data set. Therefore, extrapolation of the data begins 

earlier than in the previous example. Fortunately, the data trends 

closely mirror the earlier results, so they appear reasonable.

Calculating the expected kill ratio for the SU-27 begins to 

highlight the added difficulty of this scenario. Figure 27 indi­
Figure 26. SU-27 long missile attrition lines log scale. ATTRITION

0

0.01 0.1 1 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1

1

10

100

ATTRITION

0

0.01 0.1 1 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SU-27 w/ LONG A-A Missile

0.1

1

10

100

KILL RATIO

BLUE RED KILL RATIO

Figure 27. SU-27 long kill ratio.

y = -0.162Ln(x) + 0.209

 = 0.082

y = 0.225Ln(x) + 0.706

 = 0.104

F15/RED FORCE RATIO

ATTRITION

F15 ATTRITION RED AIR ATTRITION RED 95% CI LOW RED 95% CI HIGH

BLUE 95% CI LOW BLUE 95% CI HIGH Log. (F15 ATTRITION) Log. (RED AIR ATTRITION)

0

0.1 1.0 10.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SU-27 w/ LONG A-A Missile 
RESULTS

57

cates that the three regions of air superiority discussed in the 

MiG-23/29 scenario are still present, but their values have 

changed. The first region, decisive air superiority, does not begin until approximately 2.0 and stretches toward peak attrition 

at a force ratio of 3.5. The second region, numeric attrition, is 

obviously wider, ranging from 0.1 to 2.0. More significant is the 

average kill ratio in the center plateau of only 3.5:1. Finally, the 

third region, desperate measures, remains virtually identical to 

the lesser threat. The reason for the shift is more obvious by 

plotting both combinations together in figure 28. Red Air attrition shifted hardly at all between the two cases. As a result, the 

number of leakers expected for any force ratio remains identical to those predicted in figure 19. Based on data and experience at Red Flag, it is difficult to draw specific inferences from 

this lack of change, but there are two likely options. First, it 

could simply be a matter of chance, but given the quantity of 

data, it is unlikely that both the slope and intercept would remain the same. Second, none of the relevant factors relating to 

the Red Air attrition changed; therefore, a constant attrition 

model is expected. The aircraft simulating both threat systems 

remained identical. Similarly, the replicated defensive tactics 

Figure 28. Combined attrition and kill ratio. ATTRITION

0

0.01 0.1 1 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1

1

10

100

ATTRITION

0

0.01 0.1 1 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

LINES COMPARED

0.1

1

10

100

KILL RATIO

SHORT RED SHORT BLUE LONG BLUE

LONG RED SHORT KILL RATIO LONG KILL RATIO
RESULTS

58

for both aircraft and missile combinations are virtually identical. In conclusion, the capabilities and tactics of the F-15C remained constant. Therefore, it is possible that target aircraft 

attrition is driven by the defensive systems’ interaction with 

enemy offensive weapons. 

As expected, F-15C attrition increased against the more capable SU-27 and the long-range missile by approximately 9 

percent, with a slight increase in the slope of the line. As noted 

earlier, the slope is somewhat questionable due to the narrow 

range of the data. The number, however, correlates closely to 

the final weapons T-test indicating an overall difference in attrition between the two groups of 7.7 percent (p=0.002) in appendix A12. The increase in F-15C attrition causes the resulting drop in the kill ratio. The most significant change, however, 

is the F-15C zero attrition point shift to the right. That move 

requires a significant increase in the forces required to approach increasing returns on attrition as indicated in figure 24. 

Instead of achieving an expected kill ratio of 15.4:1 with a 2.0 

force ratio, the SU-27 threat would likely yield a kill ratio of 

only 4.5:1. Only by expanding the force ratio to 3:1 would the 

F-15C re-enter the region of decisive air superiority (table 2). As 

a result, Blue forces face a much higher chance of fighting a 

lethal war of attrition instead of the decisive battle for air superiority that America and the USAF have grown accustomed to 

since Operation Desert Storm.

Table 2. SU-27 long campaign plan analysis data.

Force 

Ratio

Expected 

F-15C 

Attrition

Expected 

F-15C 

Losses

Expected 

Red 

Attrition

Expected 

Red 

Losses

Kill 

Ratio

Red 

Leakers

4:8 (0.5) 32.1% 1.284 55.0% 4.4 3.4:1 3.600

8:8 (1.0) 20.9% 1.672 70.6% 5.648 3.4:1 2.352

8:4 (2.0) 9.7% 0.776 86.2% 3.448 4.5:1 0.552

12:4 (3.0) 3.1% 0.248 95.3% 3.812 10.3:1 0.188

As a result, the operational decisions possible in the MiG 

scenario become much more restrictive against the betterequipped SU-27. Given the same assumptions and the same 
RESULTS

59

100 F-15C aircraft, the three regions of operational outcomes 

are still possible, but everything shifts away from the F-15C’s 

advantage. Decisive air superiority is still possible, but only 

against 50 or fewer SU-27s. The second option also only extends to around 340 enemy aircraft before restrictive losses 

become a real possibility. 

The significant difference between the two scenarios helps to 

clarify how an apparently small change in weapons technology 

can affect operational outcomes. The flexibility to request additional forces, however, is only available based on long-term 

force structure decisions. 

Notes

1. Lloyd and Naval War College, Fundamentals of Force Planning, 15–16.

2. Ball, Fundamentals of Aircraft Combat Survivability Analysis and Design, 22.

3. Maintenance Metrics U.S. Air Force, 35. The daily UTE rate is calculated 

by dividing the number of sorties required by the number of available aircraft. To calculate the number of aircraft required given sorties and the UTE 

rate, divide the sorties required by the UTE. As an example, to keep four aircraft on station for one-hour vulnerability periods 24 hours a day requires 96 

sorties. A 2.0 UTE rate therefore requires 48 aircraft.

4. The F-15C accounted for 1,420 sorties with 143 losses and 829 kills 

during the ingress portion. The other conventional OCA-sweep players totaled 166 sorties with seven losses and 15 kills. 

61

Chapter 4

Strategic Implications

At the strategic level of war, governments make long-term 

decisions about force structure and what technologies to procure. On the grand scale, national military force structure is 

based on the allocation of limited resources and the relationship “among ends, ways, and risk.”1 Clausewitz believed in the 

power of quality, but he felt the surest method of ensuring success on the battlefield is by striving to “put the largest possible 

army into the field.”2 Today’s defense reality, however, requires 

a balance between both fiscal responsibility and a constant capability for victory. Colin Gray eloquently framed this dilemma 

with his question, “How should one resolve disputes between 

those who urge defense preparation according to threat-based 

military analysis of what the polity allegedly needs to be secure 

and those who assert that the polity can only afford to spend so 

much on defense functions?”3 Striking the correct balance between essential and desired capabilities is vital for enabling 

national goals without waste. 

Possibly the most important step in the process is defining 

the military’s mission within the national security strategy. 

Robert Art suggests four categories of military force including 

defense, deterrence, compellence, and swaggering.4 Because 

these functions are independent and overlapping, he concludes, 

only great nations have the potential to “develop military forces 

that can serve more than two functions at once. Even then, this 

is achievable only vis-à-vis smaller powers, not vis-à-vis the 

other great ones.”5 Understanding the subtle differences between each of the four is essential. Defense requires forces capable of repelling an attack on the nation and minimizing the 

effects of enemy action.6 Deterrence is similar to defense because its focus is passive but requires an “institutionalized 

perception” within the enemy state that military action cannot 

resolve the conflict.7 Compellence, by contrast, is necessarily 

offensive in character. It seeks to induce enemy action by the 

threat or actual use of military force.8 Finally, Art’s term swagger consists of the egoistic display of military prowess through 
STRATEGIC IMPLICATIONS

62

exercises, demonstrations, or technological expertise.9 This last 

category is similar in effect to compellence, but, like defense, it 

focuses inward by attempting to boost national pride or government legitimacy.10

The role of air superiority in each of these realms varies and 

therefore necessitates a different force structure to enable national objectives. A purely defensive force structure is relatively 

simple to construct and justify. Using traditional “threat/vulnerability” approaches to defense planning; strategists can 

simply analyze enemy capabilities and American susceptibility 

to determine the necessary force structure.11 Since victory is 

the only requirement and minimizing the effects is a goal, forces 

only need to be large enough to prevent decisive enemy action. 

Therefore, forces sufficient to win within the middle plateau of 

numerical attrition can assure defense with the minimum economic cost. 

While pure defense may appeal to a traditional isolationist, it 

is inconsistent with America’s current role as the global enforcer. Since both deterrence and compellence rely on enemy 

perceptions for effectiveness, defining force structures becomes 

more ambiguous. Daniel Byman and Mathew Waxman argue 

that “will and credibility matter as much as, and often more 

than, the overall balance of forces.”12 The threshold for success 

between deterrence and compellence, however, is different due 

to sunk costs and the need to preserve political face. Since deterrence seeks to avert enemy action before it takes place, adversaries will typically apply a lower threshold for acquiescence 

because inactive compliance is less attributable to outside influences.13 Once unacceptable action takes place and compellence becomes necessary, adversaries may calculate the value 

of their reputation outweighs the risk of confrontation.14 Consequently, as measured threats of force proceed from deterrence to compellence, credibility also needs to increase and 

may necessitate the use of force. Therefore, a more proactive 

foreign policy necessitates a more robust military. Presenting 

sufficient forces to win within the table of numeric attrition 

could augment America’s deterrent credibility to avert military 

confrontation, but these forces may not inhibit action by determined foes. If compellent war becomes necessary, the disproportional advantage offered by decisive air superiority will help 
STRATEGIC IMPLICATIONS

63

to ensure victory with less cost in lives and equipment. Employing forces within this realm also minimizes the time required 

for victory, which is essential in maintaining public support 

enabling the political will for action. The costs of maintaining a 

force large enough to accomplish this, however, are growing 

rapidly. The combined expense of the ongoing global war on 

terror with the simultaneous increase in the strength of foreign 

militaries may make maintaining an undisputed compellence 

force untenable. 

Finally, Art’s fourth category, swagger, suggests an entirely 

different approach to military force structure focused on broad 

political power instead of pure military clout. From an economic 

perspective, fielding advanced military hardware can provide 

significant advantages in the international arena. Mechanisms 

like embargos, licensing rights, and direct military sales of advanced technology provide the required political capital to influence friends and foes without the threat of violence.15 Additionally, with swagger’s focus on the tool rather than its utility, 

it is usually enough to field the system only with sufficient numbers to meet the credibility threshold. With this in mind, swaggering offers status and respect “on the cheap.”16 The critical 

element of this methodology provides the foresight, similar to 

Pres. Franklin D. Roosevelt’s, that enables increased production early enough to influence the air war and avoids a repeat 

of the blind reverence to technology that hobbled the Luftwaffe 

in World War II. 

This model, besides illustrating the role of force size, highlights the role of technology and stresses the importance acquisition priorities can have on national security. Given the significant shift between the two scenarios shown in figure 29, it 

is apparent how a longer-range air-to-air missile can affect the 

overall balance of strength between the two sides. The most 

important driver for advantage is the point for each side where 

its attrition approaches zero. This point consistently drives the 

disproportionate kill ratios on both ends of the graph. The side 

that can fight closest to this point has a distinct advantage. 

Comparing the existing kill-ratio curve with a modeled curve 

for a proposed system makes possible a direct comparison of 

required numbers. 
STRATEGIC IMPLICATIONS

64

This added fidelity suggests increasing numbers of current 

aircraft rather than producing a new system as the most costeffective strategy. Conversely, if the threat is significant or the 

new technology is revolutionary and sufficiently affordable, the 

curves may indicate a compelling reason to transform the force. 

In either case, this model can help commanders augment their 

decisions in an intuitive manner. Additionally, the shift of the 

F-15C attrition line suggests there may be a predictable linkage to focus future efforts. If the interaction between Blue attrition and Red offensive systems exists, logic suggests a similar 

relationship between Blue defensive systems and Blue attrition 

exists. Therefore, recent US Air Force emphasis on stealth technology may be logically well founded. The protection stealth 

provides from attack should negate the advantage of enemy offensive weapons and would therefore enable disproportionate 

victory with fewer aircraft by shifting the Blue minimum attrition point further left. Further study with testing data is needed 

to verify the extent of the effect relative to the increased cost.

Recommendations

While potentially interesting, this study is far from complete. 

The OCA-sweep mission area is an important enabler of airpower, but it is not an end unto itself. Modern surface-to-air 

threats suggest the need for a similar study of the OCA-SEAD 

mission area. Similarly, charting success rates for the aircraft 

putting bombs on target is also essential to building a complete 

picture of the relationship between mass and technology. To 

accomplish this, however, each mission area database needs 

synchronizing to facilitate coherent analysis. To facilitate such 

an analysis, Arcata data collection should be restructured into 

the following three blocks. The first of the three, initial sweep, 

includes all results for all players up to and including the “loss” 

of the last original Red Air player. The second, ingress, embraces all results after the initial sweep until final weapons 

release. This includes all OCA-sweep, OCA-SEAD, and Red Air 

missions until the last striker weapons release. The third, 

egress, includes all data after weapons release until flights terminate tactical maneuvering. This is not a significant change 

from most of the current collection, but it does include attempts 
STRATEGIC IMPLICATIONS

65

to make a better split for the results of the initial sweep from an 

analytical standpoint. 

Enhancing Red Flag’s fidelity will also make future analyses 

more productive. Harnessing NACTS-tracking data to produce 

real-time computer-generated air-to-air, air-to-ground, and 

ground-to-air missile fly-out models minimizes the training 

limitations of the current shot kill mechanism while maximizing data accuracy. Adding new airspace to expand the opportunities for maneuver seems also beneficial. Current initiatives 

like Red Flag–Alaska are a step in the right direction as long as 

the quality and quantity of threat replication remains high at 

the new location. Additionally, varying the numbers of Red Air 

for each mission may be more productive for altering the threat 

level than the current system of changing subtle tactical variables. This also allows participants to learn lessons about how 

variation in enemy numerical strength affects mission viability. 

These lessons could make the critical difference in averting unneeded combat attrition in future wars. 

Finally, the US Air Force must develop a set of operational 

planning aids to augment current methods. By harnessing 

DOD’s war-gaming infrastructure, a series of charts and graphs 

similar to those presented in chapter 3 are feasible for virtually 

any potential scenario. Using stochastic methods, individual 

scenarios would retain the natural variability of combat, while 

indicating trends. Additionally, Red Flag and test missions 

would serve as a verification tool to validate the reasonableness 

of the overall prediction. Once complete, they would function in 

the operational level air superiority campaign similar to an energy-maneuverability diagram in tactical level aerial dogfight. 

By suggesting areas of advantage and vulnerability in relation 

to the opponent, they would clarify a commander’s understanding of the impending battle and help to shape the strategy 

through understanding. 

Notes

1. Lloyd and Castle, Strategy and Force Planning, 5.

2. Clausewitz, On War, 195.

3. Gray, Modern Strategy, 33.

4. Art, “The Four Functions of Force,” 153.

5. Ibid., 154.
STRATEGIC IMPLICATIONS

66

6. Ibid.

7. Freedman, Deterrence, 42.

8. Schelling, Arms and Influence, 79–80.

9. Art, “Four Functions of Force,” 157.

10. Ibid., 157–58.

11. Lloyd and Castle, Strategy and Force Planning, 27.

12. Byman and Waxman, Dynamics of Coercion, 18.

13. Schelling, Arms and Influence, 82.

14. Jervis, System Effects, 387.

15. Baldwin, Economic Statecraft, 41–42.

16. Art, “Four Functions of Force,” 158.
67

Chapter 5

Conclusion

This study proposes a model for understanding the relationship between technology, mass, and attrition in aerial warfare 

that is useful for shaping operational and strategic force decision processes. The F-15C’s OCA-sweep mission within Red 

Flag highlights one potentially useful relationship that has 

value as a model for air superiority. The change of attrition as 

force ratios increase is simple to understand and logically feasible. Additionally, the regression line helps to provide a window on the expected variance within a specific scenario. Unfortunately, the character of Red Flag as a tactical exercise and 

not a test introduces excessive variation into an already chaotic 

environment. Future analyses should harness the power of computer modeling to minimize the number of variables and produce better representations for operational use. Once complete 

and validated in such exercises as Red Flag, these diagrams 

would serve as an operational planning tool. Connecting statistical relationships to the operational art of campaign planning 

helps to ensure success in campaigns against capable foes.

Most significant, however, this study helps to clarify how kill 

ratio varies in relation to force ratio and technology. The wide 

middle area of stability, identified as numerical attrition, is 

consistent with the traditional notion that kill ratio is largely 

set by training and technology. It is also consistent with most 

of the historical record, including the early campaigns of World 

War II, that suggested little change in kill ratio with nominal 

changes in the relative mass of forces. This is also the reason 

technology often produced the only observable change in kill 

ratio in closely matched forces. From the Fokker scourge of 

World War I to the need for F-86s during the Korean War, technology altered the balance between victor and vanquished by 

displacing the attrition lines and thus the kill ratio between the 

two forces. 

The rapid change in attrition rate at either end of the graph 

caused by changes in force ratios also has great explanatory 

value in other cases. By indicating regions where an increase in 
CONCLUSION

68

mass dictates a lop-sided victory, the concept accounts for several notable cases in the historical record. Primary among these 

cases is the previously discussed rapid change in kill ratio during the aerial assault on Germany. Doubling the force ratio 

during mid-1944 resulted in a sixfold increase in kill ratio in 

only three months. While the increase in force ratio is not the 

sole reason for the change, the correlation is strikingly similar 

to the Red Flag data. The uneven air supremacy enjoyed in Operations Desert Storm and Allied Force also closely mirrors the 

decisive air superiority regime predicted by the model. In both 

cases, the US Air Force fought within the region of decisive air 

superiority due to its overwhelming mass and technology. This 

advantage may prove transient, however, because, similar to 

Wall Street, “past performance does not predict future returns.” 

Adversaries will attempt to balance America’s advantage with 

their own unique combination of mass and technology.

Before the next major war begins, strategic decisions about 

military force structure will shape the feasibility of operational 

plans and preordain the costs in both the dollars and lives required for victory. The F-22 is already superseding the F-15C 

with increased capability and reduced numbers. The joint strike 

fighter will similarly supplant the F-15E, F-16, and A-10 in the 

next decade. At first glance, this change should guarantee aerial 

dominance in the future through technology. Unfortunately, 

the disproportionate advantage afforded by stealth and fifthgeneration technology remains too expensive and complex to 

field in large numbers. These shrinking inventories of hightechnology aircraft will likely result in a conflict where America 

will fight outnumbered and completely reliant on technology to 

maintain a preponderance of strength. 

The danger, however, is in dropping forces too low without 

moderating expectations. While these new systems may have 

the ability to strike the same number of targets as their more 

numerous predecessors, their dwindling numbers can cause 

other problems. Smaller numbers amplify the effects of fog and 

chance. With the study’s regression calculations, outliers defied the averages: missions where bad days conspired with possibility to produce unexpected losses. Over thousands of sorties, these anomalies did not have a significant impact on the 

outcome. As the numbers decrease, however, single events grow 
CONCLUSION

69

in meaning. The recent accidental crash of a B-2 is a perfect 

example. The loss of a single, irreplaceable aircraft will have 

long-term effects on strategic options, especially when victory 

requires maximum effort. 

Imagine the effect upon the inventory the first time an enemy 

reveals the capability to detect, target, and kill American stealth 

platforms with lethal regularity. If timed appropriately, the 

quick succession of losses could prove more damaging than 

Pearl Harbor by significantly reducing the number of available 

aircraft. Foreign aviation technology is developing at a rapid 

pace. Soon another military might balance the overwhelming 

advantage of the US Air Force. The essential problem lies in 

identifying the challenge before a confrontation erupts. The 

strategic insight provided by this model could help to identify 

the limitations of the force early enough to enable a timely correction. In some cases, a simple transition from an overt policy 

of compellence to a more conciliatory swaggering or defensive 

posture may save limited funds for other necessities. In other 

more dire situations, early recognition will build the requisite 

time for either producing additional aircraft or trading up for 

more technology. 

 Silver bullets seldom manifest themselves in warfare. When 

they do appear, their lop-sided effectiveness is usually fleeting 

as the enemy adapts to the new tactics or technology. America’s 

aerial dominance, enabled by stealth and precision, is a transitory advantage with a finite duration. The inevitable rebalancing of military capability will force a return to inventory comparisons and small incremental changes in technologies, 

countertactics, and organizations. America can minimize its 

risk of falling victim to hubris by anticipating the impending 

enemy changes and planning for them. By avoiding the pitfall 

of assuming future disproportionate advantages and planning 

for parity, the Air Force can avoid defeat in the next war. Understanding the relationship between mass and technology is the 

best way to offset the impending rebalance of global military 

force. By returning to brutal honesty and strategic introspection, the Air Force can identify its weaknesses and be ready to 

win the next war.

