Therefore,

N=Xi(Pit Pot Pst Po) +-X2
(Pi + Ps + Po!) + Xo(Po! + Po")

And,
N= Xi—Xi(P2t+ Pst Pr)
Na=X2—Xa(Ps'+Po!) +Xi(P2)
Ns=Xi—X<(Po') +Xi(Ps) +X2(P2’)
No=Xi(Po) +-X2(Po!) +Xa(Po")

Or

Ni=Xi(Pi)

N2=X2(Ps') +-Xi(Ps)
Ns=Xi(Ps") +Xi(Ps) +. X2(P2)
No=XitXo+Xs—(Nit+Ne+Ns)

A systematic random sample was taken from the
three medical classes on the Aeromedical Certifi-

‘cation active master tape file as of October 1, 1966.

A 95% confidence interval and a +5% sampling
error were accepted with respect to sample propor-
tions. In the sample, from the medical tape file:

n= total number of airmen in the sample.

umber of Class 1 airmen in the sample.
%2= number of Class 2 airmen in the sample.
%3=number of Class 3 airmen in the sample.

a can be defined as consisting of:

a;—those medically certified first class airmen who
were usage classified under airline transport
purposes.

a,—those medically certified first class airmen who
were usage classified under commercial
purposes.

a;—those medically certified first class airmen who
were usage classified under private or
student purposes.

ay—those medically certified first class airmen
whose airman rating and usage classifi-
cation were unknown or who did not require
medical certification of any class.

And,
t= atagtast+ay
% can be defined as consisting of:

a,'—those medically certified second class airmen
who were usage classified under commercial
purposes.

a,'—those medically certified second class airmen
who were usage classified under private
or student purposes.

ao'—those medically certified second class airmen
whose airman rating and usage classifi-
cation were unknown or- who did not
require medical certification of any class.

And,
®2= an! +05! +00!
% can be defined as consisting of:

a3"——those medically certified third class airmen
who were usage classified under private
or student purposes.

ao"—those medically certified third class airmen
whose airman rating and usage classifi-
cation were unknown or who did not
require medical certification of any class.

And,

T= 3" +a5"
n=mtat2,

Therefore
N= at a2t 3+ dot ae! +43’ +a! +45" a9"

In expansion of the P Q relationship for the
three classes of medical certification in the sample,
the following proportions were of interest. P is
defined as the proportion of the active airman
population who have medical certification com-
mensurate with their derived usage classification.
Q is defined as those airmen who have obtained
higher medical certification than that which is
required for their usage classification.

In the sample, “p” and “q” are the estimates of
“P” and “Q” population values.

And,

a ay dD
= io gy
PM bab agpag FPG,

_ ae or =@_D, _
Pe Gat ay bag PAG, Pe
a3 a A A
Pe artartag bag PIG, = P= 11
= gf
PO Fart as-fay PO, = Po


Usage of Combined Airman Certification By Active Airmen:

An Active Airman Population Estimate

I. Introduction

Statistical data concerning the final usage of
medical and/or airman certification has historically
been elusive at best. Volumes of data are generated
which serve to define the airman population by
active or inactive status, class of medical certifi-
cation, and numbers of airmen with specific ratings.
These data all serve the purpose for which accu-
mulated but collectively they fail to illuminate the
important area of what final airman usage is made
of the various combinations of medical and airman
certification. Such a description would appear to
be of significant value to all facets of the civilian
aviation community. Obvious benefits are apparent
to the administration in terms of descriptive
statistics for workload projections in airman/
aircraft certification, future facility requirements,
economic and budget considerations, and aviation
research in general.

The problem of usage determination is com-
pounded by the fact that no single source of airman
data, which accounts for the numerous variables
involved, has emerged as a reliable means of defining
the active airman population by usage of certifi-
cation.

Current Federal Aviation Regulations provide
that all airman certificates, except student and
certain special categories, are to be of indefinite
duration. The number of airman certificates per se
issued, therefore, reflects the cumulative total of
airmen by ratings but are of limited value in a
further description of the current airman population.
The fact that a rating is of indefinite duration
creates further inconsistencies because of the
possibility of a voluntary downgrade by the airman
in usage of his airman certification.