71

Appendix A

Data Set Variance

A1. Year Attrition Analysis of Variance (ANOVA) 2001–2005

Author’s original work using Statistical Program for the Social Sciences 

(SPSS) 12.0.1

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum

Lower 

Bound

Upper 

Bound

F15_ING_

ATT 2001 72 .177083 .1409508 .0166112 .143962 .210205 .0000 .6250

2002 92 .133742 .1578904 .0164612 .101043 .166440 .0000 .6250

2003 47 .125532 .1671652 .0243835 .076450 .174613 .0000 .7500

2004 54 .089267 .1383443 .0188263 .051506 .127027 .0000 .7500

2005 34 .105252 .1443346 .0247532 .054891 .155613 .0000 .5000

Total 299 .131616 .1525829 .0088241 .114251 .148981 .0000 .7500

OCA_ING_

ATT 2001 74 .154636 .1192056 .0138574 .127018 .182254 .0000 .5000

2002 93 .123534 .1383595 .0143472 .095039 .152028 .0000 .5000

2003 47 .123759 .1673870 .0244159 .074612 .172906 .0000 .7500

2004 59 .091821 .1363615 .0177528 .056285 .127357 .0000 .7500

2005 34 .105252 .1443346 .0247532 .054891 .155613 .0000 .5000

Total 307 .122946 .1399754 .0079888 .107226 .138666 .0000 .7500

RED_ING_

ATT 2001 74 .569337 .2307686 .0268263 .515873 .622802 .0000 1.0000

2002 93 .748192 .1909472 .0198003 .708867 .787517 .2500 1.0000

2003 47 .770652 .1967436 .0286980 .712886 .828418 .3750 1.0000

2004 59 .784759 .2209083 .0287598 .727190 .842328 .0000 1.0000

2005 34 .766667 .1957723 .0335747 .698358 .834975 .5000 1.1250

Total 307 .717593 .2236921 .0127668 .692471 .742714 .0000 1.1250
APPENDIX A

72

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT .511 4 294 .728

OCA_ING_ATT .596 4 302 .666

RED_ING_ATT .562 4 302 .690

ANOVA

Sum of 

Squares Df Mean Square F Sig.

F15_ING_

ATT Between Groups .271 4 .068 2.993 .019

Within Groups 6.666 294 .023

Total 6.938 298

OCA_ING_

ATT Between Groups .142 4 .036 1.834 .122

Within Groups 5.853 302 .019

Total 5.995 306

RED_ING_

ATT Between Groups 2.194 4 .548 12.627 .000

Within Groups 13.118 302 .043

Total 15.312 306
APPENDIX A

73

Post-Hoc Tests

Multiple Comparisons

Tukey honestly significant difference (HSD) test

Dependent 

Variable (I) Year (J) Year

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_ING_

ATT 2001 2002 .0433418 .0236938 .359 -.021692 .108376

2003 .0515514 .0282378 .361 -.025955 .129058

2004 .0878166(*) .0271078 .012 .013412 .162222

2005 .0718312 .0313343 .150 -.014175 .157837

2002 2001 -.0433418 .0236938 .359 -.108376 .021692

2003 .0082096 .0269983 .998 -.065895 .082314

2004 .0444748 .0258142 .421 -.026379 .115329

2005 .0284894 .0302221 .880 -.054464 .111443

2003 2001 -.0515514 .0282378 .361 -.129058 .025955

2002 -.0082096 .0269983 .998 -.082314 .065895

2004 .0362652 .0300391 .747 -.046186 .118716

2005 .0202798 .0339021 .975 -.072774 .113334

2004 2001 -.0878166(*) .0271078 .012 -.162222 -.013412

2002 -.0444748 .0258142 .421 -.115329 .026379

2003 -.0362652 .0300391 .747 -.118716 .046186

2005 -.0159854 .0329669 .989 -.106472 .074501

2005 2001 -.0718312 .0313343 .150 -.157837 .014175

2002 -.0284894 .0302221 .880 -.111443 .054464

2003 -.0202798 .0339021 .975 -.113334 .072774

2004 .0159854 .0329669 .989 -.074501 .106472

OCA_ING_

ATT 2001 2002 .0311024 .0216869 .606 -.028414 .090619

2003 .0308773 .0259672 .758 -.040385 .102140

2004 .0628153 .0242986 .076 -.003868 .129499

2005 .0493840 .0288439 .428 -.029773 .128541

2002 2001 -.0311024 .0216869 .606 -.090619 .028414

2003 -.0002252 .0249156 1.000 -.068602 .068151

2004 .0317129 .0231714 .648 -.031877 .095303

2005 .0182816 .0279009 .966 -.058288 .094851

2003 2001 -.0308773 .0259672 .758 -.102140 .040385

2002 .0002252 .0249156 1.000 -.068151 .068602

2004 .0319380 .0272192 .767 -.042760 .106637
APPENDIX A

74

Dependent 

Variable (I) Year (J) Year

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

2005 .0185068 .0313438 .976 -.067511 .104524

2004 2001 -.0628153 .0242986 .076 -.129499 .003868

2002 -.0317129 .0231714 .648 -.095303 .031877

2003 -.0319380 .0272192 .767 -.106637 .042760

2005 -.0134313 .0299760 .992 -.095695 .068833

2005 2001 -.0493840 .0288439 .428 -.128541 .029773

2002 -.0182816 .0279009 .966 -.094851 .058288

2003 -.0185068 .0313438 .976 -.104524 .067511

2004 .0134313 .0299760 .992 -.068833 .095695

RED_ING_

ATT 2001 2002 -.1788551(*) .0324658 .000 -.267952 -.089758

2003 -.2013145(*) .0388735 .000 -.307996 -.094633

2004 -.2154219(*) .0363756 .000 -.315249 -.115595

2005 -.1973294(*) .0431800 .000 -.315830 -.078829

2002 2001 .1788551(*) .0324658 .000 .089758 .267952

2003 -.0224594 .0372992 .975 -.124821 .079902

2004 -.0365668 .0346881 .830 -.131762 .058629

2005 -.0184743 .0417683 .992 -.133100 .096152

2003 2001 .2013145(*) .0388735 .000 .094633 .307996

2002 .0224594 .0372992 .975 -.079902 .124821

2004 -.0141074 .0407478 .997 -.125933 .097718

2005 .0039851 .0469224 1.000 -.124785 .132756

2004 2001 .2154219(*) .0363756 .000 .115595 .315249

2002 .0365668 .0346881 .830 -.058629 .131762

2003 .0141074 .0407478 .997 -.097718 .125933

2005 .0180925 .0448747 .994 -.105059 .141244

2005 2001 .1973294(*) .0431800 .000 .078829 .315830

2002 .0184743 .0417683 .992 -.096152 .133100

2003 -.0039851 .0469224 1.000 -.132756 .124785

2004 -.0180925 .0448747 .994 -.141244 .105059

*The mean difference is significant at the .05 level.

Post-Hoc Tests (continued)
APPENDIX A

75

Homogeneous Subsets

F15_ING_ATT

Tukey HSD

Year N Subset for alpha = .05

1 2

2004 54 .089267

2005 34 .105252 .105252

2003 47 .125532 .125532

2002 92 .133742 .133742

2001 72 .177083

Sig. .548 .103

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 53.211.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_ING_ATT

Tukey HSD

Year N Subset for alpha = .05

1

2004 59 .091821

2005 34 .105252

2002 93 .123534

2003 47 .123759

2001 74 .154636

Sig. .131

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

76

RED_ING_ATT

Tukey HSD

Year N Subset for alpha = .05

1 2

2001 74 .569337

2002 93 .748192

2005 34 .766667

2003 47 .770652

2004 59 .784759

Sig. 1.000 .891

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

2001 2002 2003 2004 2005

Year

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

Mean of F15_ING_ATT
APPENDIX A

77

2001 2002 2003 2004 2005

Year

0.0900

0.1000

0.1100

0.1200

0.1300

0.1400

0.1500

0.1600

Mean of OCA_ING_ATT

2001 2002 2003 2004 2005

Year

0.5500

0.6000

0.6500

0.7000

0.7500

0.8000

Mean of RED_ING_ATT
APPENDIX A

78

Year Force Ratio ANOVA 2001–2005

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_

FLOWN_

RATIO

2001 74 .850290 .2106658 .0244894 .801482 .899097 .0000 1.6000

2002 93 1.114696 .3389543 .0351479 1.044889 1.184503 .0000 2.6667

2003 47 1.597357 .8036187 .1172198 1.361406 1.833309 .5556 4.0000

2004 59 1.363875 .7199627 .0937312 1.176252 1.551499 .0000 2.8000

2005 34 1.084886 .3197288 .0548330 .973327 1.196444 .6667 2.0000

Total 307 1.169442 .5596747 .0319423 1.106588 1.232297 .0000 4.0000

FLOWN_

RATIO

2001 74 1.044235 .3277100 .0380955 .968311 1.120160 .4444 2.4000

2002 93 1.405164 .4664773 .0483714 1.309094 1.501234 .8889 3.5000

2003 47 1.824308 1.3103846 .1911392 1.439564 2.209051 .5556 6.0000

2004 59 1.502051 .5958926 .0775786 1.346761 1.657342 .4444 2.8000

2005 34 1.084886 .3197288 .0548330 .973327 1.196444 .6667 2.0000

Total 307 1.365483 .7054171 .0402603 1.286261 1.444705 .4444 6.0000

OCA_

F15_FL

2001 72 7.74 1.256 .148 7.44 8.03 4 10

2002 92 8.62 1.518 .158 8.31 8.93 4 12

2003 47 7.83 .524 .076 7.68 7.98 5 8

2004 54 9.59 2.904 .395 8.80 10.39 4 14

2005 34 7.12 1.343 .230 6.65 7.59 4 8

Total 299 8.29 1.851 .107 8.08 8.50 4 14

OCA_

TOT_

FTR_FL

2001 74 9.08 2.052 .239 8.61 9.56 4 12

2002 93 10.54 1.862 .193 10.15 10.92 4 14

2003 47 8.43 1.543 .225 7.97 8.88 5 12

2004 59 9.46 2.920 .380 8.70 10.22 4 14

2005 34 7.12 1.343 .230 6.65 7.59 4 8

Total 307 9.28 2.312 .132 9.02 9.54 4 14

RED_

TOT_

FTR_FL

2001 74 9.04 1.763 .205 8.63 9.45 4 13

2002 93 7.94 1.673 .174 7.59 8.28 3 11

2003 47 5.89 2.189 .319 5.25 6.54 2 9

2004 59 6.76 1.775 .231 6.30 7.23 4 10

2005 34 6.82 1.487 .255 6.30 7.34 4 9

Total 307 7.54 2.079 .119 7.31 7.77 2 13
APPENDIX A

79

Test of Homogeneity of Variances

Levene 

Statistic df1 df2 Sig.

F15_FLOWN_RATIO 33.964 4 302 .000

FLOWN_RATIO 20.181 4 302 .000

OCA_F15_FL 41.497 4 294 .000

OCA_TOT_FTR_FL 16.740 4 302 .000

RED_TOT_FTR_FL 5.622 4 302 .000

ANOVA

Sum of 

Squares Df Mean Square F Sig.

F15_FLOWN_

RATIO Between Groups 18.896 4 4.724 18.539 .000

Within Groups 76.954 302 .255

Total 95.850 306

FLOWN_RATIO Between Groups 21.455 4 5.364 12.383 .000

Within Groups 130.815 302 .433

Total 152.270 306

OCA_F15_FL Between Groups 180.389 4 45.097 15.768 .000

Within Groups 840.876 294 2.860

Total 1021.265 298

OCA_TOT_FTR_FL Between Groups 345.171 4 86.293 20.197 .000

Within Groups 1290.295 302 4.272

Total 1635.466 306

RED_TOT_FTR_FL Between Groups 361.663 4 90.416 28.426 .000

Within Groups 960.579 302 3.181

Total 1322.241 306
APPENDIX A

80

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) Year (J) Year

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_

FLOWN_

RATIO

2001 2002 -.2644065(*) .0786345 .008 -.480206 -.048607

2003 -.7470677(*) .0941543 .000 -1.005458 -.488677

2004 -.5135858(*) .0881042 .000 -.755373 -.271799

2005 -.2345960 .1045849 .167 -.521612 .052420

2002 2001 .2644065(*) .0786345 .008 .048607 .480206

2003 -.4826612(*) .0903413 .000 -.730587 -.234735

2004 -.2491793(*) .0840169 .027 -.479750 -.018609

2005 .0298105 .1011657 .998 -.247822 .307443

2003 2001 .7470677(*) .0941543 .000 .488677 1.005458

2002 .4826612(*) .0903413 .000 .234735 .730587

2004 .2334819 .0986939 .128 -.037367 .504331

2005 .5124717(*) .1136493 .000 .200581 .824363

2004 2001 .5135858(*) .0881042 .000 .271799 .755373

2002 .2491793(*) .0840169 .027 .018609 .479750

2003 -.2334819 .0986939 .128 -.504331 .037367

2005 .2789898 .1086897 .079 -.019291 .577270

2005 2001 .2345960 .1045849 .167 -.052420 .521612

2002 -.0298105 .1011657 .998 -.307443 .247822

2003 -.5124717(*) .1136493 .000 -.824363 -.200581

2004 -.2789898 .1086897 .079 -.577270 .019291

FLOWN_

RATIO

2001 2002 -.3609284(*) .1025240 .004 -.642288 -.079569

2003 -.7800723(*) .1227588 .000 -1.116963 -.443182

2004 -.4578160(*) .1148705 .001 -.773059 -.142573

2005 -.0406503 .1363582 .998 -.414862 .333562

2002 2001 .3609284(*) .1025240 .004 .079569 .642288

2003 -.4191439(*) .1177872 .004 -.742391 -.095897

2004 -.0968876 .1095416 .902 -.397506 .203731

2005 .3202782 .1319002 .111 -.041700 .682256

2003 2001 .7800723(*) .1227588 .000 .443182 1.116963

2002 .4191439(*) .1177872 .004 .095897 .742391

2004 .3222563 .1286775 .092 -.030877 .675390

2005 .7394220(*) .1481763 .000 .332777 1.146067
APPENDIX A

81

Dependent 

Variable (I) Year (J) Year

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

2004 2001 .4578160(*) .1148705 .001 .142573 .773059

2002 .0968876 .1095416 .902 -.203731 .397506

2003 -.3222563 .1286775 .092 -.675390 .030877

2005 .4171658(*) .1417100 .029 .028267 .806065

2005 2001 .0406503 .1363582 .998 -.333562 .414862

2002 -.3202782 .1319002 .111 -.682256 .041700

2003 -.7394220(*) .1481763 .000 -1.146067 -.332777

2004 -.4171658(*) .1417100 .029 -.806065 -.028267

OCA_F15_

FL

2001 2002 -.883(*) .266 .009 -1.61 -.15

2003 -.094 .317 .998 -.96 .78

2004 -1.856(*) .304 .000 -2.69 -1.02

2005 .618 .352 .401 -.35 1.58

2002 2001 .883(*) .266 .009 .15 1.61

2003 .790 .303 .072 -.04 1.62

2004 -.973(*) .290 .008 -1.77 -.18

2005 1.502(*) .339 .000 .57 2.43

2003 2001 .094 .317 .998 -.78 .96

2002 -.790 .303 .072 -1.62 .04

2004 -1.763(*) .337 .000 -2.69 -.84

2005 .712 .381 .336 -.33 1.76

2004 2001 1.856(*) .304 .000 1.02 2.69

2002 .973(*) .290 .008 .18 1.77

2003 1.763(*) .337 .000 .84 2.69

2005 2.475(*) .370 .000 1.46 3.49

2005 2001 -.618 .352 .401 -1.58 .35

2002 -1.502(*) .339 .000 -2.43 -.57

2003 -.712 .381 .336 -1.76 .33

2004 -2.475(*) .370 .000 -3.49 -1.46

OCA_

TOT_FTR_

FL

2001 2002 -1.457(*) .322 .000 -2.34 -.57

2003 .656 .386 .435 -.40 1.71

2004 -.377 .361 .835 -1.37 .61

2005 1.963(*) .428 .000 .79 3.14

2002 2001 1.457(*) .322 .000 .57 2.34

2003 2.112(*) .370 .000 1.10 3.13

Post-Hoc Tests (continued)
APPENDIX A

82

Dependent 

Variable (I) Year (J) Year

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

2004 1.080(*) .344 .016 .14 2.02

2005 3.420(*) .414 .000 2.28 4.56

2003 2001 -.656 .386 .435 -1.71 .40

2002 -2.112(*) .370 .000 -3.13 -1.10

2004 -1.032 .404 .082 -2.14 .08

2005 1.308(*) .465 .042 .03 2.59

2004 2001 .377 .361 .835 -.61 1.37

2002 -1.080(*) .344 .016 -2.02 -.14

2003 1.032 .404 .082 -.08 2.14

2005 2.340(*) .445 .000 1.12 3.56

2005 2001 -1.963(*) .428 .000 -3.14 -.79

2002 -3.420(*) .414 .000 -4.56 -2.28

2003 -1.308(*) .465 .042 -2.59 -.03

2004 -2.340(*) .445 .000 -3.56 -1.12

RED_

TOT_FTR_

FL

2001 2002 1.105(*) .278 .001 .34 1.87

2003 3.147(*) .333 .000 2.23 4.06

2004 2.278(*) .311 .000 1.42 3.13

2005 2.217(*) .370 .000 1.20 3.23

2002 2001 -1.105(*) .278 .001 -1.87 -.34

2003 2.042(*) .319 .000 1.17 2.92

2004 1.173(*) .297 .001 .36 1.99

2005 1.112(*) .357 .017 .13 2.09

2003 2001 -3.147(*) .333 .000 -4.06 -2.23

2002 -2.042(*) .319 .000 -2.92 -1.17

2004 -.869 .349 .095 -1.83 .09

2005 -.930 .402 .143 -2.03 .17

2004 2001 -2.278(*) .311 .000 -3.13 -1.42

2002 -1.173(*) .297 .001 -1.99 -.36

2003 .869 .349 .095 -.09 1.83

2005 -.061 .384 1.000 -1.11 .99

2005 2001 -2.217(*) .370 .000 -3.23 -1.20

2002 -1.112(*) .357 .017 -2.09 -.13

2003 .930 .402 .143 -.17 2.03

2004 .061 .384 1.000 -.99 1.11

* The mean difference is significant at the .05 level.

Post-Hoc Tests (continued)
APPENDIX A

83

Homogeneous Subsets

F15_FLOWN_RATIO

Tukey HSD

Year N Subset for alpha = .05

1 2 3

2001 74 .850290

2005 34 1.084886

2002 93 1.114696 1.114696

2004 59 1.363875 1.363875

2003 47 1.597357

Sig. .052 .078 .115

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

FLOWN_RATIO

Tukey HSD

Year N Subset for alpha = .05

1 2 3 4

2001 74 1.044235

2005 34 1.084886 1.084886

2002 93 1.405164 1.405164

2004 59 1.502051 1.502051

2003 47 1.824308

Sig. .998 .085 .940 .082

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

84

OCA_F15_FL

Tukey HSD

Year N Subset for alpha = .05

1 2 3

2005 34 7.12

2001 72 7.74 7.74

2003 47 7.83 7.83

2002 92 8.62

2004 54 9.59

Sig. .193 .057 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 53.211.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_TOT_FTR_FL

Tukey HSD

Year N Subset for alpha = .05

1 2 3

2005 34 7.12

2003 47 8.43

2001 74 9.08

2004 59 9.46 9.46

2002 93 10.54

Sig. 1.000 .072 .053

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

85

RED_TOT_FTR_FL

Tukey HSD

Year N Subset for alpha = .05

1 2 3

2003 47 5.89

2004 59 6.76

2005 34 6.82

2002 93 7.94

2001 74 9.04

Sig. .053 1.000 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 54.405.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

2001 2002 2003 2004 2005

Year

1.0000

1.2500

1.5000

1.7500

Mean of F15_FLOWN_RATIO
APPENDIX A

86

2001 2002 2003 2004 2005

Year

1.0000

1.2000

1.4000

1.6000

1.8000

Mean of FLOWN_RATIO

2001 2002 2003 2004 2005

Year

7.0

7.5

8.0

8.5

9.0

9.5

10.0

Mean of OCA_F15_FL
APPENDIX A

87

2001 2002 2003 2004 2005

Year

7

8

9

10

11

Mean of OCA_TOT_FTR_FL

2001 2002 2003 2004 2005

Year

6

7

8

9

Mean of RED_TOT_FTR_FL
APPENDIX A

88

A2. 2001 Attrition ANOVA

Author’s original work using SPSS 12.0.1

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_

ATT 3-1 12 .119048 .1170558 .0337911 .044674 .193421 .0000 .2857

3-2 15 .194444 .1108081 .0286105 .133081 .255808 .0000 .5000

3-3 16 .228795 .1785975 .0446494 .133627 .323963 .0000 .6250

4-1 15 .190079 .1521141 .0392757 .105841 .274317 .0000 .3750

4-2 14 .135204 .1146017 .0306286 .069035 .201373 .0000 .2500

Total 72 .177083 .1409508 .0166112 .143962 .210205 .0000 .6250

OCA_ING_

ATT 3-1 13 .119505 .1120846 .0310867 .051773 .187238 .0000 .2857

3-2 15 .194444 .1108081 .0286105 .133081 .255808 .0000 .5000

3-3 17 .178591 .1435578 .0348179 .104780 .252401 .0000 .5000

4-1 15 .136263 .1049751 .0271044 .078129 .194396 .0000 .2727

4-2 14 .135204 .1146017 .0306286 .069035 .201373 .0000 .2500

Total 74 .154636 .1192056 .0138574 .127018 .182254 .0000 .5000

RED_ING_

ATT 3-1 13 .578144 .3011503 .0835241 .396161 .760127 .0000 1.0000

3-2 15 .406402 .1149174 .0296716 .342763 .470042 .1667 .5833

3-3 17 .575817 .1964744 .0476520 .474799 .676835 .3333 1.0000

4-1 15 .629233 .2551380 .0658763 .487942 .770523 .0000 1.0000

4-2 14 .663690 .1974868 .0527806 .549665 .777716 .3333 1.0000

Total 74 .569337 .2307686 .0268263 .515873 .622802 .0000 1.0000
APPENDIX A

89

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT 1.896 4 67 .121

OCA_ING_ATT .971 4 69 .429

RED_ING_ATT 2.178 4 69 .080

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .115 4 .029 1.484 .217

Within Groups 1.296 67 .019

Total 1.411 71

OCA_ING_ATT Between Groups .060 4 .015 1.058 .384

Within Groups .977 69 .014

Total 1.037 73

RED_ING_ATT Between Groups .578 4 .145 3.015 .024

Within Groups 3.309 69 .048

Total 3.888 73
APPENDIX A

90

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence Interval

Lower 

Bound

Upper 

Bound

F15_ING_

ATT

3-1 3-2 -.0753968 .0538604 .630 -.226392 .075598

3-3 -.1097470 .0531071 .247 -.258630 .039136

4-1 -.0710317 .0538604 .681 -.222027 .079963

4-2 -.0161565 .0547087 .998 -.169530 .137217

3-2 3-1 .0753968 .0538604 .630 -.075598 .226392

3-3 -.0343502 .0499803 .959 -.174468 .105767

4-1 .0043651 .0507801 1.000 -.137994 .146725

4-2 .0592404 .0516789 .781 -.085639 .204120

3-3 3-1 .1097470 .0531071 .247 -.039136 .258630

3-2 .0343502 .0499803 .959 -.105767 .174468

4-1 .0387153 .0499803 .937 -.101402 .178833

4-2 .0935906 .0508933 .360 -.049086 .236267

4-1 3-1 .0710317 .0538604 .681 -.079963 .222027

3-2 -.0043651 .0507801 1.000 -.146725 .137994

3-3 -.0387153 .0499803 .937 -.178833 .101402

4-2 .0548753 .0516789 .825 -.090004 .199755

4-2 3-1 .0161565 .0547087 .998 -.137217 .169530

3-2 -.0592404 .0516789 .781 -.204120 .085639

3-3 -.0935906 .0508933 .360 -.236267 .049086

4-1 -.0548753 .0516789 .825 -.199755 .090004

OCA_ING_

ATT

3-1 3-2 -.0749389 .0450998 .464 -.201274 .051396

3-3 -.0590850 .0438508 .663 -.181921 .063751

4-1 -.0167571 .0450998 .996 -.143092 .109577

4-2 -.0156986 .0458416 .997 -.144111 .112714

3-2 3-1 .0749389 .0450998 .464 -.051396 .201274

3-3 .0158539 .0421617 .996 -.102250 .133958

4-1 .0581818 .0434593 .668 -.063557 .179921

4-2 .0592404 .0442286 .668 -.064654 .183134

3-3 3-1 .0590850 .0438508 .663 -.063751 .181921

3-2 -.0158539 .0421617 .996 -.133958 .102250

4-1 .0423279 .0421617 .853 -.075776 .160432

4-2 .0433864 .0429542 .850 -.076938 .163711
APPENDIX A

91

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence Interval

Lower 

Bound

Upper 

Bound

4-1 3-1 .0167571 .0450998 .996 -.109577 .143092

3-2 -.0581818 .0434593 .668 -.179921 .063557

3-3 -.0423279 .0421617 .853 -.160432 .075776

4-2 .0010585 .0442286 1.000 -.122835 .124952

4-2 3-1 .0156986 .0458416 .997 -.112714 .144111

3-2 -.0592404 .0442286 .668 -.183134 .064654

3-3 -.0433864 .0429542 .850 -.163711 .076938

4-1 -.0010585 .0442286 1.000 -.124952 .122835

RED_ING_

ATT

3-1 3-2 .1717416 .0829844 .245 -.060716 .404199

3-3 .0023271 .0806862 1.000 -.223693 .228347

4-1 -.0510887 .0829844 .972 -.283546 .181369

4-2 -.0855464 .0843492 .848 -.321827 .150734

3-2 3-1 -.1717416 .0829844 .245 -.404199 .060716

3-3 -.1694145 .0775782 .198 -.386728 .047899

4-1 -.2228303 .0799658 .052 -.446832 .001171

4-2 -.2572880(*) .0813812 .019 -.485255 -.029321

3-3 3-1 -.0023271 .0806862 1.000 -.228347 .223693

3-2 .1694145 .0775782 .198 -.047899 .386728

4-1 -.0534158 .0775782 .958 -.270729 .163898

4-2 -.0878735 .0790364 .800 -.309272 .133525

4-1 3-1 .0510887 .0829844 .972 -.181369 .283546

3-2 .2228303 .0799658 .052 -.001171 .446832

3-3 .0534158 .0775782 .958 -.163898 .270729

4-2 -.0344577 .0813812 .993 -.262424 .193509

4-2 3-1 .0855464 .0843492 .848 -.150734 .321827

3-2 .2572880(*) .0813812 .019 .029321 .485255

3-3 .0878735 .0790364 .800 -.133525 .309272

4-1 .0344577 .0813812 .993 -.193509 .262424

* The mean difference is significant at the .05 level.

Post-Hoc Tests (continued)
APPENDIX A

92

Homogeneous Subsets

F15_ING_ATT

Tukey HSD

F1 N Subset for alpha = .05

1

3-1 12 .119048

4-2 14 .135204

4-1 15 .190079

3-2 15 .194444

3-3 16 .228795

Sig. .229

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.261.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_ING_ATT

Tukey HSD

F1 N Subset for alpha = .05

1

3-1 13 .119505

4-2 14 .135204

4-1 15 .136263

3-3 17 .178591

3-2 15 .194444

Sig. .437

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

93

RED_ING_ATT

Tukey HSD

F1 N Subset for alpha = .05

1 2

3-2 15 .406402

3-3 17 .575817 .575817

3-1 13 .578144 .578144

4-1 15 .629233 .629233

4-2 14 .663690

Sig. .056 .812

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

3-1 3-2 3-3 4-1 4-2

RF

0.1000

0.1250

0.1500

0.1750

0.2000

0.2250

0.2500

Mean of F15_ING_ATT
APPENDIX A

94

3-1 3-2 3-3 4-1 4-2

RF

0.1200

0.1400

0.1600

0.1800

0.2000

Mean of OCA_ING_ATT

3-1 3-2 3-3 4-1 4-2

RF

0.4000

0.4500

0.5000

0.5500

0.6000

0.6500

0.7000

Mean of RED_ING_ATT
APPENDIX A

95

2001 Force Ratio ANOVA

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_FLOWN_

RATIO 3-1 13 .881716 .2762661 .0766224 .714770 1.048661 .0000 1.1429

3-2 15 .729868 .1320880 .0341050 .656720 .803016 .5000 .9091

3-3 17 .866667 .3190456 .0773799 .702629 1.030705 .0000 1.6000

4-1 15 .896296 .0887565 .0229168 .847145 .945448 .6667 1.0000

4-2 14 .880952 .0684142 .0182845 .841451 .920454 .7778 1.0000

Total 74 .850290 .2106658 .0244894 .801482 .899097 .0000 1.6000

FLOWN_RATIO 3-1 13 .950092 .0804809 .0223214 .901457 .998726 .8750 1.1429

3-2 15 .729868 .1320880 .0341050 .656720 .803016 .5000 .9091

3-3 17 1.283497 .4437793 .1076323 1.055326 1.511667 .4444 2.4000

4-1 15 1.321429 .1222615 .0315678 1.253722 1.389135 1.1111 1.5714

4-2 14 .880952 .0684142 .0182845 .841451 .920454 .7778 1.0000

Total 74 1.044235 .3277100 .0380955 .968311 1.120160 .4444 2.4000

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_FLOWN_RATIO 2.199 4 69 .078

FLOWN_RATIO 6.293 4 69 .000

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_FLOWN_RATIO Between Groups .280 4 .070 1.631 .176

Within Groups 2.960 69 .043

Total 3.240 73

FLOWN_RATIO Between Groups 4.097 4 1.024 18.879 .000

Within Groups 3.743 69 .054

Total 7.840 73
APPENDIX A

96

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence Interval

Lower 

Bound

Upper 

Bound

F15_FLOWN_

RATIO

3-1 3-2 .1518476 .0784832 .309 -.068001 .371696

3-3 .0150488 .0763097 1.000 -.198711 .228809

4-1 -.0145808 .0784832 1.000 -.234430 .205268

4-2 .0007631 .0797740 1.000 -.222701 .224228

3-2 3-1 -.1518476 .0784832 .309 -.371696 .068001

3-3 -.1367988 .0733702 .346 -.342325 .068727

4-1 -.1664284 .0756283 .192 -.378280 .045423

4-2 -.1510845 .0769670 .295 -.366686 .064517

3-3 3-1 -.0150488 .0763097 1.000 -.228809 .198711

3-2 .1367988 .0733702 .346 -.068727 .342325

4-1 -.0296296 .0733702 .994 -.235156 .175897

4-2 -.0142857 .0747493 1.000 -.223675 .195104

4-1 3-1 .0145808 .0784832 1.000 -.205268 .234430

3-2 .1664284 .0756283 .192 -.045423 .378280

3-3 .0296296 .0733702 .994 -.175897 .235156

4-2 .0153439 .0769670 1.000 -.200257 .230945

4-2 3-1 -.0007631 .0797740 1.000 -.224228 .222701

3-2 .1510845 .0769670 .295 -.064517 .366686

3-3 .0142857 .0747493 1.000 -.195104 .223675

4-1 -.0153439 .0769670 1.000 -.230945 .200257

FLOWN_

RATIO

3-1 3-2 .2202237 .0882583 .104 -.027007 .467455

3-3 -.3334052(*) .0858140 .002 -.573789 -.093021

4-1 -.3713370(*) .0882583 .001 -.618568 -.124106

4-2 .0691392 .0897098 .938 -.182158 .320436

3-2 3-1 -.2202237 .0882583 .104 -.467455 .027007

3-3 -.5536288(*) .0825085 .000 -.784753 -.322504

4-1 -.5915607(*) .0850478 .000 -.829798 -.353323

4-2 -.1510845 .0865532 .414 -.393539 .091370

3-3 3-1 .3334052(*) .0858140 .002 .093021 .573789

3-2 .5536288(*) .0825085 .000 .322504 .784753

4-1 -.0379318 .0825085 .991 -.269056 .193193

4-2 .4025444(*) .0840594 .000 .167076 .638013
APPENDIX A

97

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence Interval

Lower 

Bound

Upper 

Bound

4-1 3-1 .3713370(*) .0882583 .001 .124106 .618568

3-2 .5915607(*) .0850478 .000 .353323 .829798

3-3 .0379318 .0825085 .991 -.193193 .269056

4-2 .4404762(*) .0865532 .000 .198022 .682931

4-2 3-1 -.0691392 .0897098 .938 -.320436 .182158

3-2 .1510845 .0865532 .414 -.091370 .393539

3-3 -.4025444(*) .0840594 .000 -.638013 -.167076

4-1 -.4404762(*) .0865532 .000 -.682931 -.198022

* The mean difference is significant at the .05 level.

Homogeneous Subsets

F15_FLOWN_RATIO

Tukey HSD

F1 N Subset for alpha = .05

1

3-2 15 .729868

3-3 17 .866667

4-2 14 .880952

3-1 13 .881716

4-1 15 .896296

Sig. .201

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Post-Hoc Tests (continued)
APPENDIX A

98

FLOWN_RATIO

Tukey HSD

F1 N Subset for alpha = .05

1 2

3-2 15 .729868

4-2 14 .880952

3-1 13 .950092

3-3 17 1.283497

4-1 15 1.321429

Sig. .089 .992

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

3-1 3-2 3-3 4-1 4-2

RF

0.7000

0.7500

0.8000

0.8500

0.9000

Mean of F15_FLOWN_RATIO
APPENDIX A

99

3-1 3-2 3-3 4-1 4-2

RF

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

1.4000

Mean of FLOWN_RATIO
APPENDIX A

100

2001 Force Ratio and Aircraft Sortie ANOVA

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_FLOWN_

RATIO 3-1 13 .881716 .2762661 .0766224 .714770 1.048661 .0000 1.1429

3-2 15 .729868 .1320880 .0341050 .656720 .803016 .5000 .9091

3-3 17 .866667 .3190456 .0773799 .702629 1.030705 .0000 1.6000

4-1 15 .896296 .0887565 .0229168 .847145 .945448 .6667 1.0000

4-2 14 .880952 .0684142 .0182845 .841451 .920454 .7778 1.0000

Total 74 .850290 .2106658 .0244894 .801482 .899097 .0000 1.6000

FLOWN_

RATIO 3-1 13 .950092 .0804809 .0223214 .901457 .998726 .8750 1.1429

3-2 15 .729868 .1320880 .0341050 .656720 .803016 .5000 .9091

3-3 17 1.283497 .4437793 .1076323 1.055326 1.511667 .4444 2.4000

4-1 15 1.321429 .1222615 .0315678 1.253722 1.389135 1.1111 1.5714

4-2 14 .880952 .0684142 .0182845 .841451 .920454 .7778 1.0000

Total 74 1.044235 .3277100 .0380955 .968311 1.120160 .4444 2.4000

OCA_F15_FL 3-1 12 7.58 .669 .193 7.16 8.01 6 8

3-2 15 8.53 1.767 .456 7.55 9.51 4 10

3-3 16 7.06 1.611 .403 6.20 7.92 4 8

4-1 15 7.73 .594 .153 7.40 8.06 6 8

4-2 14 7.79 .426 .114 7.54 8.03 7 8

Total 72 7.74 1.256 .148 7.44 8.03 4 10

OCA_TOT_

FTR_FL 3-1 13 7.62 .650 .180 7.22 8.01 6 8

3-2 15 8.53 1.767 .456 7.55 9.51 4 10

3-3 17 9.71 2.568 .623 8.39 11.03 4 12

4-1 15 11.40 .737 .190 10.99 11.81 10 12

4-2 14 7.79 .426 .114 7.54 8.03 7 8

Total 74 9.08 2.052 .239 8.61 9.56 4 12

RED_TOT_

FTR_FL 3-1 13 8.08 1.038 .288 7.45 8.70 6 9

3-2 15 11.67 1.345 .347 10.92 12.41 8 13

3-3 17 7.94 1.638 .397 7.10 8.78 4 9

4-1 15 8.67 .617 .159 8.32 9.01 7 9

4-2 14 8.86 .363 .097 8.65 9.07 8 9

Total 74 9.04 1.763 .205 8.63 9.45 4 13
APPENDIX A

101

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_FLOWN_RATIO 2.199 4 69 .078

FLOWN_RATIO 6.293 4 69 .000

OCA_F15_FL 7.536 4 67 .000

OCA_TOT_FTR_FL 12.991 4 69 .000

RED_TOT_FTR_FL 3.835 4 69 .007

ANOVA

Sum of 

Squares Df Mean Square F Sig.

F15_FLOWN_RATIO Between Groups .280 4 .070 1.631 .176

Within Groups 2.960 69 .043

Total 3.240 73

FLOWN_RATIO Between Groups 4.097 4 1.024 18.879 .000

Within Groups 3.743 69 .054

Total 7.840 73

OCA_F15_FL Between Groups 17.108 4 4.277 3.020 .024

Within Groups 94.878 67 1.416

Total 111.986 71

OCA_TOT_FTR_FL Between Groups 143.217 4 35.804 15.037 .000

Within Groups 164.297 69 2.381

Total 307.514 73

RED_TOT_FTR_FL Between Groups 138.633 4 34.658 27.100 .000

Within Groups 88.245 69 1.279

Total 226.878 73
APPENDIX A

102

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_FLOWN_

RATIO

3-1 3-2 .1518476 .0784832 .309 -.068001 .371696

3-3 .0150488 .0763097 1.000 -.198711 .228809

4-1 -.0145808 .0784832 1.000 -.234430 .205268

4-2 .0007631 .0797740 1.000 -.222701 .224228

3-2 3-1 -.1518476 .0784832 .309 -.371696 .068001

3-3 -.1367988 .0733702 .346 -.342325 .068727

4-1 -.1664284 .0756283 .192 -.378280 .045423

4-2 -.1510845 .0769670 .295 -.366686 .064517

3-3 3-1 -.0150488 .0763097 1.000 -.228809 .198711

3-2 .1367988 .0733702 .346 -.068727 .342325

4-1 -.0296296 .0733702 .994 -.235156 .175897

4-2 -.0142857 .0747493 1.000 -.223675 .195104

4-1 3-1 .0145808 .0784832 1.000 -.205268 .234430

3-2 .1664284 .0756283 .192 -.045423 .378280

3-3 .0296296 .0733702 .994 -.175897 .235156

4-2 .0153439 .0769670 1.000 -.200257 .230945

4-2 3-1 -.0007631 .0797740 1.000 -.224228 .222701

3-2 .1510845 .0769670 .295 -.064517 .366686

3-3 .0142857 .0747493 1.000 -.195104 .223675

4-1 -.0153439 .0769670 1.000 -.230945 .200257

FLOWN_

RATIO

3-1 3-2 .2202237 .0882583 .104 -.027007 .467455

3-3 -.3334052(*) .0858140 .002 -.573789 -.093021

4-1 -.3713370(*) .0882583 .001 -.618568 -.124106

4-2 .0691392 .0897098 .938 -.182158 .320436

3-2 3-1 -.2202237 .0882583 .104 -.467455 .027007

3-3 -.5536288(*) .0825085 .000 -.784753 -.322504

4-1 -.5915607(*) .0850478 .000 -.829798 -.353323

4-2 -.1510845 .0865532 .414 -.393539 .091370

3-3 3-1 .3334052(*) .0858140 .002 .093021 .573789

3-2 .5536288(*) .0825085 .000 .322504 .784753

4-1 -.0379318 .0825085 .991 -.269056 .193193

4-2 .4025444(*) .0840594 .000 .167076 .638013
APPENDIX A

103

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

4-1 3-1 .3713370(*) .0882583 .001 .124106 .618568

3-2 .5915607(*) .0850478 .000 .353323 .829798

3-3 .0379318 .0825085 .991 -.193193 .269056

4-2 .4404762(*) .0865532 .000 .198022 .682931

4-2 3-1 -.0691392 .0897098 .938 -.320436 .182158

3-2 .1510845 .0865532 .414 -.091370 .393539

3-3 -.4025444(*) .0840594 .000 -.638013 -.167076

4-1 -.4404762(*) .0865532 .000 -.682931 -.198022

OCA_F15_FL 3-1 3-2 -.950 .461 .249 -2.24 .34

3-3 .521 .454 .781 -.75 1.79

4-1 -.150 .461 .998 -1.44 1.14

4-2 -.202 .468 .993 -1.51 1.11

3-2 3-1 .950 .461 .249 -.34 2.24

3-3 1.471(*) .428 .009 .27 2.67

4-1 .800 .435 .359 -.42 2.02

4-2 .748 .442 .447 -.49 1.99

3-3 3-1 -.521 .454 .781 -1.79 .75

3-2 -1.471(*) .428 .009 -2.67 -.27

4-1 -.671 .428 .523 -1.87 .53

4-2 -.723 .435 .465 -1.94 .50

4-1 3-1 .150 .461 .998 -1.14 1.44

3-2 -.800 .435 .359 -2.02 .42

3-3 .671 .428 .523 -.53 1.87

4-2 -.052 .442 1.000 -1.29 1.19

4-2 3-1 .202 .468 .993 -1.11 1.51

3-2 -.748 .442 .447 -1.99 .49

3-3 .723 .435 .465 -.50 1.94

4-1 .052 .442 1.000 -1.19 1.29

OCA_TOT_

FTR_FL

3-1 3-2 -.918 .585 .522 -2.56 .72

3-3 -2.090(*) .569 .004 -3.68 -.50

4-1 -3.785(*) .585 .000 -5.42 -2.15

4-2 -.170 .594 .998 -1.84 1.49

3-2 3-1 .918 .585 .522 -.72 2.56

3-3 -1.173 .547 .213 -2.70 .36

Post-Hoc Tests (continued)
APPENDIX A

104

Dependent 

Variable (I) F1 (J) F1

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

4-1 -2.867(*) .563 .000 -4.45 -1.29

4-2 .748 .573 .690 -.86 2.35

3-3 3-1 2.090(*) .569 .004 .50 3.68

3-2 1.173 .547 .213 -.36 2.70

4-1 -1.694(*) .547 .023 -3.23 -.16

4-2 1.920(*) .557 .008 .36 3.48

4-1 3-1 3.785(*) .585 .000 2.15 5.42

3-2 2.867(*) .563 .000 1.29 4.45

3-3 1.694(*) .547 .023 .16 3.23

4-2 3.614(*) .573 .000 2.01 5.22

4-2 3-1 .170 .594 .998 -1.49 1.84

3-2 -.748 .573 .690 -2.35 .86

3-3 -1.920(*) .557 .008 -3.48 -.36

4-1 -3.614(*) .573 .000 -5.22 -2.01

RED_TOT_

FTR_FL

3-1 3-2 -3.590(*) .429 .000 -4.79 -2.39

3-3 .136 .417 .998 -1.03 1.30

4-1 -.590 .429 .645 -1.79 .61

4-2 -.780 .436 .387 -2.00 .44

3-2 3-1 3.590(*) .429 .000 2.39 4.79

3-3 3.725(*) .401 .000 2.60 4.85

4-1 3.000(*) .413 .000 1.84 4.16

4-2 2.810(*) .420 .000 1.63 3.99

3-3 3-1 -.136 .417 .998 -1.30 1.03

3-2 -3.725(*) .401 .000 -4.85 -2.60

4-1 -.725 .401 .376 -1.85 .40

4-2 -.916 .408 .176 -2.06 .23

4-1 3-1 .590 .429 .645 -.61 1.79

3-2 -3.000(*) .413 .000 -4.16 -1.84

3-3 .725 .401 .376 -.40 1.85

4-2 -.190 .420 .991 -1.37 .99

4-2 3-1 .780 .436 .387 -.44 2.00

3-2 -2.810(*) .420 .000 -3.99 -1.63

3-3 .916 .408 .176 -.23 2.06

4-1 .190 .420 .991 -.99 1.37

* The mean difference is significant at the .05 level.

Post-Hoc Tests (continued)
APPENDIX A

105

Homogeneous Subsets

F15_FLOWN_RATIO

Tukey HSD

F1 N Subset for alpha = .05

1

3-2 15 .729868

3-3 17 .866667

4-2 14 .880952

3-1 13 .881716

4-1 15 .896296

Sig. .201

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

FLOWN_RATIO

Tukey HSD

F1 N Subset for alpha = .05

1 2

3-2 15 .729868

4-2 14 .880952

3-1 13 .950092

3-3 17 1.283497

4-1 15 1.321429

Sig. .089 .992

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

106

OCA_F15_FL

Tukey HSD

F1 N Subset for alpha = .05

1 2

3-3 16 7.06

3-1 12 7.58 7.58

4-1 15 7.73 7.73

4-2 14 7.79 7.79

3-2 15 8.53

Sig. .488 .219

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.261.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_TOT_FTR_FL

Tukey HSD

F1 N Subset for alpha = .05

1 2 3

3-1 13 7.62

4-2 14 7.79

3-2 15 8.53 8.53

3-3 17 9.71

4-1 15 11.40

Sig. .495 .250 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

107

RED_TOT_FTR_FL

Tukey HSD

F1 N Subset for alpha = .05

1 2

3-3 17 7.94

3-1 13 8.08

4-1 15 8.67

4-2 14 8.86

3-2 15 11.67

Sig. .194 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 14.684.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

3-1 3-2 3-3 4-1 4-2

RF

0.7000

0.7500

0.8000

0.8500

0.9000

Mean of F15_FLOWN_RATIO
APPENDIX A

108

3-1 3-2 3-3 4-1 4-2

RF

0.7000

0.8000

0.9000

1.0000

1.1000

1.2000

1.3000

1.4000

Mean of FLOWN_RATIO

3-1 3-2 3-3 4-1 4-2

RF

7.0

7.2

7.4

7.6

7.8

8.0

8.2

8.4

8.6

Mean of OCA_F15_FL
APPENDIX A

109

3-1 3-2 3-3 4-1 4-2

RF

89

10

11

Mean of OCA_TOT_FTR_FL

3-1 3-2 3-3 4-1 4-2

RF

89

10

11

12

Mean of RED_TOT_FTR_FL
APPENDIX A

110

A3. Variation in Attrition by Week and Day T-Test

Author’s original work using SPSS 12.0.1

Group Statistics

WK N Mean Std. Deviation Std. Error Mean

F15_ING_ATT 1 140 .122828 .1533635 .0129616

2 159 .139354 .1519543 .0120508

OCA_ING_ATT 1 140 .113246 .1414239 .0119525

2 167 .131077 .1386506 .0107291

RED_ING_ATT 1 140 .698957 .2210454 .0186817

2 167 .733215 .2253592 .0174388

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. T df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed .059 .809 -.934 297 .351 -.0165254 .0176877 -.0513345 .0182837

Equal variances 

not assumed -.934 291.529 .351 -.0165254 .0176981 -.0513577 .0183069

OCA_ING_

ATT

Equal variances 

assumed .169 .681 -1.112 305 .267 -.0178308 .0160336 -.0493812 .0137197

Equal variances 

not assumed -1.110 293.621 .268 -.0178308 .0160616 -.0494413 .0137797

RED_ING_

ATT

Equal variances 

assumed .331 .565 -1.338 305 .182 -.0342581 .0255998 -.0846328 .0161165

Equal variances 

not assumed -1.341 297.582 .181 -.0342581 .0255562 -.0845519 .0160357
APPENDIX A

111

WEEK 1: Monday–Friday ANOVA

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .026 4 .006 .266 .899

Within Groups 3.244 135 .024

Total 3.269 139

OCA_ING_ATT Between Groups .017 4 .004 .213 .931

Within Groups 2.763 135 .020

Total 2.780 139

RED_ING_ATT Between Groups .223 4 .056 1.145 .338

Within Groups 6.569 135 .049

Total 6.792 139

WEEK 2: Monday–Friday ANOVA

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .278 4 .069 3.175 .015

Within Groups 3.370 154 .022

Total 3.648 158

OCA_ING_ATT Between Groups .278 4 .069 3.863 .005

Within Groups 2.913 162 .018

Total 3.191 166

RED_ING_ATT Between Groups .202 4 .051 .994 .412

Within Groups 8.229 162 .051

Total 8.431 166
APPENDIX A

112

WEEK 2: Monday–Friday ANOVA

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_

ATT

MON 37 .091763 .1170542 .0192436 .052735 .130791 .0000 .3750

TUE 37 .104794 .1051496 .0172865 .069735 .139853 .0000 .3750

WED 35 .149107 .1618597 .0273593 .093506 .204708 .0000 .7500

THU 34 .190278 .1720798 .0295114 .130236 .250319 .0000 .6250

FRI 16 .199777 .2018430 .0504607 .092222 .307331 .0000 .5714

Total 159 .139354 .1519543 .0120508 .115552 .163155 .0000 .7500

OCA_ING_

ATT

MON 38 .085617 .1045232 .0169559 .051262 .119973 .0000 .2727

TUE 37 .096101 .0878778 .0144470 .066801 .125401 .0000 .2727

WED 36 .141738 .1501752 .0250292 .090926 .192550 .0000 .7500

THU 36 .162207 .1483514 .0247252 .112012 .212402 .0000 .5000

FRI 20 .206932 .1879903 .0420359 .118950 .294914 .0000 .5000

Total 167 .131077 .1386506 .0107291 .109894 .152260 .0000 .7500

RED_ING_

ATT

MON 38 .773405 .2335313 .0378838 .696646 .850165 .0000 1.0000

TUE 37 .724625 .2155671 .0354390 .652751 .796498 .2857 1.0000

WED 36 .726546 .2080172 .0346695 .656163 .796929 .2727 1.0000

THU 36 .681468 .2435892 .0405982 .599050 .763887 .1111 1.0000

FRI 20 .777895 .2232032 .0499098 .673433 .882357 .2500 1.0000

Total 167 .733215 .2253592 .0174388 .698785 .767646 .0000 1.0000
APPENDIX A

113

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT 3.300 4 154 .013

OCA_ING_ATT 4.818 4 162 .001

RED_ING_ATT .349 4 162 .844

ANOVA

Sum of 

Squares Df Mean Square F Sig.

F15_ING_ATT Between Groups .278 4 .069 3.175 .015

Within Groups 3.370 154 .022

Total 3.648 158

OCA_ING_ATT Between Groups .278 4 .069 3.863 .005

Within Groups 2.913 162 .018

Total 3.191 166

RED_ING_ATT Between Groups .202 4 .051 .994 .412

Within Groups 8.229 162 .051

Total 8.431 166
APPENDIX A

114

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) DAY2 (J) DAY2

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_ING_ATT MON TUE -.0130309 .0343946 .996 -.107973 .081911

WED -.0573437 .0348825 .472 -.153632 .038945

THU -.0985146(*) .0351451 .045 -.195528 -.001501

FRI -.1080136 .0442642 .110 -.230199 .014172

TUE MON .0130309 .0343946 .996 -.081911 .107973

WED -.0443128 .0348825 .710 -.140601 .051976

THU -.0854837 .0351451 .112 -.182497 .011530

FRI -.0949827 .0442642 .206 -.217168 .027203

WED MON .0573437 .0348825 .472 -.038945 .153632

TUE .0443128 .0348825 .710 -.051976 .140601

THU -.0411709 .0356227 .776 -.139503 .057161

FRI -.0506699 .0446444 .788 -.173905 .072565

THU MON .0985146(*) .0351451 .045 .001501 .195528

TUE .0854837 .0351451 .112 -.011530 .182497

WED .0411709 .0356227 .776 -.057161 .139503

FRI -.0094990 .0448499 1.000 -.133301 .114303

FRI MON .1080136 .0442642 .110 -.014172 .230199

TUE .0949827 .0442642 .206 -.027203 .217168

WED .0506699 .0446444 .788 -.072565 .173905

THU .0094990 .0448499 1.000 -.114303 .133301

OCA_ING_ATT MON TUE -.0104835 .0309724 .997 -.095929 .074962

WED -.0561209 .0311896 .378 -.142165 .029923

THU -.0765899 .0311896 .106 -.162634 .009454

FRI -.1213144(*) .0370463 .011 -.223516 -.019113

TUE MON .0104835 .0309724 .997 -.074962 .095929

WED -.0456374 .0313940 .594 -.132245 .040971

THU -.0661064 .0313940 .223 -.152714 .020502

FRI -.1108308(*) .0372185 .027 -.213507 -.008154

WED MON .0561209 .0311896 .378 -.029923 .142165

TUE .0456374 .0313940 .594 -.040971 .132245
APPENDIX A

115

Dependent 

Variable (I) DAY2 (J) DAY2

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

THU -.0204690 .0316083 .967 -.107668 .066730

FRI -.0651935 .0373994 .411 -.168369 .037982

THU MON .0765899 .0311896 .106 -.009454 .162634

TUE .0661064 .0313940 .223 -.020502 .152714

WED .0204690 .0316083 .967 -.066730 .107668

FRI -.0447244 .0373994 .754 -.147900 .058451

FRI MON .1213144(*) .0370463 .011 .019113 .223516

TUE .1108308(*) .0372185 .027 .008154 .213507

WED .0651935 .0373994 .411 -.037982 .168369

THU .0447244 .0373994 .754 -.058451 .147900

RED_ING_ATT MON TUE .0487808 .0520526 .882 -.094819 .192381

WED .0468593 .0524176 .899 -.097748 .191466

THU .0919370 .0524176 .404 -.052670 .236544

FRI -.0044896 .0622604 1.000 -.176250 .167271

TUE MON -.0487808 .0520526 .882 -.192381 .094819

WED -.0019216 .0527611 1.000 -.147476 .143633

THU .0431562 .0527611 .925 -.102398 .188711

FRI -.0532704 .0625498 .914 -.225829 .119289

WED MON -.0468593 .0524176 .899 -.191466 .097748

TUE .0019216 .0527611 1.000 -.143633 .147476

THU .0450778 .0531213 .915 -.101470 .191626

FRI -.0513488 .0628539 .925 -.224747 .122049

THU MON -.0919370 .0524176 .404 -.236544 .052670

TUE -.0431562 .0527611 .925 -.188711 .102398

WED -.0450778 .0531213 .915 -.191626 .101470

FRI -.0964266 .0628539 .542 -.269825 .076971

FRI MON .0044896 .0622604 1.000 -.167271 .176250

TUE .0532704 .0625498 .914 -.119289 .225829

WED .0513488 .0628539 .925 -.122049 .224747

THU .0964266 .0628539 .542 -.076971 .269825

* The mean difference is significant at the .05 level.

Post-Hoc Tests (continued)
APPENDIX A

116

Homogeneous Subsets

F15_ING_ATT

Tukey HSD

DAY2 N Subset for alpha = .05

1 2

MON 37 .091763

TUE 37 .104794 .104794

WED 35 .149107 .149107

THU 34 .190278 .190278

FRI 16 .199777

Sig. .091 .113

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 28.647.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_ING_ATT

Tukey HSD

DAY2 N Subset for alpha = .05

1 2

MON 38 .085617

TUE 37 .096101

WED 36 .141738 .141738

THU 36 .162207 .162207

FRI 20 .206932

Sig. .162 .307

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 31.467.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

117

RED_ING_ATT

Tukey HSD

DAY2 N Subset for alpha = .05

1

THU 36 .681468

TUE 37 .724625

WED 36 .726546

MON 38 .773405

FRI 20 .777895

Sig. .439

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 31.467.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

Means Plots

MON TUE WED THU FRI

DAY

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000

Mean of F15_ING_ATT
APPENDIX A

118

MON TUE WED THU FRI

DAY

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000

0.2200

Mean of OCA_ING_ATT

MON TUE WED THU FRI

DAY

0.6800

0.7000

0.7200

0.7400

0.7600

0.7800

Mean of RED_ING_ATT
APPENDIX A

119

Univariate Analysis of Variance–F-15C Attrition

Between-Subjects Factors

Value Label N

DAY2 1 MON 41

2 TUE 68

3 WED 71

4 THU 70

5 FRI 49

WK 1 140

2 159

Tests of Between-Subjects Effects

Dependent Variable: F15_ING_ATT

Source Type III Sum 

of Squares Df Mean Square F Sig.

Corrected Model .324(a) 9 .036 1.572 .123

Intercept 3.263 1 3.263 142.559 .000

DAY2 .117 4 .029 1.276 .280

WK .037 1 .037 1.597 .207

DAY2 * WK .108 4 .027 1.185 .318

Error 6.614 289 .023

Total 12.117 299

Corrected Total 6.938 298

a R Squared = .047 (Adjusted R Squared = .017)
APPENDIX A

120

Profile Plots

MON TUE WED THU FRI

DAY

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000

Estimated Marginal Means

WK

1

2

Estimated Marginal Means of F15_ING_ATT
APPENDIX A

121

Univariate Analysis of Variance-Red Air Attrition

Between-Subjects Factors

Value Label N

DAY2 1 MON 42

2 TUE 68

3 WED 72

4 THU 72

5 FRI 53

WK 1 140

2 167

Tests of Between-Subjects Effects

Dependent Variable: RED_ING_ATT

Source Type III Sum 

of Squares Df Mean Square F Sig.

Corrected Model .514(a) 9 .057 1.147 .329

Intercept 96.023 1 96.023 1927.284 .000

DAY2 .078 4 .019 .390 .816

WK .123 1 .123 2.460 .118

DAY2 * WK .320 4 .080 1.604 .173

Error 14.797 297 .050

Total 173.398 307

Corrected Total 15.312 306

a R Squared = .034 (Adjusted R Squared = .004)
APPENDIX A

122

Profile Plots

MON TUE WED THU FRI

DAY

0.6300

0.6600

0.6900

0.7200

0.7500

0.7800

Estimated Marginal Means

WK

1

2

Estimated Marginal Means of RED_ING_ATT
APPENDIX A

123

A4. Day-Night Independent Samples T-test

Author’s original work using SPSS 12.0.1

Group Statistics

LIGHT N Mean Std. 

Deviation

Std. Error 

Mean

F15_ING_ATT DAY 185 .145597 .1589280 .0116846

NIGHT 114 .108928 .1393907 .0130551

OCA_ING_ATT DAY 190 .133635 .1439208 .0104411

NIGHT 117 .105587 .1320833 .0122111

RED_ING_ATT DAY 190 .693107 .2195623 .0159287

NIGHT 117 .757356 .2255554 .0208526

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t Df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 5.253 .023 2.029 297 .043 .0366686 .0180736 .0011000 .0722371

Equal variances 

not assumed 2.093 262.933 .037 .0366686 .0175205 .0021703 .0711668

OCA_ING_

ATT

Equal variances 

assumed 2.234 .136 1.710 305 .088 .0280486 .0163979 -.0042188 .0603160

Equal variances 

not assumed 1.746 261.751 .082 .0280486 .0160664 -.0035871 .0596844

RED_ING_

ATT

Equal variances 

assumed .801 .371 -2.464 305 .014 -.0642494 .0260723 -.1155539 -.0129450

Equal variances 

not assumed -2.448 240.591 .015 -.0642494 .0262403 -.1159396 -.0125593
APPENDIX A

124

A5. Threat Aircraft ANOVA

Author’s original work using SPSS 12.0.1

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_ATT MiG-23 34 .073214 .1245783 .0213650 .029747 .116682 .0000 .4286

MiG-29 141 .115802 .1453636 .0122418 .091599 .140005 .0000 .7500

SU-27 124 .165611 .1606120 .0144234 .137061 .194162 .0000 .7500

Total 299 .131616 .1525829 .0088241 .114251 .148981 .0000 .7500

OCA_ING_ATT MiG-23 34 .073214 .1245783 .0213650 .029747 .116682 .0000 .4286

MiG-29 142 .106489 .1305409 .0109548 .084832 .128145 .0000 .7500

SU-27 131 .153692 .1476529 .0129005 .128170 .179215 .0000 .7500

Total 307 .122946 .1399754 .0079888 .107226 .138666 .0000 .7500

RED_ING_ATT MiG-23 34 .751471 .2415154 .0414196 .667202 .835739 .0000 1.0000

MiG-29 142 .717246 .2228020 .0186971 .680283 .754208 .0000 1.1250

SU-27 131 .709176 .2208224 .0192933 .671007 .747346 .1111 1.0000

Total 307 .717593 .2236921 .0127668 .692471 .742714 .0000 1.1250

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT 1.625 2 296 .199

OCA_ING_ATT 1.695 2 304 .185

RED_ING_ATT .024 2 304 .976
APPENDIX A

125

ANOVA

Sum of 

Squares Df Mean Square F Sig.

F15_ING_ATT Between Groups .295 2 .147 6.562 .002

Within Groups 6.643 296 .022

Total 6.938 298

OCA_ING_ATT Between Groups .246 2 .123 6.514 .002

Within Groups 5.749 304 .019

Total 5.995 306

RED_ING_ATT Between Groups .048 2 .024 .481 .619

Within Groups 15.263 304 .050

Total 15.312 306

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) THRT_AC (J) THRT_AC

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_ING_

ATT

MiG-23 MiG-29 -.0425879 .0286232 .298 -.110012 .024836

SU-27 -.0923971(*) .0290019 .005 -.160713 -.024081

MiG-29 MiG-23 .0425879 .0286232 .298 -.024836 .110012

SU-27 -.0498092(*) .0184438 .020 -.093255 -.006364

SU-27 MiG-23 .0923971(*) .0290019 .005 .024081 .160713

MiG-29 .0498092(*) .0184438 .020 .006364 .093255

OCA_ING_

ATT

MiG-23 MiG-29 -.0332743 .0262564 .415 -.095115 .028566

SU-27 -.0804782(*) .0264686 .007 -.142818 -.018138

MiG-29 MiG-23 .0332743 .0262564 .415 -.028566 .095115

SU-27 -.0472039(*) .0166596 .014 -.086441 -.007966

SU-27 MiG-23 .0804782(*) .0264686 .007 .018138 .142818

MiG-29 .0472039(*) .0166596 .014 .007966 .086441

RED_ING_

ATT

MiG-23 MiG-29 .0342250 .0427820 .703 -.066537 .134987

SU-27 .0422944 .0431276 .590 -.059282 .143871

MiG-29 MiG-23 -.0342250 .0427820 .703 -.134987 .066537

SU-27 .0080694 .0271450 .952 -.055864 .072003

SU-27 MiG-23 -.0422944 .0431276 .590 -.143871 .059282

MiG-29 -.0080694 .0271450 .952 -.072003 .055864

* The mean difference is significant at the .05 level.
APPENDIX A

126

Homogeneous Subsets

F15_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1 2

MiG-23 34 .073214

MiG-29 141 .115802 .115802

SU-27 124 .165611

Sig. .227 .132

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 67.312.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1 2

MiG-23 34 .073214

MiG-29 142 .106489 .106489

SU-27 131 .153692

Sig. .336 .113

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 68.046.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

RED_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1

SU-27 131 .709176

MIG-29 142 .717246

MiG-23 34 .751471

Sig. .514

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 68.046.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

127

Means Plots

MIG-23 MIG-29 SU-27

THRT AC

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

Mean of OCA_ING_ATT

MIG-23 MIG-29 SU-27

THRT AC

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

Mean of F15_ING_ATT
APPENDIX A

128

MIG-23 MIG-29 SU-27

THRT AC

0.7000

0.7100

0.7200

0.7300

0.7400

0.7500

0.7600

Mean of RED_ING_ATT
APPENDIX A

129

A6. Threat Weapons T-test

Author’s original work using SPSS 12.0.1

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 227 .117505 .1409548 .0093555

LONG 72 .176104 .1784115 .0210260

OCA_ING_ATT SHORT 228 .108016 .1272607 .0084280

LONG 79 .166034 .1649272 .0185558

RED_ING_ATT SHORT 228 .714948 .2232472 .0147849

LONG 79 .725225 .2262275 .0254526

Independent Samples Test

Levene’s 

Test for 

Equality of 

Variances

T-test for Equality of Means

F Sig. T df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 4.010 .046 -2.874 297 .004 -.0585981 .0203909 -.0987271 -.0184691

Equal variances 

not assumed -2.546 100.657 .012 -.0585981 .0230134 -.1042525 -.0129438

OCA_ING_

ATT

Equal variances 

assumed 6.344 .012 -3.223 305 .001 -.0580178 .0180002 -.0934381 -.0225975

Equal variances 

not assumed -2.847 111.866 .005 -.0580178 .0203801 -.0983989 -.0176368

RED_ING_

ATT

Equal variances 

assumed .038 .845 -.351 305 .726 -.0102764 .0292457 -.0678253 .0472724

Equal variances 

not assumed -.349 134.266 .728 -.0102764 .0294351 -.0684930 .0479401
APPENDIX A

130

Univariate Analysis of Variance

Between-Subjects Factors

Value Label N

WEAPON2 2 SHORT 227

3 LONG 72

THRT_AC 3 MiG-23 34

4 MiG-29 141

5 SU-27 124

Tests of Between-Subjects Effects

Dependent Variable: F15_ING_ATT

Source Type III Sum 

of Squares Df Mean Square F Sig.

Corrected Model .362(a) 4 .090 4.044 .003

Intercept .733 1 .733 32.771 .000

WEAPON2 .003 1 .003 .133 .716

THRT_AC .173 2 .087 3.872 .022

WEAPON2 * THRT_AC .041 1 .041 1.832 .177

Error 6.576 294 .022

Total 12.117 299

Corrected Total 6.938 298

a R Squared = .052 (Adjusted R Squared = .039)
APPENDIX A

131

Profile Plots

MIG-23 MIG-29 SU-27

THRT AC

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

0.1800

0.2000

Estimated Marginal Means

WEAPON2

SHORT

LONG

Non-estimable means are not plotted

Estimated Marginal Means of F15_ING_ATT
APPENDIX A

132

One Way

Warnings

Post-hoc tests are not performed for F15_ING_ATT because there are fewer than three 

groups.

Post-hoc tests are not performed for OCA_ING_ATT because there are fewer than three 

groups.

Post-hoc tests are not performed for RED_ING_ATT because there are fewer than three 

groups.

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_

ATT SHORT 227 .117505 .1409548 .0093555 .099070 .135941 .0000 .7500

LONG 72 .176104 .1784115 .0210260 .134179 .218028 .0000 .7500

Total 299 .131616 .1525829 .0088241 .114251 .148981 .0000 .7500

OCA_ING_

ATT SHORT 228 .108016 .1272607 .0084280 .091409 .124623 .0000 .7500

LONG 79 .166034 .1649272 .0185558 .129092 .202976 .0000 .7500

Total 307 .122946 .1399754 .0079888 .107226 .138666 .0000 .7500

RED_ING_

ATT SHORT 228 .714948 .2232472 .0147849 .685815 .744081 .0000 1.1250

LONG 79 .725225 .2262275 .0254526 .674552 .775897 .1111 1.0000

Total 307 .717593 .2236921 .0127668 .692471 .742714 .0000 1.1250

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT 4.010 1 297 .046

OCA_ING_ATT 6.344 1 305 .012

RED_ING_ATT .038 1 305 .845
APPENDIX A

133

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .188 1 .188 8.258 .004

Within Groups 6.750 297 .023

Total 6.938 298

OCA_ING_ATT Between Groups .197 1 .197 10.389 .001

Within Groups 5.798 305 .019

Total 5.995 306

RED_ING_ATT Between Groups .006 1 .006 .123 .726

Within Groups 15.305 305 .050

Total 15.312 306

Means Plots

SHORT LONG

WEAPON2

0.1100

0.1200

0.1300

0.1400

0.1500

0.1600

0.1700

0.1800

Mean of F15_ING_ATT
APPENDIX A

134

SHORT LONG

WEAPON2

0.1000

0.1100

0.1200

0.1300

0.1400

0.1500

0.1600

0.1700

Mean of OCA_ING_ATT

SHORT LONG

WEAPON2

0.7140

0.7160

0.7180

0.7200

0.7220

0.7240

0.7260

Mean of RED_ING_ATT
APPENDIX A

135

MIG-23 MIG-29 SU-27

THRT AC

0

20

40

60

80

100

120

140

Count

WEAPON2

SHORT

LONG
APPENDIX A

136

One Way

Warnings

Post-hoc tests are not performed for F15_ING_ATT because there are fewer than three 

groups.

Post-hoc tests are not performed for OCA_ING_ATT because there are fewer than three 

groups.

Post-hoc tests are not performed for RED_ING_ATT because there are fewer than three 

groups.

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_ATT SHORT 171 .108906 .1434054 .0109665 .087258 .130554 .0000 .7500

LONG 68 .183603 .1804347 .0218809 .139929 .227278 .0000 .7500

Total 239 .130159 .1580984 .0102265 .110013 .150305 .0000 .7500

OCA_ING_ATT SHORT 172 .101257 .1307787 .0099718 .081573 .120941 .0000 .7500

LONG 75 .172297 .1665932 .0192365 .133967 .210626 .0000 .7500

Total 247 .122828 .1459749 .0092882 .104533 .141122 .0000 .7500

RED_ING_ATT SHORT 172 .726931 .2277614 .0173666 .692651 .761212 .0000 1.1250

LONG 75 .732348 .2296481 .0265175 .679511 .785185 .1111 1.0000

Total 247 .728576 .2278820 .0144998 .700016 .757136 .0000 1.1250

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT 3.983 1 237 .047

OCA_ING_ATT 5.856 1 245 .016

RED_ING_ATT .025 1 245 .874
APPENDIX A

137

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .271 1 .271 11.332 .001

Within Groups 5.677 237 .024

Total 5.948 238

OCA_ING_ATT Between Groups .264 1 .264 12.971 .000

Within Groups 4.978 245 .020

Total 5.242 246

RED_ING_ATT Between Groups .002 1 .002 .029 .864

Within Groups 12.773 245 .052

Total 12.775 246

Means Plots

SHORT LONG

WEAPON2

0.1000

0.1200

0.1400

0.1600

0.1800

Mean of F15_ING_ATT
APPENDIX A

138

SHORT LONG

WEAPON2

0.1000

0.1100

0.1200

0.1300

0.1400

0.1500

0.1600

0.1700

0.1800

Mean of OCA_ING_ATT

SHORT LONG

WEAPON2

0.7260

0.7280

0.7300

0.7320

0.7340

Mean of RED_ING_ATT
APPENDIX A

139

Correlations

Correlations

THRT_AC WEAPON2

THRT_AC Pearson Correlation 1 .564(**)

Sig. (2-tailed) .000

N 307 307

WEAPON2 Pearson Correlation .564(**) 1

Sig. (2-tailed) .000

N 307 307

** Correlation is significant at the 0.01 level (2-tailed).
APPENDIX A

140

A7. Aircraft and Weapons ANOVA

Author’s original work using SPSS 12.0.1

Short Only

Descriptives

N Mean Std. 

Deviation Std. Error 95% Confidence Interval for Mean

MinimumMaximum

Lower 

Bound

Upper 

Bound

F15_ING_

ATT

MiG-23 34 .073214 .1245783 .0213650 .029747 .116682 .0000 .4286

MiG-29 147 .122143 .1503563 .0124012 .097634 .146652 .0000 .7500

SU-27 56 .143764 .1309335 .0174967 .108700 .178828 .0000 .3750

Total 237 .120233 .1435386 .0093238 .101864 .138601 .0000 .7500

OCA_ING_

ATT

MiG-23 34 .073214 .1245783 .0213650 .029747 .116682 .0000 .4286

MiG-29 147 .112801 .1375646 .0113461 .090377 .135225 .0000 .7500

SU-27 56 .128776 .1143925 .0152863 .098142 .159411 .0000 .3750

Total 237 .110896 .1311857 .0085214 .094109 .127684 .0000 .7500

RED_ING_

ATT

MiG-23 34 .751471 .2415154 .0414196 .667202 .835739 .0000 1.0000

MiG-29 147 .727339 .2156728 .0177884 .692183 .762495 .0000 1.1667

SU-27 56 .678143 .2063667 .0275769 .622877 .733408 .2727 1.0000

Total 237 .719177 .2178271 .0141494 .691301 .747052 .0000 1.1667

Test of Homogeneity of Variances

Levene Statistic df1 df2 Sig.

F15_ING_ATT .424 2 234 .655

OCA_ING_ATT .131 2 234 .877

RED_ING_ATT .298 2 234 .743
APPENDIX A

141

ANOVA

Sum of 

Squares df Mean Square F Sig.

F15_ING_ATT Between Groups .107 2 .053 2.625 .075

Within Groups 4.756 234 .020

Total 4.863 236

OCA_ING_ATT Between Groups .067 2 .033 1.954 .144

Within Groups 3.995 234 .017

Total 4.062 236

RED_ING_ATT Between Groups .140 2 .070 1.476 .231

Within Groups 11.058 234 .047

Total 11.198 236

Post-Hoc Tests

Multiple Comparisons

Tukey HSD

Dependent 

Variable (I) THRT_AC (J) THRT_AC

Mean 

Difference 

(I-J)

Std. Error Sig. 95% Confidence 

Interval

Lower 

Bound

Upper 

Bound

F15_ING_

ATT

MiG-23 MiG-29 -.0489292 .0271293 .171 -.112920 .015062

SU-27 -.0705499 .0309946 .061 -.143658 .002558

MiG-29 MiG-23 .0489292 .0271293 .171 -.015062 .112920

SU-27 -.0216207 .0223869 .599 -.074425 .031184

SU-27 MiG-23 .0705499 .0309946 .061 -.002558 .143658

MiG-29 .0216207 .0223869 .599 -.031184 .074425

OCA_

ING_ATT

MiG-23 MiG-29 -.0395863 .0248645 .251 -.098235 .019062

SU-27 -.0555620 .0284070 .126 -.122566 .011442

MiG-29 MiG-23 .0395863 .0248645 .251 -.019062 .098235

SU-27 -.0159756 .0205179 .717 -.064372 .032420

SU-27 MiG-23 .0555620 .0284070 .126 -.011442 .122566

MiG-29 .0159756 .0205179 .717 -.032420 .064372

RED_ING_

ATT

MiG-23 MiG-29 .0241312 .0413693 .829 -.073448 .121710

SU-27 .0733278 .0472634 .269 -.038153 .184809

MiG-29 MiG-23 -.0241312 .0413693 .829 -.121710 .073448

SU-27 .0491966 .0341375 .322 -.031324 .129718

SU-27 MiG-23 -.0733278 .0472634 .269 -.184809 .038153

MiG-29 -.0491966 .0341375 .322 -.129718 .031324
APPENDIX A

142

Homogeneous Subsets

F15_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1 2

MiG-23 34 .073214

MiG-29 147 .122143 .122143

SU-27 56 .143764

Sig. .169 .704

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 55.482.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

OCA_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1

MiG-23 34 .073214

MiG-29 147 .112801

SU-27 56 .128776

Sig. .067

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 55.482.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.

RED_ING_ATT

Tukey HSD

THRT_AC N Subset for alpha = .05

1

SU-27 56 .678143

MiG-29 147 .727339

MiG-23 34 .751471

Sig. .180

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 55.482.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error 

levels are not guaranteed.
APPENDIX A

143

Means Plots

MIG-23 MIG-29 SU-27

THRT AC

0.0700

0.0800

0.0900

0.1000

0.1100

0.1200

0.1300

0.1400

0.1500

Mean of F15_ING_ATT

MIG-23 MIG-29 SU-27

THRT AC

0.0700

0.0800

0.0900

0.1000

0.1100

0.1200

0.1300

Mean of OCA_ING_ATT
APPENDIX A

144

MIG-23 MIG-29 SU-27

THRT AC

0.6800

0.7000

0.7200

0.7400

0.7600

Mean of RED_ING_ATT
APPENDIX A

145

T-test Short Only

Group Statistics

THRT_AC N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT MiG-29 147 .122143 .1503563 .0124012

SU-27 56 .143764 .1309335 .0174967

OCA_ING_ATT MiG-29 147 .112801 .1375646 .0113461

SU-27 56 .128776 .1143925 .0152863

RED_ING_ATT MiG-29 147 .727339 .2156728 .0177884

SU-27 56 .678143 .2063667 .0275769

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t Df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed .016 .899 -.948 201 .344 -.0216207 .0228171 -.0666123 .0233709

Equal variances 

not assumed -1.008 113.362 .316 -.0216207 .0214459 -.0641074 .0208659

OCA_ING_

ATT

Equal variances 

assumed .194 .660 -.773 201 .441 -.0159756 .0206705 -.0567344 .0247831

Equal variances 

not assumed -.839 118.720 .403 -.0159756 .0190370 -.0536717 .0217204

RED_ING_

ATT

Equal variances 

assumed .284 .595 1.470 201 .143 .0491966 .0334746 -.0168097 .1152030

Equal variances 

not assumed 1.499 103.539 .137 .0491966 .0328164 -.0158828 .1142761
APPENDIX A

146

T-test MiG–29 Only

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 147 .122143 .1503563 .0124012

LONG 4 .048611 .0572654 .0286327

OCA_ING_ATT SHORT 147 .112801 .1375646 .0113461

LONG 4 .048611 .0572654 .0286327

RED_ING_ATT SHORT 147 .727339 .2156728 .0177884

LONG 4 .591667 .0687184 .0343592

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.817 .180 .973 149 .332 .0735323 .0755355 -.0757268 .2227915

Equal variances 

not assumed 2.357 4.228 .074 .0735323 .0312029 -.0112888 .1583535

OCA_ING_

ATT

Equal variances 

assumed 1.552 .215 .929 149 .355 .0641895 .0691292 -.0724107 .2007898

Equal variances 

not assumed 2.084 4.014 .105 .0641895 .0307988 -.0212033 .1495824

RED_ING_

ATT

Equal variances 

assumed 4.915 .028 1.253 149 .212 .1356727 .1083007 -.0783308 .3496762

Equal variances 

not assumed 3.507 4.817 .018 .1356727 .0386909 .0350648 .2362806
APPENDIX A

147

T-test SU–27 Only

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 56 .143764 .1309335 .0174967

LONG 120 .165708 .1639277 .0149645

OCA_ING_ATT SHORT 56 .128776 .1143925 .0152863

LONG 120 .152881 .1470661 .0134252

RED_ING_ATT SHORT 56 .678143 .2063667 .0275769

LONG 120 .736021 .2264059 .0206679

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig.

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.105 .295 -.879 174 .381 -.0219443 .0249651 -.0712177 .0273292

Equal variances 

not assumed -.953 132.200 .342 -.0219443 .0230233 -.0674859 .0235974

OCA_ING_

ATT

Equal variances 

assumed 1.337 .249 -1.083 174 .280 -.0241048 .0222651 -.0680493 .0198398

Equal variances 

not assumed -1.185 135.350 .238 -.0241048 .0203448 -.0643395 .0161300

RED_ING_

ATT

Equal variances 

assumed .178 .674 -1.624 174 .106 -.0578785 .0356471 -.1282349 .0124780

Equal variances 

not assumed -1.679 117.068 .096 -.0578785 .0344623 -.1261288 .0103719
APPENDIX A

148

T-test MiG–29/Short versus Long SU-27

Group Statistics

THRT_AC N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT MiG-29 147 .122143 .1503563 .0124012

SU-27 120 .165708 .1639277 .0149645

OCA_ING_ATT MiG-29 147 .112801 .1375646 .0113461

SU-27 120 .152881 .1470661 .0134252

RED_ING_ATT MiG-29 147 .727339 .2156728 .0177884

SU-27 120 .736021 .2264059 .0206679

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.280 .259 -2.261 265 .025 -.0435650 .0192658 -.0814986 -.0056314

Equal variances 

not assumed -2.242 244.560 .026 -.0435650 .0194352 -.0818466 -.0052833

OCA_ING_

ATT

Equal variances 

assumed .773 .380 -2.296 265 .022 -.0400804 .0174590 -.0744564 -.0057044

Equal variances 

not assumed -2.280 246.997 .023 -.0400804 .0175776 -.0747015 -.0054593

RED_ING_

ATT

Equal variances 

assumed .003 .955 -.320 265 .749 -.0086818 .0271349 -.0621092 .0447455

Equal variances 

not assumed -.318 249.162 .750 -.0086818 .0272689 -.0623887 .0450250
APPENDIX A

149

T-test MiG–23 and MiG–29 Short versus Long SU-27

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 181 .112952 .1467970 .0109113

LONG 120 .165708 .1639277 .0149645

OCA_ING_ATT SHORT 181 .105365 .1357762 .0100922

LONG 120 .152881 .1470661 .0134252

RED_ING_ATT SHORT 181 .731872 .2202539 .0163713

LONG 120 .736021 .2264059 .0206679

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. T df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.453 .229 -2.913 299 .004 -.0527561 .0181106 -.0883965 -.0171157

Equal variances 

not assumed -2.849 235.216 .005 -.0527561 .0185201 -.0892425 -.0162697

OCA_ING_

ATT

Equal variances 

assumed .731 .393 -2.875 299 .004 -.0475165 .0165255 -.0800375 -.0149956

Equal variances 

not assumed -2.829 240.683 .005 -.0475165 .0167955 -.0806015 -.0144316

RED_ING_

ATT

Equal variances 

assumed .055 .815 -.158 299 .874 -.0041489 .0262191 -.0557462 .0474484

Equal variances 

not assumed -.157 250.089 .875 -.0041489 .0263663 -.0560773 .0477795
APPENDIX A

150

A8.T-test

Author’s original work using SPSS 12.0.1

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 181 .112952 .1467970 .0109113

LONG 120 .165708 .1639277 .0149645

OCA_ING_ATT SHORT 181 .105365 .1357762 .0100922

LONG 120 .152881 .1470661 .0134252

RED_ING_ATT SHORT 181 .731872 .2202539 .0163713

LONG 120 .736021 .2264059 .0206679

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. T df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.453 .229 -2.913 299 .004 -.0527561 .0181106 -.0883965 -.0171157

Equal variances 

not assumed -2.849 235.216 .005 -.0527561 .0185201 -.0892425 -.0162697

OCA_ING_

ATT

Equal variances 

assumed .731 .393 -2.875 299 .004 -.0475165 .0165255 -.0800375 -.0149956

Equal variances 

not assumed -2.829 240.683 .005 -.0475165 .0167955 -.0806015 -.0144316

RED_ING_

ATT

Equal variances 

assumed .055 .815 -.158 299 .874 -.0041489 .0262191 -.0557462 .0474484

Equal variances 

not assumed -.157 250.089 .875 -.0041489 .0263663 -.0560773 .0477795
APPENDIX A

151

T-test

Group Statistics

LIGHT N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT DAY 178 .150025 .1637746 .0122754

NIGHT 123 .110772 .1407805 .0126937

OCA_ING_ATT DAY 178 .138753 .1481119 .0111015

NIGHT 123 .103403 .1306123 .0117769

RED_ING_ATT DAY 178 .717010 .2134606 .0159995

NIGHT 123 .757429 .2334584 .0210502

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 4.849 .028 2.163 299 .031 .0392530 .0181513 .0035326 .0749734

Equal variances 

not assumed 2.223 285.050 .027 .0392530 .0176584 .0044957 .0740103

OCA_ING_

ATT

Equal variances 

assumed 2.562 .111 2.135 299 .034 .0353498 .0165600 .0027610 .0679387

Equal variances 

not assumed 2.184 281.786 .030 .0353498 .0161845 .0034920 .0672077

RED_ING_

ATT

Equal variances 

assumed 1.719 .191 -1.554 299 .121 -.0404192 .0260110 -.0916070 .0107686

Equal variances 

not assumed -1.529 246.883 .128 -.0404192 .0264405 -.0924968 .0116584
APPENDIX A

152

A9. Red Tactics Pearson Correlation Test

Author’s original work using SPSS 12.0.1

Correlations

TACTIC2 EA2 REGEN RXN_LVL MAX_LIVE_

GRPS SAM_LVL SAM_ROE2 REC BIG_CROW2

TACTIC2 Pearson 

Correlation 1 .809(**) -.586(**) .736(**) .635(**) .710(**) .879(**) .778(**) .827(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

EA2 Pearson 

Correlation .809(**) 1 -.501(**) .619(**) .571(**) .669(**) .760(**) .698(**) .796(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

REGEN Pearson 

Correlation -.586(**) -.501(**) 1 -.521(**) -.302(**) -.559(**) -.629(**) -.662(**) -.589(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

RXN_LVL Pearson 

Correlation .736(**) .619(**) -.521(**) 1 .727(**) .509(**) .768(**) .699(**) .773(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

MAX_

LIVE_

GRPS

Pearson 

Correlation .635(**) .571(**) -.302(**) .727(**) 1 .317(**) .771(**) .614(**) .747(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

SAM_LVL Pearson 

Correlation .710(**) .669(**) -.559(**) .509(**) .317(**) 1 .634(**) .580(**) .736(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

SAM_

ROE2

Pearson 

Correlation .879(**) .760(**) -.629(**) .768(**) .771(**) .634(**) 1 .897(**) .929(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 210 210 210 210 210 210 210 210 137

REC Pearson 

Correlation .778(**) .698(**) -.662(**) .699(**) .614(**) .580(**) .897(**) 1 .913(**)

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 301 301 301 301 301 301 210 301 174

BIG_

CROW2

Pearson 

Correlation .827(**) .796(**) -.589(**) .773(**) .747(**) .736(**) .929(**) .913(**) 1

Sig. (2-tailed) .000 .000 .000 .000 .000 .000 .000 .000

N 174 174 174 174 174 174 137 174 174

** Correlation is significant at the 0.01 level (2-tailed).
APPENDIX A

153

A10. Force Ratio Pearson Correlation Test

Author’s original work using SPSS 12.0.1

Correlations

F15_ING_

ATT

RED_ING_

ATT

LOG_F15_

FLOWN_

RATIO

F15_FLOWN_

RATIO

OCA_F15_

FL

RED_TOT_

FTR_FL

F15_ING_ATT Pearson Correlation 1 -.253(**) -.297(**) -.270(**) -.180(**) .219(**)

Sig. (2-tailed) .000 .000 .000 .002 .000

N 299 299 299 299 299 299

RED_ING_ATT Pearson Correlation -.253(**) 1 .396(**) .351(**) .097 -.411(**)

Sig. (2-tailed) .000 .000 .000 .094 .000

N 299 307 299 307 299 307

LOG_F15_

FLOWN_RATIO Pearson Correlation -.297(**) .396(**) 1 .966(**) .501(**) -.773(**)

Sig. (2-tailed) .000 .000 .000 .000 .000

N 299 299 299 299 299 299

F15_FLOWN_

RATIO Pearson Correlation -.270(**) .351(**) .966(**) 1 .431(**) -.644(**)

Sig. (2-tailed) .000 .000 .000 .000 .000

N 299 307 299 307 299 307

OCA_F15_FL Pearson Correlation -.180(**) .097 .501(**) .431(**) 1 .103

Sig. (2-tailed) .002 .094 .000 .000 .077

N 299 299 299 299 299 299

RED_TOT_

FTR_FL

Pearson Correlation .219(**) -.411(**) -.773(**) -.644(**) .103 1

Sig. (2-tailed) .000 .000 .000 .000 .077

N 299 307 299 307 299 307

** Correlation is significant at the 0.01 level (2-tailed).
APPENDIX A

154

A11. Independent Variable Factor Analysis

Author’s original work using SPSS 12.0.1

Communalities

Initial Extraction

LOG_F15_FLOWN_

RATIO 1.000 .952

THRT_AC2 1.000 .848

WEAPON2 1.000 .859

TACTIC2 1.000 .812

EA2 1.000 .791

RXN_LVL 1.000 .808

MAX_LIVE_GRPS 1.000 .784

SAM_ROE2 1.000 .932

REC 1.000 .911

BIG_CROW2 1.000 .935

LIGHT 1.000 .992

Extraction Method: Principal Component Analysis.

Total Variance Explained

Component Initial Eigenvalues Extraction Sums of Squared 

Loadings

Rotation Sums of Squared 

Loadings

Total % of 

Variance

Cumulative 

% Total % of Variance

Cumulative 

% Total % of Variance

Cumulative 

%

1 6.407 58.241 58.241 6.407 58.241 58.241 5.679 51.627 51.627

2 1.188 10.797 69.038 1.188 10.797 69.038 1.860 16.913 68.540

3 1.170 10.639 79.676 1.170 10.639 79.676 1.069 9.718 78.258

4 .860 7.814 87.491 .860 7.814 87.491 1.016 9.232 87.491

5 .454 4.132 91.622

6 .302 2.741 94.363

7 .226 2.052 96.415

8 .166 1.508 97.923

9 .134 1.216 99.139

10 .056 .508 99.647

11 .039 .353 100.000

Extraction Method: Principal Component Analysis.
APPENDIX A

155

Component Matrix (a)

Component

1 2 3 4

LOG_F15_FLOWN_RATIO .072 .586 .587 -.509

THRT_AC2 .650 -.413 .454 .222

WEAPON2 .516 -.353 .673 .123

TACTIC2 .899 .042 -.025 -.028

EA2 .844 .139 .021 -.242

RXN_LVL .845 .212 -.219 -.024

MAX_LIVE_GRPS .857 .022 -.187 .120

SAM_ROE2 .959 .032 -.102 .024

REC .941 .055 -.148 .016

BIG_CROW2 .962 .047 -.078 .010

LIGHT -.105 .690 .209 .679

Extraction Method: Principal Component Analysis.

a 4 components extracted.

1 2 3 4 5 6 7 8 9 10 11

Component Number

0

1

2

3

4

5

6

7

Eigenvalue

Scree Plot
APPENDIX A

156

Rotated Component Matrix (a)

Component

1 2 3 4

LOG_F15_FLOWN_RATIO .028 .040 .970 .092

THRT_AC2 .369 .839 -.084 -.042

WEAPON2 .194 .896 .129 -.032

TACTIC2 .852 .284 .060 -.046

EA2 .815 .194 .267 -.134

RXN_LVL .896 .037 .041 .031

MAX_LIVE_GRPS .853 .196 -.134 .025

SAM_ROE2 .927 .267 -.018 -.031

REC .930 .213 -.028 -.030

BIG_CROW2 .926 .275 .012 -.027

LIGHT -.041 -.051 .089 .990

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a Rotation converged in 5 iterations.

Component Transformation Matrix

Component 1 2 3 4

1 .928 .367 .037 -.052

2 .209 -.497 .559 .630

3 -.306 .743 .565 .186

4 -.036 .258 -.606 .752

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.
APPENDIX A

157

Component Score Coefficient Matrix

Component

1 2 3 4

LOG_F15_FLOWN_RATIO -.019 -.021 .918 -.042

THRT_AC2 -.107 .565 -.128 .042

WEAPON2 -.169 .641 .076 .023

TACTIC2 .145 .010 .033 -.014

EA2 .151 -.069 .251 -.141

RXN_LVL .218 -.186 .016 .050

MAX_LIVE_GRPS .172 -.042 -.159 .080

SAM_ROE2 .170 -.016 -.045 .014

REC .184 -.058 -.051 .012

BIG_CROW2 .168 -.011 -.017 .013

LIGHT .023 .042 -.053 .994

Extraction Method: Principal Component Analysis. 

Rotation Method: Varimax with Kaiser Normalization. Component Scores.

Component Score Covariance Matrix

Component 1 2 3 4

1 1.000 .000 .000 .000

2 .000 1.000 .000 .000

3 .000 .000 1.000 .000

4 .000 .000 .000 1.000

Extraction Method: Principal Component Analysis. 

Rotation Method: Varimax with Kaiser Normalization. Component Scores.
APPENDIX A

158

A12. Final Data Set TestingAuthor’s original work using SPSS 12.0.1

Correlations

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

LOG_F15_FLOWN_RATIO

Pearson Correlation 1 -.304 (**) .368 (**) .214 (**) .031 .031 -.012 .047 -.046 -.006 -.083 .025 -.022 -.041 .014Sig. (2-tailed) .000 .000 .001 .631 .631 .854 .473 .479 .924 .201 .702 .794 .524 .859N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

F15_ING_ATT

Pearson Correlation

-.304

(**) 1 -.241 (**) -.095 .214 (**) .214 (**) .152 (*) .098 .113 .112 .102 .134 (*) .171 (*) .177 (**) .064

Sig. (2-tailed) .000 .000 .144 .001 .001 .019 .132 .082 .084 .116 .038 .037 .006 .400N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

RED_ING_ATT

Pearson Correlation

.368

(**)

-.241

(**) 1 .122 .013 .013 .044 .087 .015 -.035 -.078 .017 .074 .011 .093

Sig. (2-tailed) .000 .000 .061 .844 .844 .501 .182 .816 .592 .227 .799 .369 .870 .223N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

LIGHT Pearson Correlation .214 (**) -.095 .122 1 -.118 -.118 -.101 -.090 .046 -.023 -.040 -.053 -.057 -.078 -.070

Sig. (2-tailed) .001 .144 .061 .069 .069 .120 .164 .476 .723 .542 .411 .491 .227 .356N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

THRT_AC2

Pearson Correlation .031 .214 (**) .013 -.118 1 1.000 (**) .506 (**) .358 (**) .307 (**) .343 (**) .346 (**) .517 (**) .531 (**) .521 (**) .579 (**)Sig. (2-tailed) .631 .001 .844 .069 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
APPENDIX A

159

Correlations (continued)

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

WEAPON2 Pearson Correlation .031 .214 (**) .013 -.118 1.000 (**) 1 .506 (**) .358 (**) .307 (**) .343 (**) .346 (**) .517 (**) .531 (**) .521 (**) .579 (**)

Sig. (2-tailed) .631 .001 .844 .069 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

TACTIC2 Pearson Correlation -.012 .152(*) .044 -.101 .506 (**) .506 (**) 1 .807 (**) .537 (**) .728 (**) .668 (**) .771 (**) .915 (**) .821 (**) .827 (**)

Sig. (2-tailed) .854 .019 .501 .120 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

EA2 Pearson Correlation .047 .098 .087 -.090 .358 (**) .358 (**) .807 (**) 1 .441 (**) .633 (**) .621 (**) .629 (**) .820 (**) .740 (**) .796 (**)

Sig. (2-tailed) .473 .132 .182 .164 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

REGEN2 Pearson Correlation -.046 .113 .015 .046 .307 (**) .307 (**) .537 (**) .441 (**) 1 .490 (**) .314 (**) .544 (**) .623 (**) .656 (**) .589 (**)

Sig. (2-tailed) .479 .082 .816 .476 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

RXN_LVL

Pearson Correlation -.006 .112 -.035 -.023 .343 (**) .343 (**) .728 (**) .633 (**) .490 (**) 1 .763 (**) .593 (**) .793 (**) .707 (**) .773 (**)Sig. (2-tailed) .924 .084 .592 .723 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

MAX_LIVE_GRPS

Pearson Correlation -.083 .102 -.078 -.040 .346 (**) .346 (**) .668 (**) .621 (**) .314 (**) .76 (**) 1 .416 (**) .812 (**) .640 (**) .747 (**)
APPENDIX A

160

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

Sig. (2-tailed) .201 .116 .227 .542 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

SAM_LVL

Pearson Correlation .025 .134(*) .017 -.053 .517 (**) .517 (**) .771 (**) .629 (**) .544 (**) .593 (**) .416 (**) 1 .852 (**) .747 (**) .736 (**)Sig. (2-tailed) .702 .038 .799 .411 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

SAM_ROE2

Pearson Correlation -.022 .171(*) .074 -.057 .531 (**) .531 (**) .915 (**) .820 (**) .623 (**) .793 (**) .812 (**) .852 (**) 1 .951 (**) .929 (**)Sig. (2-tailed) .794 .037 .369 .491 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 148 148 148 148 148 148 148 148 148 148 148 148 148 148 137

REC Pearson Correlation -.041 .177 (**) .011 -.078 .521 (**) .521 (**) .821 (**) .740 (**) .656 (**) .707 (**) .640 (**) .747 (**) .951 (**) 1 .913 (**)

Sig. (2-tailed) .524 .006 .870 .227 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 239 239 239 239 239 239 239 239 239 239 239 239 148 239 174

BIG_CROW2

Pearson Correlation .014 .064 .093 -.070 .579 (**) .579 (**) .827 (**) .796 (**) .589 (**) .773 (**) .747 (**) .736 (**) .929 (**) .913 (**) 1Sig. (2-tailed) .859 .400 .223 .356 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000N 174 174 174 174 174 174 174 174 174 174 174 174 137 174 174

Correlations (continued)

** Correlation is significant at the 0.01 level (2-tailed).* Correlation is significant at the 0.05 level (2-tailed).
APPENDIX A

161

T-test

Group Statistics

WEAPON2 N Mean Std. Deviation Std. Error 

Mean

F15_ING_ATT SHORT 171 .108906 .1434054 .0109665

LONG 67 .186343 .1803651 .0220351

RED_ING_ATT SHORT 172 .726205 .2266806 .0172842

LONG 74 .733235 .2310861 .0268632

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 3.940 .048 -3.475 236 .001 -.0774374 .0222873 -.1213449 -.0335298

Equal variances 

not assumed -3.146 100.354 .002 -.0774374 .0246132 -.1262671 -.0286076

RED_ING_

ATT

Equal variances 

assumed .078 .780 -.222 244 .825 -.0070307 .0316984 -.0694680 .0554066

Equal variances 

not assumed -.220 136.002 .826 -.0070307 .0319433 -.0702006 .0561392
APPENDIX A

162

THRT_AC2*LIGHT

Case Processing Summary

THRT_AC2 LIGHT Cases

Valid Missing Total

N Percent N Percent N Percent

F15_ING_

ATT MiG-23/29 DAY 99 100.0% 0 .0% 99 100.0%

NIGHT 72 100.0% 0 .0% 72 100.0%

SU-27 DAY 48 100.0% 0 .0% 48 100.0%

NIGHT 20 100.0% 0 .0% 20 100.0%

F15_ING_ATT

MiG-23/29 SU-27

THREAT AIRCRAFT

0.0000

0.2000

0.4000

0.6000

0.8000

F15_ING_ATT

210

290

30

221

101

LIGHT

DAY

NIGHT
APPENDIX A

163

THRT_AC2*LIGHT

Case Processing Summary

THRT_AC2

LIGHT

Cases

Valid Missing Total

N Percent N Percent N Percent

RED_ING_

ATT MiG-23/29 DAY 99 100.0% 0 .0% 99 100.0%

NIGHT 72 100.0% 0 .0% 72 100.0%

SU-27 DAY 48 100.0% 0 .0% 48 100.0%

NIGHT 20 100.0% 0 .0% 20 100.0%

RED_ING_ATT

MiG-23/29 SU-27

THREAT AIRCRAFT

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

RED_ING_ATT

259

11

LIGHT

DAY

NIGHT
APPENDIX A

164

DAY-NIGHT T-test N=239

Group Statistics

LIGHT N Mean Std. Deviation Std. Error Mean

F15_ING_ATT DAY 147 .141996 .1647666 .0135897

NIGHT 92 .111244 .1456968 .0151899

RED_ING_ATT DAY 147 .711131 .2143393 .0176784

NIGHT 92 .765910 .2253483 .0234942

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. T df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 3.347 .069 1.467 237 .144 .0307522 .0209665 -.0105523 .0720567

Equal variances 

not assumed 1.509 210.799 .133 .0307522 .0203817 -.0094259 .0709303

RED_ING_

ATT

Equal variances 

assumed .649 .421 -1.885 237 .061 -.0547795 .0290643 -.1120369 .0024779

Equal variances 

not assumed -1.863 186.046 .064 -.0547795 .0294024 -.1127845 .0032255
APPENDIX A

165

DAY-NIGHT T-test Short MiG-23/29 N=171

Group Statistics

LIGHT N Mean Std. Deviation Std. Error Mean

F15_ING_ATT DAY 99 .121074 .1472703 .0148012

NIGHT 72 .092175 .1371633 .0161648

RED_ING_ATT DAY 99 .698647 .2210243 .0222138

NIGHT 72 .774182 .2133213 .0251402

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.528 .218 1.304 169 .194 .0288997 .0221660 -.0148583 .0726576

Equal variances 

not assumed 1.319 158.992 .189 .0288997 .0219175 -.0143874 .0721867

RED_ING_

ATT

Equal variances 

assumed .083 .773 -2.239 169 .026 -.0755349 .0337376 -.1421363 -.0089334

Equal variances 

not assumed -2.252 156.175 .026 -.0755349 .0335482 -.1418016 -.0092682
APPENDIX A

166

DAY-NIGHT T-test Long SU-27 N=68

Group Statistics

LIGHT N Mean Std. Deviation Std. Error Mean

F15_ING_ATT DAY 48 .185148 .1904875 .0274945

NIGHT 20 .179895 .1581954 .0353736

RED_ING_ATT DAY 48 .736878 .1996123 .0288115

NIGHT 20 .736131 .2682850 .0599903

Independent Samples Test

Levene’s Test 

for Equality of 

Variances

T-test for Equality of Means

F Sig. t df Sig. 

(2-tailed)

Mean 

Difference

Std. Error 

Difference

95% Confidence 

Interval of the 

Difference

Lower Upper

F15_ING_

ATT

Equal variances 

assumed 1.332 .253 .109 66 .914 .0052536 .0483800 -.0913401 .1018473

Equal variances 

not assumed .117 42.606 .907 .0052536 .0448022 -.0851228 .0956300

RED_ING_

ATT

Equal variances 

assumed 5.214 .026 .013 66 .990 .0007468 .0589709 -.1169925 .1184860

Equal variances 

not assumed .011 28.170 .991 .0007468 .0665503 -.1355384 .1370319
APPENDIX A

167

Correlations Short MiG-23/29 N=171

Correlations

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

LOG_F15_FLOWN_RATIO

Pearson Correlation 1 -.366 (**) .386 (**) .196 (*) .(a) .(a) .003 .040 -.101 -.008 -.081 .012 -.016 -.065 -.001Sig. (2-tailed) .000 .000 .010 . . .971 .606 .188 .915 .291 .880 .872 .399 .989N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

F15_ING_ATT

Pearson Correlation

-.366

(**) 1 -.304 (**) -.100 .(a) .(a) .031 .041 .058 .026 -.004 .036 .073 .074 -.081

Sig. (2-tailed) .000 .000 .194 . . .686 .592 .447 .740 .960 .640 .450 .339 .374N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

RED_ING_ATT

Pearson Correlation

.386

(**)

-.304

(**) 1 .170 (*) .(a) .(a) .019 .008 .036 .018 -.030 .014 .105 .043 .127

Sig. (2-tailed) .000 .000 .026 . . .808 .915 .641 .816 .699 .859 .277 .575 .161N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

LIGHT Pearson Correlation .196(*) -.100 .170(*) 1 .(a) .(a) .003 -.016 .077 -.006 -.016 .010 -.001 -.016 .008

Sig. (2-tailed) .010 .194 .026 . . .970 .836 .320 .939 .840 .896 .991 .833 .929N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

THRT_AC2

Pearson Correlation .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a)Sig. (2-tailed) . . . . . . . . . . . . . .
APPENDIX A

168

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

WEAPON2 Pearson Correlation .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a)

Sig. (2-tailed) . . . . . . . . . . . . . .N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

TACTIC2 Pearson Correlation .003 .031 .019 .003 .(a) .(a) 1 .759 (**) .536 (**) .726 (**) .644 (**) .801 (**) .910 (**) .790 (**) .778 (**)

Sig. (2-tailed) .971 .686 .808 .970 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

EA2 Pearson Correlation .040 .041 .008 -.016 .(a) .(a) .759 (**) 1 .449 (**) .610 (**) .582 (**) .660 (**) .775 (**) .762 (**) .787 (**)

Sig. (2-tailed) .606 .592 .915 .836 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

REGEN2 Pearson Correlation -.101 .058 .036 .077 .(a) .(a) .536 (**) .449 (**) 1 .418 (**) .274 (**) .495 (**) .589 (**) .648 (**) .549 (**)

Sig. (2-tailed) .188 .447 .641 .320 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

RXN_LVL

Pearson Correlation -.008 .026 .018 -.006 .(a) .(a) .726 (**) .610 (**) .418 (**) 1 .655 (**) .600 (**) .768 (**) .670 (**) .775 (**)Sig. (2-tailed) .915 .740 .816 .939 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

MAX_LIVE_GRPS

Pearson Correlation -.081 -.004 -.030 -.016 .(a) .(a) .644 (**) .582 (**) .274 (**) .655 (**) 1 .412 (**) .749 (**) .623 (**) .759 (**)

Correlations (continued)
APPENDIX A

169

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

Sig. (2-tailed) .291 .960 .699 .840 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

SAM_LVL

Pearson Correlation .012 .036 .014 .010 .(a) .(a) .801 (**) .660 (**) .495 (**) .600 (**) .412 (**) 1 .866 (**) .711 (**) .689 (**)Sig. (2-tailed) .880 .640 .859 .896 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

SAM_ROE2

Pearson Correlation -.016 .073 .105 -.001 .(a) .(a) .910 (**) .775 (**) .589 (**) .768 (**) .749 (**) .866 (**) 1 .924 (**) .886 (**)Sig. (2-tailed) .872 .450 .277 .991 . . .000 .000 .000 .000 .000 .000 .000 .000N 110 110 110 110 110 110 110 110 110 110 110 110 110 110 100

REC Pearson Correlation -.065 .074 .043 -.016 .(a) .(a) .790 (**) .762 (**) .648 (**) .670 (**) .623 (**) .711 (**) .924 (**) 1 .857 (**)

Sig. (2-tailed) .399 .339 .575 .833 . . .000 .000 .000 .000 .000 .000 .000 .000N 171 171 171 171 171 171 171 171 171 171 171 171 110 171 123

BIG_CROW2

Pearson Correlation -.001 -.081 .127 .008 .(a) .(a) .778 (**) .787 (**) .549 (**) .775 (**) .759 (**) .689 (**) .886 (**) .857 (**) 1Sig. (2-tailed) .989 .374 .161 .929 . . .000 .000 .000 .000 .000 .000 .000 .000N 123 123 123 123 123 123 123 123 123 123 123 123 100 123 123

Correlations (continued)

** Correlation is significant at the 0.01 level (2-tailed).* Correlation is significant at the 0.05 level (2-tailed).a Cannot be computed because at least one of the variables is constant.
APPENDIX A

170

Correlations Long SU-27 N=68

Correlations

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

LOG_F15_FLOWN_RATIO

Pearson Correlation 1 -.223 .316 (**) .292 (*) .(a) .(a) -.141 .033 .185 -.048 -.146 .(a) -.140 -.081 -.165Sig. (2-tailed) .068 .009 .016 . . .252 .788 .132 .695 .236 . .401 .514 .248N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

F15_ING_ATT

Pearson Correlation -.223 1 -.144 -.013 .(a) .(a) .098 -.012 .038 .079 .076 .(a) .130 .104 .145Sig. (2-tailed) .068 .242 .914 . . .429 .922 .757 .524 .539 . .436 .397 .312N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

RED_ING_ATT

Pearson Correlation

.316

(**) -.144 1 -.002 .(a) .(a) .110 .286 (*) -.111 -.202 -.190 .(a) -.240 -.139 -.186

Sig. (2-tailed) .009 .242 .990 . . .371 .018 .369 .098 .121 . .147 .260 .190N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

LIGHT Pearson Correlation .292(*) -.013 -.002 1 .(a) .(a) -.198 -.149 .161 .090 .031 .(a) .006 -.037 -.071

Sig. (2-tailed) .016 .914 .990 . . .106 .226 .189 .466 .804 . .970 .767 .619N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

THRT_AC2

Pearson Correlation .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a)Sig. (2-tailed) . . . . . . . . . . . . . .
APPENDIX A

171

Correlations (continued)

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

WEAPON2 Pearson Correlation .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a)

Sig. (2-tailed) . . . . . . . . . . . . . .N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

TACTIC2 Pearson Correlation -.141 .098 .110 -.198 .(a) .(a) 1 .828 (**) .161 .562 (**) .595 (**) .(a) .725 (**) .656 (**) .719 (**)

Sig. (2-tailed) .252 .429 .371 .106 . . .000 .190 .000 .000 . .000 .000 .000N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

EA2 Pearson Correlation .033 -.012 .286(*) -.149 .(a) .(a) .828 (**) 1 .076 .509 (**) .573 (**) .(a) .651 (**) .489 (**) .674 (**)

Sig. (2-tailed) .788 .922 .018 .226 . . .000 .537 .000 .000 . .000 .000 .000N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

REGEN2 Pearson Correlation .185 .038 -.111 .161 .(a) .(a) .161 .076 1 .578 (**) .216 .(a) .449 (**) .361 (**) .379 (**)

Sig. (2-tailed) .132 .757 .369 .189 . . .190 .537 .000 .077 . .005 .002 .006N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

RXN_LVL

Pearson Correlation -.048 .079 -.202 .090 .(a) .(a) .562 (**) .509 (**) .578 (**) 1 .922 (**) .(a) .884 (**) .642 (**) .739 (**)Sig. (2-tailed) .695 .524 .098 .466 . . .000 .000 .000 .000 . .000 .000 .000N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

MAX_LIVE_GRPS

Pearson Correlation -.146 .076 -.190 .031 .(a) .(a) .595 (**) .573 (**) .216 .922 (**) 1 .(a) .946 (**) .596 (**) .726 (**)
APPENDIX A

172

LOG_

F15_

FLOWN_

RATIO

F15_

ING_

ATT

RED_

ING_

ATT

LIGHT THRT_ AC2 WEAP- ON2 TAC- TIC2 EA2 REGEN2 RXN_ LVL MAX_ LIVE_ GRPS SAM_ LVL SAM_ ROE2 REC BIG_ CROW2

Sig. (2-tailed) .236 .539 .121 .804 . . .000 .000 .077 .000 . .000 .000 .000N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

SAM_LVL

Pearson Correlation .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a) .(a)Sig. (2-tailed) . . . . . . . . . . . . . .N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

SAM_ROE2

Pearson Correlation -.140 .130 -.240 .006 .(a) .(a) .725 (**) .651 (**) .449 (**) .884 (**) .946 (**) .(a) 1 1.000 (**) 1.000 (**)Sig. (2-tailed) .401 .436 .147 .970 . . .000 .000 .005 .000 .000 . .000 .000N 38 38 38 38 38 38 38 38 38 38 38 38 38 38 37

REC Pearson Correlation -.081 .104 -.139 -.037 .(a) .(a) .656 (**) .489 (**) .361 (**) .642 (**) .596 (**) .(a) 1.000 (**) 1 1.000 (**)

Sig. (2-tailed) .514 .397 .260 .767 . . .000 .000 .002 .000 .000 . .000 .000N 68 68 68 68 68 68 68 68 68 68 68 68 38 68 51

BIG_CROW2

Pearson Correlation -.165 .145 -.186 -.071 .(a) .(a) .719 (**) .674 (**) .379 (**) .739 (**) .726 (**) .(a) 1.000 (**) 1.000 (**) 1Sig. (2-tailed) .248 .312 .190 .619 . . .000 .000 .006 .000 .000 . .000 .000N 51 51 51 51 51 51 51 51 51 51 51 51 37 51 51

Correlations (continued)

** Correlation is significant at the 0.01 level (2-tailed).* Correlation is significant at the 0.05 level (2-tailed).a Cannot be computed because at least one of the variables is constant.
173

Appendix B

Regression Analysis

B1. MiG-23/29 Short Air-to-Air Missile Regression Lines

Author’s original work using SPSS 12.0.1

Variables Entered/Removed (b)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_FLOWN_RATIO(a) . Enter

a All requested variables entered.

b Dependent Variable: F15_ING_ATT

Model Summary

Model R R Square Adjusted 

R Square

Std. Error of 

the Estimate

1 .366(a) .134 .129 .1338707

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

ANOVA (b)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression .467 1 .467 26.078 .000(a)

Residual 3.029 169 .018

Total 3.496 170

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT
APPENDIX B

174

Coefficients (a)

Model

Unstandardized 

Coefficients

Standardized 

Coefficients t Sig. Correlations

Collinearity 

Statistics

B Std. 

Error Beta Zeroorder Partial Part Tolerance VIF

1 (Constant) .123 .011 11.599 .000

LOG_F15_

FLOWN_

RATIO

-.137 .027 -.366 -5.107 .000 -.366 -.366 -.366 1.000 1.000

a Dependent Variable: F15_ING_ATT

Collinearity Diagnostics (a)

Model Dimension Eigen value Condition 

Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO

1 1 1.260 1.000 .37 .37

2 .740 1.304 .63 .63

a Dependent Variable: F15_ING_ATT
APPENDIX B

175

Regression MiG Short

Variables Entered/Removed (b)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_FLOWN_RATIO(a) . Enter

a All requested variables entered.

b Dependent Variable: RED_ING_ATT

Model Summary

Model R R Square Adjusted R 

Square

Std. Error of the 

Estimate

1 .386(a) .149 .144 .2038830

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

ANOVA (b)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression 1.231 1 1.231 29.618 .000(a)

Residual 7.025 169 .042

Total 8.256 170

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: RED_ING_ATT
APPENDIX B

176

Coefficients (a)

Model Unstandardized 

Coefficients

Standardized 

Coefficients T Sig. Correlations Collinearity Statistics

B Std. 

Error Beta Zeroorder Partial Part Tolerance VIF

1 (Constant) .708 .016 43.829 .000

LOG_F15_

FLOWN_

RATIO

.222 .041 .386 5.442 .000 .386 .386 .386 1.000 1.000

a Dependent Variable: RED_ING_ATT

Collinearity Diagnostics (a)

Model Dimension Eigenvalue Condition 

Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO

1 1 1.260 1.000 .37 .37

2 .740 1.304 .63 .63

a Dependent Variable: RED_ING_ATT
APPENDIX B

177

B2. SU-27 Long Air-to-Air Missile Regression Lines

Author’s original work using SPSS 12.0.1

Descriptive Statistics

Mean Std. Deviation N

F15_ING_ATT .183603 .1804347 68

LOG_F15_FLOWN_RATIO .128302 .3356707 68

Correlations

F15_ING_ATT LOG_F15_

FLOWN_RATIO

Pearson Correlation F15_ING_ATT 1.000 -.223

LOG_F15_FLOWN_RATIO -.223 1.000

Sig. (1-tailed) F15_ING_ATT . .034

LOG_F15_FLOWN_RATIO .034 .

N F15_ING_ATT 68 68

LOG_F15_FLOWN_RATIO 68 68

Variables Entered/Removed (b)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_FLOWN_RATIO(a) . Enter

a All requested variables entered.

b Dependent Variable: F15_ING_ATT

Model Summary (b)

Model R R 

Square

Adjusted R 

Square

Std. Error of 

the Estimate Change Statistics

R Square 

Change

F 

Change df1 df2 Sig. F Change

1 .223(a) .050 .035 .1772188 .050 3.454 1 66 .068

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT
APPENDIX B

178

ANOVA (b)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression .108 1 .108 3.454 .068(a)

Residual 2.073 66 .031

Total 2.181 67

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT

Coefficients (a)

Model Unstandardized 

Coefficients

Standardized 

Coefficients T Sig.

95% 

Confidence 

Interval for B

Correlations Collinearity 

Statistics

B Std. 

Error Beta Lower Bound

Upper 

Bound

Zeroorder Partial Part Tolerance VIF

1 (Constant) .199 .023 8.640 .000 .153 .245

LOG_F15_

FLOWN_

RATIO

-.120 .064 -.223 -1.858 .068 -.249 .009 -.223 -.223 -.223 1.000 1.000

a Dependent Variable: F15_ING_ATT

Collinearity Diagnostics (a)

Model Dimension Eigenvalue Condition Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO

1 1 1.359 1.000 .32 .32

2 .641 1.457 .68 .68

a Dependent Variable: F15_ING_ATT

Casewise Diagnostics (a, b)

Case Number Std. Residual F15_ING_ATT

210 3.109 .750

a Dependent Variable: F15_ING_ATT

b When values are missing, the substituted mean has been used in the statistical computation.
APPENDIX B

179

Residuals Statistics (a)

Minimum Maximum Mean Std. 

Deviation N

Predicted Value .081413 .296186 .183603 .0402359 68

Std. Predicted Value -2.540 2.798 .000 1.000 68

Standard Error of 

Predicted Value .021 .064 .029 .009 68

Adjusted Predicted Value .075972 .341055 .183988 .0422238 68

Residual -.2961861 .5510176 .0000000 .1758913 68

Std. Residual -1.671 3.109 .000 .993 68

Stud. Residual -1.793 3.136 -.001 1.008 68

Deleted Residual -.3410555 .5604822 -.0003847 .1813765 68

Stud. Deleted Residual -1.825 3.373 .008 1.033 68

Mahal. Distance .000 7.829 .985 1.532 68

Cook’s Distance .000 .244 .016 .035 68

Centered Leverage Value .000 .117 .015 .023 68

a Dependent Variable: F15_ING_ATT

Charts

-2 -1 0 1 2 3 4

Regression Standardized Residual

0

2

4

6

8

10

12

14

Frequency

Mean = 3.09E-16

Std. Dev. = 0.993

N = 68

Dependent Variable: F15_ING_ATT

Histogram
APPENDIX B

180

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Dependent Variable: F15_ING_ATT

Normal P-P Plot of Regression Standardized Residual Expected Cum Prob

-3 -2 -1 0 1 2 3

Regression Standardized Predicted Value

-2

-1

0

1

2

3

4

Regression Studentized Deleted (Press)

Residual

Dependent Variable: F15_ING_ATT

Scatterplot
APPENDIX B

181

-1.0000 -0.5000 0.0000 0.5000 1.0000

LOG F15/RED FORCE RATIO

-2.00000

-1.00000

0.00000

1.00000

2.00000

3.00000

4.00000

Standardized Residual

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000

Centered Leverage Value

0.00000

0.05000

0.10000

0.15000

0.20000

0.25000

Cook's Distance

101

119

228
APPENDIX B

182

Regression

Notes

Descriptive Statistics

Mean Std. Deviation N

RED_ING_ATT .736658 .2199147 68

LOG_F15_FLOWN_RATIO .128302 .3356707 68

Correlations

RED_ING_ATT LOG_F15_

FLOWN_RATIO

Pearson Correlation RED_ING_ATT 1.000 .316

LOG_F15_FLOWN_RATIO .316 1.000

Sig. (1-tailed) RED_ING_ATT . .004

LOG_F15_FLOWN_RATIO .004 .

N RED_ING_ATT 68 68

LOG_F15_FLOWN_RATIO 68 68

Variables Entered/Removed (b)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_FLOWN_RATIO(a) . Enter

a All requested variables entered.

b Dependent Variable: RED_ING_ATT
APPENDIX B

183

Model Summary (b)

Model R R 

Square

Adjusted 

R Square

Std. Error of 

the Estimate Change Statistics

R Square 

Change F Change df1 df2 Sig. F Change

1 .316(a) .100 .086 .2102374 .100 7.310 1 66 .009

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: RED_ING_ATT

ANOVA (b)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression .323 1 .323 7.310 .009(a)

Residual 2.917 66 .044

Total 3.240 67

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: RED_ING_ATT

Coefficients (a)

Model Unstandardized 

Coefficients

Standardized 

Coefficients t Sig.

95% 

Confidence 

Interval for B

Correlations Collinearity 

Statistics

B Std. 

Error Beta Lower Bound

Upper 

Bound

Zeroorder Partial Part Tolerance VIF

1 (Constant) .710 .027 25.993 .000 .656 .765

LOG_F15_

FLOWN_

RATIO

.207 .077 .316 2.704 .009 .054 .360 .316 .316 .316 1.000 1.000

a Dependent Variable: RED_ING_ATT
APPENDIX B

184

Collinearity Diagnostics (a)

Model Dimension Eigen value Condition Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO

1 1 1.359 1.000 .32 .32

2 .641 1.457 .68 .68

a Dependent Variable: RED_ING_ATT

Residuals Statistics (a)

Minimum Maximum Mean Std. 

Deviation N

Predicted Value .542350 .913029 .736658 .0694435 68

Std. Predicted Value -2.798 2.540 .000 1.000 68

Standard Error of 

Predicted Value .025 .076 .034 .011 68

Adjusted Predicted Value .523517 .943783 .736960 .0715145 68

Residual -.5746369 .3142520 .0000000 .2086626 68

Std. Residual -2.733 1.495 .000 .993 68

Stud. Residual -2.765 1.512 -.001 1.007 68

Deleted Residual -.5880008 .3215603 -.0003016 .2146556 68

Stud. Deleted Residual -2.918 1.527 -.005 1.020 68

Mahal. Distance .000 7.829 .985 1.532 68

Cook’s Distance .000 .096 .014 .022 68

Centered Leverage Value .000 .117 .015 .023 68

a Dependent Variable: RED_ING_ATT
APPENDIX B

185

Charts

-3 -2 -1 0 1 2

Regression Standardized Residual

0

2

4

6

8

10

12

Frequency

Mean = -4.09E-16

Std. Dev. = 0.993

N = 68

Dependent Variable: RED_ING_ATT

Histogram

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Expected Cum Prob

Dependent Variable: RED_ING_ATT

Normal P-P Plot of Regression Standardized Residual
APPENDIX B

186

-3 -2 -1 0 1 2 3

Regression Standardized Predicted Value

-3

-2

-1

0

1

2

Regression Studentized Deleted (Press)

Residual

Dependent Variable: RED_ING_ATT

Scatterplot

-1.0000 -0.5000 0.0000 0.5000 1.0000

LOG F15/RED FORCE RATIO

-3.00000

-2.00000

-1.00000

0.00000

1.00000

2.00000

Standardized Residual
APPENDIX B

187

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000

Centered Leverage Value

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

Cook's Distance

11

119

198

228

304
APPENDIX B

188

Long SU-27 Regression Analysis w/o Mission #228

Warnings

For models with dependent variable F15_ING_ATT, the following variables are constants or 

have missing correlations: SAM_LVL. They will be deleted from the analysis.

Descriptive Statistics

Mean Std. Deviation N

F15_ING_ATT .186343 .1803651 67

LOG_F15_FLOWN_RATIO .142321 .3175161 67

LIGHT 1.30 .461 67

TACTIC2 3.37 .599 67

EA2 3.19 .680 67

REGEN2 2.94 .239 67

RXN_LVL 2.36 .595 67

MAX_LIVE_GRPS 3.42 .497 67

SAM_LVL 2.00 .000 67

SAM_ROE2 3.62 .363 67

REC 2.67 .473 67

BIG_CROW2 3.62 .422 67
APPENDIX B

189

Correlations

F15_

ING_

ATT

LOG_

F15_

FLOWN_

RATIO

LIGHT TACTIC2 EA2

RE

GE

N2

RXN_

LVL

MAX_

LIVE_

GRPS

SAM_

LVL

SAM_

ROE2 REC BIG_CROW2

Pearson 

Correlation

F15_

ING_ATT 1.000 -.286 -.023 .115 .006 .042 .097 .095 . .114 .116 .136

LOG_

F15_

FLOWN_

RATIO

-.286 1.000 .283 -.104 .089 .208 -.004 -.104 . -.069 -.055 -.120

LIGHT -.023 .283 1.000 -.190 -.139 .164 .101 .042 . .015 -.030 -.053

TACTIC2 .115 -.104 -.190 1.000 .825 .158 .554 .588 . .448 .653 .649

EA2 .006 .089 -.139 .825 1.000 .072 .500 .564 . .348 .484 .557

REGEN2 .042 .208 .164 .158 .072 1.000 .579 .214 . .435 .360 .373

RXN_LVL .097 -.004 .101 .554 .500 .579 1.000 .920 . .758 .639 .676

MAX_

LIVE_

GRPS

.095 -.104 .042 .588 .564 .214 .920 1.000 . .699 .592 .631

SAM_LVL . . . . . . . . 1.000 . . .

SAM_

ROE2 .114 -.069 .015 .448 .348 .435 .758 .699 . 1.000 .767 .821

REC .116 -.055 -.030 .653 .484 .360 .639 .592 . .767 1.000 .893

BIG_

CROW2 .136 -.120 -.053 .649 .557 .373 .676 .631 . .821 .893 1.000

Sig. 

(1-tailed)

F15_

ING_ATT . .010 .425 .177 .481 .367 .219 .222 .000 .179 .174 .137

LOG_

F15_

FLOWN_

RATIO

.010 . .010 .200 .237 .046 .488 .200 .000 .289 .329 .167

LIGHT .425 .010 . .062 .130 .092 .207 .367 .000 .453 .405 .335

TACTIC2 .177 .200 .062 . .000 .101 .000 .000 .000 .000 .000 .000

EA2 .481 .237 .130 .000 . .280 .000 .000 .000 .002 .000 .000

REGEN2 .367 .046 .092 .101 .280 . .000 .041 .000 .000 .001 .001

RXN_LVL .219 .488 .207 .000 .000 .000 . .000 .000 .000 .000 .000

MAX_

LIVE_

GRPS

.222 .200 .367 .000 .000 .041 .000 . .000 .000 .000 .000

SAM_LVL .000 .000 .000 .000 .000 .000 .000 .000 . .000 .000 .000

SAM_

ROE2 .179 .289 .453 .000 .002 .000 .000 .000 .000 . .000 .000
APPENDIX B

190

F15_

ING_

ATT

LOG_

F15_

FLOWN_

RATIO

LIGHT TACTIC2 EA2

RE

GE

N2

RXN_

LVL

MAX_

LIVE_

GRPS

SAM_

LVL

SAM_

ROE2 REC BIG_CROW2

REC .174 .329 .405 .000 .000 .001 .000 .000 .000 .000 . .000

BIG_

CROW2 .137 .167 .335 .000 .000 .001 .000 .000 .000 .000 .000 .

N F15_

ING_ATT 67 67 67 67 67 67 67 67 67 67 67 67

LOG_

F15_

FLOWN_

RATIO

67 67 67 67 67 67 67 67 67 67 67 67

LIGHT 67 67 67 67 67 67 67 67 67 67 67 67

TACTIC2 67 67 67 67 67 67 67 67 67 67 67 67

EA2 67 67 67 67 67 67 67 67 67 67 67 67

REGEN2 67 67 67 67 67 67 67 67 67 67 67 67

RXN_LVL 67 67 67 67 67 67 67 67 67 67 67 67

MAX_

LIVE_

GRPS

67 67 67 67 67 67 67 67 67 67 67 67

SAM_LVL 67 67 67 67 67 67 67 67 67 67 67 67

SAM_

ROE2 67 67 67 67 67 67 67 67 67 67 67 67

REC 67 67 67 67 67 67 67 67 67 67 67 67

BIG_

CROW2 67 67 67 67 67 67 67 67 67 67 67 67

Variables Entered/Removed (a)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_

FLOWN_RATIO . Forward (Criterion: Probability-of-F-to-enter <= .050)

a Dependent Variable: F15_ING_ATT

Correlations (continued)
APPENDIX B

191

Model Summary (b)

Model R R 

Square

Adjusted 

R Square

Std. Error 

of the 

Estimate

Change Statistics

R Square 

Change

F 

Change df1 df2 Sig. F Change

1 .286(a) .082 .068 .1741711 .082 5.778 1 65 .019

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT

ANOVA (b)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression .175 1 .175 5.778 .019(a)

Residual 1.972 65 .030

Total 2.147 66

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT

Coefficients (a)

Model Unstandardized 

Coefficients

Standardized 

Coefficients t Sig.

95% 

Confidence 

Interval for B

Correlations Collinearity 

Statistics

B Std. 

Error Beta Lower Bound

Upper 

Bound

Zeroorder Partial Part Tolerance VIF

1 (Constant) .209 .023 8.971 .000 .163 .256

LOG_

F15_

FLOWN_

RATIO

-.162 .068 -.286 -2.404 .019 -.297 -.027 -.286 -.286 -.286 1.000 1.000

a Dependent Variable: F15_ING_ATT
APPENDIX B

192

Excluded Variables (b)

Model Beta In T Sig. Partial 

Correlation Collinearity Statistics

Tolerance VIF Minimum 

Tolerance

1 LIGHT .062(a) .501 .618 .062 .920 1.087 .920

TACTIC2 .086(a) .720 .474 .090 .989 1.011 .989

EA2 .032(a) .263 .793 .033 .992 1.008 .992

REGEN2 .106(a) .874 .385 .109 .957 1.045 .957

RXN_LVL .095(a) .801 .426 .100 1.000 1.000 1.000

MAX_LIVE_GRPS .066(a) .551 .584 .069 .989 1.011 .989

SAM_ROE2 .095(a) .792 .431 .099 .995 1.005 .995

REC .101(a) .846 .401 .105 .997 1.003 .997

BIG_CROW2 .103(a) .858 .394 .107 .986 1.015 .986

a Predictors in the Model: (Constant), LOG_F15_FLOWN_RATIO

b Dependent Variable: F15_ING_ATT

Collinearity Diagnostics (a)

Model Dimension Eigen value Condition Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO

1 1 1.412 1.000 .29 .29

2 .588 1.549 .71 .71

a Dependent Variable: F15_ING_ATT

Casewise Diagnostics (a, b)

Case Number Std. Residual F15_ING_ATT

210 3.104 .750

a Dependent Variable: F15_ING_ATT

b When values are missing, the substituted mean has been used in the statistical computation.
APPENDIX B

193

Residuals Statistics (a)

Minimum Maximum Mean Std. Deviation N

Predicted Value .050254 .275249 .186343 .0515327 67

Std. Predicted Value -2.641 1.725 .000 1.000 67

Standard Error of 

Predicted Value .021 .060 .029 .009 67

Adjusted Predicted Value .040004 .260897 .185932 .0519537 67

Residual -.2285581 .5405580 .0000000 .1728466 67

Std. Residual -1.312 3.104 .000 .992 67

Stud. Residual -1.329 3.132 .001 1.006 67

Deleted Residual -.2344409 .5504493 .0004114 .1775729 67

Stud. Deleted Residual -1.337 3.373 .010 1.032 67

Mahal. Distance .001 6.974 .985 1.376 67

Cook’s Distance .000 .132 .014 .023 67

Centered Leverage Value .000 .106 .015 .021 67

a Dependent Variable: F15_ING_ATT

Charts

-2 -1 0 1 2 3 4

Regression Standardized Residual

0

3

6

9

12

15

Frequency

Mean = 2.05E-16

Std. Dev. = 0.992

N = 67

Dependent Variable: F15_ING_ATT

Histogram
APPENDIX B

194

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Expected Cum Prob

Dependent Variable: F15_ING_ATT

Normal P-P Plot of Regression Standardized Residual

-3 -2 -1 0 1 2

Regression Standardized Predicted Value

-2

-1

0

1

2

3

4

Regression Studentized Deleted (Press)

Residual

Dependent Variable: F15_ING_ATT

Scatterplot
APPENDIX B

195

-0.5000 -0.2500 0.0000 0.2500 0.5000 0.7500 1.0000

LOG F15/RED FORCE RATIO

-2.00000

-1.00000

0.00000

1.00000

2.00000

3.00000

4.00000

Standardized Residual

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000

Centered Leverage Value

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

Cook's Distance
















APPENDIX B

196

Regression

Warnings

For models with dependent variable RED_ING_ATT, the following variables are constants or 

have missing correlations: SAM_LVL. They will be deleted from the analysis.

Descriptive Statistics

Mean Std. Deviation N

RED_ING_ATT .737703 .2214044 67

LOG_F15_FLOWN_RATIO .142321 .3175161 67

LIGHT 1.30 .461 67

TACTIC2 3.37 .599 67

EA2 3.19 .680 67

REGEN2 2.94 .239 67

RXN_LVL 2.36 .595 67

MAX_LIVE_GRPS 3.42 .497 67

SAM_LVL 2.00 .000 67

SAM_ROE2 3.62 .363 67

REC 2.67 .473 67

BIG_CROW2 3.62 .422 67
APPENDIX B

197

Correlations

RED_

ING_

ATT

LOG_

F15_

FLOWN_

RATIO

LIGHT TACTIC2 EA2

RE

GE

N2

RXN_

LVL

MAX_

LIVE_

GRPS

SAM_

LVL

SAM_

ROE2 REC BIG_CROW2

Pearson 

Correlation

RED_

ING_ATT 1.000 .322 -.005 .116 .295 -.110 -.199 -.186 . -.179 -.136 -.153

LOG_

F15_

FLOWN_

RATIO

.322 1.000 .283 -.104 .089 .208 -.004 -.104 . -.069 -.055 -.120

LIGHT -.005 .283 1.000 -.190 -.139 .164 .101 .042 . .015 -.030 -.053

TACTIC2 .116 -.104 -.190 1.000 .825 .158 .554 .588 . .448 .653 .649

EA2 .295 .089 -.139 .825 1.000 .072 .500 .564 . .348 .484 .557

REGEN2 -.110 .208 .164 .158 .072 1.000 .579 .214 . .435 .360 .373

RXN_LVL -.199 -.004 .101 .554 .500 .579 1.000 .920 . .758 .639 .676

MAX_

LIVE_

GRPS

-.186 -.104 .042 .588 .564 .214 .920 1.000 . .699 .592 .631

SAM_

LVL . . . . . . . . 1.000 . . .

SAM_

ROE2 -.179 -.069 .015 .448 .348 .435 .758 .699 . 1.000 .767 .821

REC -.136 -.055 -.030 .653 .484 .360 .639 .592 . .767 1.000 .893

BIG_

CROW2 -.153 -.120 -.053 .649 .557 .373 .676 .631 . .821 .893 1.000

Sig. 

(1-tailed)

RED_

ING_ATT . .004 .485 .175 .008 .189 .053 .066 .000 .074 .137 .108

LOG_

F15_

FLOWN_

RATIO

.004 . .010 .200 .237 .046 .488 .200 .000 .289 .329 .167

LIGHT .485 .010 . .062 .130 .092 .207 .367 .000 .453 .405 .335

TACTIC2 .175 .200 .062 . .000 .101 .000 .000 .000 .000 .000 .000

EA2 .008 .237 .130 .000 . .280 .000 .000 .000 .002 .000 .000

REGEN2 .189 .046 .092 .101 .280 . .000 .041 .000 .000 .001 .001

RXN_LVL .053 .488 .207 .000 .000 .000 . .000 .000 .000 .000 .000

MAX_

LIVE_

GRPS

.066 .200 .367 .000 .000 .041 .000 . .000 .000 .000 .000

SAM_

LVL .000 .000 .000 .000 .000 .000 .000 .000 . .000 .000 .000

SAM_

ROE2 .074 .289 .453 .000 .002 .000 .000 .000 .000 . .000 .000
APPENDIX B

198

RED_

ING_

ATT

LOG_

F15_

FLOWN_

RATIO

LIGHT TACTIC2 EA2

RE

GE

N2

RXN_

LVL

MAX_

LIVE_

GRPS

SAM_

LVL

SAM_

ROE2 REC BIG_CROW2

REC .137 .329 .405 .000 .000 .001 .000 .000 .000 .000 . .000

BIG_

CROW2 .108 .167 .335 .000 .000 .001 .000 .000 .000 .000 .000 .

N RED_

ING_ATT 67 67 67 67 67 67 67 67 67 67 67 67

LOG_

F15_

FLOWN_

RATIO

67 67 67 67 67 67 67 67 67 67 67 67

LIGHT 67 67 67 67 67 67 67 67 67 67 67 67

TACTIC2 67 67 67 67 67 67 67 67 67 67 67 67

EA2 67 67 67 67 67 67 67 67 67 67 67 67

REGEN2 67 67 67 67 67 67 67 67 67 67 67 67

RXN_LVL 67 67 67 67 67 67 67 67 67 67 67 67

MAX_

LIVE_

GRPS

67 67 67 67 67 67 67 67 67 67 67 67

SAM_

LVL 67 67 67 67 67 67 67 67 67 67 67 67

SAM_

ROE2 67 67 67 67 67 67 67 67 67 67 67 67

REC 67 67 67 67 67 67 67 67 67 67 67 67

BIG_

CROW2 67 67 67 67 67 67 67 67 67 67 67 67

Correlations (continued)
APPENDIX B

199

Variables Entered/Removed (a)

Model Variables Entered Variables 

Removed Method

1 LOG_F15_

FLOWN_RATIO . Forward (Criterion: Probability-of-F-to-enter <= .050)

2 EA2 . Forward 

(Criterion: Probability-of-F-to-enter <= .050)

3 RXN_LVL . Forward 

(Criterion: Probability-of-F-to-enter <= .050)

a Dependent Variable: RED_ING_ATT

Model Summary (d)

Model R R 

Square

Adjusted 

R Square

Std. Error of 

the Estimate Change Statistics

R Square 

Change

F 

Change df1 df2 Sig. F Change

1 .322(a) .104 .090 .2112013 .104 7.531 1 65 .008

2 .419(b) .175 .149 .2041876 .071 5.542 1 64 .022

3 .568(c) .323 .291 .1864914 .148 13.722 1 63 .000

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Predictors: (Constant), LOG_F15_FLOWN_RATIO, EA2

c Predictors: (Constant), LOG_F15_FLOWN_RATIO, EA2, RXN_LVL

d Dependent Variable: RED_ING_ATT

ANOVA (d)

Model Sum of 

Squares df Mean Square F Sig.

1 Regression .336 1 .336 7.531 .008(a)

Residual 2.899 65 .045

Total 3.235 66

2 Regression .567 2 .283 6.800 .002(b)

Residual 2.668 64 .042

Total 3.235 66

3 Regression 1.044 3 .348 10.008 .000(c)

Residual 2.191 63 .035

Total 3.235 66

a Predictors: (Constant), LOG_F15_FLOWN_RATIO

b Predictors: (Constant), LOG_F15_FLOWN_RATIO, EA2

c Predictors: (Constant), LOG_F15_FLOWN_RATIO, EA2, RXN_LVL

d Dependent Variable: RED_ING_ATT
APPENDIX B

200

Coefficients (a)

Model Unstandardized 

Coefficients

Standardized 

Coefficients t Sig.

95% 

Confidence 

Interval for B

Correlations Collinearity 

Statistics

B Std. 

Error Beta Lower Bound

Upper 

Bound

Zeroorder Partial Part Tolerance VIF

1 (Constant) .706 .028 24.927 .000 .649 .762

LOG_F15_

FLOWN_

RATIO

.225 .082 .322 2.744 .008 .061 .388 .322 .322 .322 1.000 1.000

2 (Constant) .429 .121 3.552 .001 .188 .670

LOG_F15_

FLOWN_

RATIO

.208 .079 .298 2.618 .011 .049 .367 .322 .311 .297 .992 1.008

EA2 .087 .037 .268 2.354 .022 .013 .162 .295 .282 .267 .992 1.008

3 (Constant) .588 .118 4.966 .000 .351 .824

LOG_F15_

FLOWN_

RATIO

.193 .073 .277 2.655 .010 .048 .338 .322 .317 .275 .989 1.011

EA2 .160 .039 .492 4.089 .000 .082 .239 .295 .458 .424 .742 1.347

RXN_LVL -.165 .045 -.444 -3.704 .000 -.254 -.076 -.199 -.423 -.384 .748 1.337

a Dependent Variable: RED_ING_ATT
APPENDIX B

201

Excluded Variables (d)

Model Beta In t Sig. Partial 

Correlation Collinearity Statistics

Tolerance VIF Minimum 

Tolerance

1 LIGHT -.104(a) -.850 .398 -.106 .920 1.087 .920

TACTIC2 .151(a) 1.289 .202 .159 .989 1.011 .989

EA2 .268(a) 2.354 .022 .282 .992 1.008 .992

REGEN2 -.185(a) -1.555 .125 -.191 .957 1.045 .957

RXN_LVL -.198(a) -1.711 .092 -.209 1.000 1.000 1.000

MAX_LIVE_GRPS -.154(a) -1.313 .194 -.162 .989 1.011 .989

SAM_ROE2 -.157(a) -1.344 .184 -.166 .995 1.005 .995

REC -.118(a) -1.007 .318 -.125 .997 1.003 .997

BIG_CROW2 -.116(a) -.981 .330 -.122 .986 1.015 .986

2 LIGHT -.058(b) -.480 .633 -.060 .892 1.120 .892

TACTIC2 -.257(b) -1.219 .227 -.152 .288 3.471 .288

REGEN2 -.200(b) -1.752 .085 -.216 .954 1.048 .951

RXN_LVL -.444(b) -3.704 .000 -.423 .748 1.337 .742

MAX_LIVE_GRPS -.465(b) -3.628 .001 -.416 .658 1.520 .658

SAM_ROE2 -.290(b) -2.472 .016 -.297 .868 1.151 .866

REC -.330(b) -2.640 .010 -.316 .756 1.322 .752

BIG_CROW2 -.404(b) -3.077 .003 -.362 .660 1.514 .660

3 LIGHT .036(c) .317 .752 .040 .847 1.181 .691

TACTIC2 -.055(c) -.273 .786 -.035 .264 3.784 .264

REGEN2 .099(c) .706 .483 .089 .546 1.833 .428

MAX_LIVE_GRPS -.207(c) -.706 .483 -.089 .126 7.943 .126

SAM_ROE2 .013(c) .078 .938 .010 .421 2.375 .363

REC -.136(c) -.975 .333 -.123 .550 1.817 .544

BIG_CROW2 -.205(c) -1.349 .182 -.169 .458 2.183 .458

a Predictors in the Model: (Constant), LOG_F15_FLOWN_RATIO

b Predictors in the Model: (Constant), LOG_F15_FLOWN_RATIO, EA2

c Predictors in the Model: (Constant), LOG_F15_FLOWN_RATIO, EA2, RXN_LVL

d Dependent Variable: RED_ING_ATT
APPENDIX B

202

Collinearity Diagnostics (a)

Model Dimension Eigen 

value

Condition 

Index Variance Proportions

(Constant) LOG_F15_

FLOWN_RATIO EA2 RXN_LVL

1 1 1.412 1.000 .29 .29

2 .588 1.549 .71 .71

2 1 2.254 1.000 .01 .07 .01

2 .725 1.764 .01 .93 .01

3 .022 10.230 .99 .00 .99

3 1 3.180 1.000 .00 .02 .00 .00

2 .769 2.033 .00 .97 .00 .00

3 .031 10.210 .42 .01 .04 .89

4 .021 12.349 .58 .00 .95 .10

a Dependent Variable: RED_ING_ATT

Residuals Statistics (a)

Minimum Maximum Mean Std. Deviation N

Predicted Value .494902 1.032380 .737703 .1257844 67

Std. Predicted Value -1.930 2.343 .000 1.000 67

Standard Error of 

Predicted Value .027 .070 .044 .011 67

Adjusted Predicted Value .486527 1.036057 .738585 .1280233 67

Residual -.4393155 .3313461 .0000000 .1822037 67

Std. Residual -2.356 1.777 .000 .977 67

Stud. Residual -2.422 1.858 -.002 1.008 67

Deleted Residual -.4644304 .3623375 -.0008825 .1940250 67

Stud. Deleted Residual -2.523 1.896 -.004 1.020 67

Mahal. Distance .363 8.380 2.955 1.981 67

Cook’s Distance .000 .092 .016 .023 67

Centered Leverage Value .006 .127 .045 .030 67

a Dependent Variable: RED_ING_ATT
APPENDIX B

203

Charts

-3 -2 -1 0 1 2

Regression Standardized Residual

0

2

4

6

8

10

Frequency

Mean = -1.88E-15

Std. Dev. = 0.977

N = 67

Dependent Variable: RED_ING_ATT

Histogram

0.0 0.2 0.4 0.6 0.8 1.0

Observed Cum Prob

0.0

0.2

0.4

0.6

0.8

1.0

Expected Cum Prob

Dependent Variable: RED_ING_ATT

Normal P-P Plot

of Regression Standardized Residual
APPENDIX B

204

-2 -1 0 1 2 3

Regression Standardized Predicted Value

-3

-2

-1

0

1

2

Regression Studentized Deleted (Press)

Residual

Dependent Variable: RED_ING_ATT

Scatterplot

-0.5000 -0.2500 0.0000 0.2500 0.5000 0.7500 1.0000

LOG F15/RED FORCE RATIO

-3.00000

-2.00000

-1.00000

0.00000

1.00000

2.00000

Standardized Residual
APPENDIX B

205

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.14000

Centered Leverage Value

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

Cook's Distance







 











 

207

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