Continued validity, for operational purposes, of
all airman ratings (certificates) has, by regulation,
been made contingent upon possession of a current
medical certificate which is commensurate with

usage (See Figure 1). Aeromedical Certification
records provide a definition of the members of the
current airman population but these files are limited
in that the class of medical certification does not
imply utilization for the corresponding airman
rating for which it is required, i.e., first class medical
certification does not imply that the airman is airline
transport rated. Conversely, the fact that an airman
is airline transport rated does not imply that he is
utilizing this rating and in turn is required to be
medically certified under first class medical criteria.

Ficure 1. Minimum Medical Certification Required
for Operational Usage of Airman Ratings

Minimum

Required

Medical

Airman Category Certificate

Airline Transport Pilot* First Class
‘Air Traffic Control Tower Operator Second Class

Second Class

Commercial Lighter-Than-Air Pilot.
Second Class

Commercial Pilot**-

Flight Engineer. - Second Class
Flight Navigato = Second Claas
Free Balloon Pilot. > Third Class
Private Lighter-Than-Air _ Third Class
Private Pilot. > Third Class
Student Lighter-Than-Air > ‘Third Class
Student: Pilot. > Third Class

¥Co-pilots are required by regulation to have second class medical

certification. Co-pilots, therefore, are treated as commercial pilots in
this study.

“Flight Instructors, though not required by regulation to have a
specific level of medical certification, would normally possess secon
Class medical gertification in conjunction with a commercial or higher
airman rating, Plight Instructors are ‘treated as commercial pilots in this
study.

Source: Federal Aviation Regulations—Parts 61, 63, and 65.

Finally, an airman may obtain airman and
medical certification at a given level and use both
for some lower level, as would be the case if an
individual was rated as a commercial pilot with
second class medical certification and was using his
certification for private purposes. The problem of
usage is virtually nonexistent among medically
certified third class airmen since a third class
medical certificate can be used for private and
student purposes only, regardless of the airman
rating held.



Tani IV.—Study population estimates by usage classification—October 1, 1966

‘Usage Classification Estimated Percent.

Population: of Total

Airline Transport Pilot Purposes (Excluding Co-Pilots) 13,926 25
Commercial Pilot Purposes*.____ 91,451 16.6
Private or Student Pilot Purposes 419,972 76.4
Unknown Purposes 1538 4.5
‘Total (Actual)... 222 eee 549,887 100.0

; Includes Air Traffic Controllers, Flight Engineers, Flight Navigators, Flight Instructors, Co-Pilots, and Military

Pilot personnel.

Tapie V.—Current population estimates by usage classification—October 1, 1967

‘Usage Classification Estimated Percent

Population of Total

Airline Transport Pilot Purposes (Excluding Co-Pilots). 17,750 2.9
Commercial Pilot Purposes* 107,304 17.2
Private or Student Pilot Pui 470,883 75.5
Unknown Purposes 27,597 44
Total (Actual). 623,534 100.0

{Includes Air Traffic Controllers, Flight Engineers, Flight Navigators, Flight Instructors, Co-Pilots, and Military

Pilot personnel.

IV. Discussion

‘The preceding analysis, although broad in scope,
provides valuable insight with respect to a deserip-
tion of the active airman population. The population
estimates by usage deviate quite dramatically from
what might be surmised from available statistical
data which considers either airman rating or medical
certification separately. Available statistical data
tends to overemphasize professional usage categories
and underemphasize the general aviation ‘usage
categories. For example, reference to Table V would
indicate that approximately 20% of the active
airman population is occupationally connected to
aviation. Using current First and Second Class
Medical Certification totals (72,155 and 182,654
respectively) would indicate that approximately
40% of total airmen currently certified (623,534)
are occupationally connected to aviation. The most
current airman rating data available would, like-
wise, tend to overestimate the proportion of the
total airman population occupationally related to
aviation.®

The general aviation population makes up
approximately 75% of the active airman population
as indicated by Table V. About 4.5% of the medi-
cally certified active airman population have not
yet obtained any type of airman rating.

“SFAA Statistical Handbook of Aviation, 1966 Edition, Table 4.9.
Categories are not mutually exclusive, but the effect is obvious by adding
commercial and airline transport ratings for the year ending December 31,

1965, which would indicate approximately 29% of the total in the" pilot”
category.

Reference to Table VI and VII provides signifi-
cant testimony to the growth in civil aviation by
comparison of the net population totals at the 12-
month interval provided by this study. The active
airman population experienced a net growth of
73,647 from 549,887 as of October 1, 1966, to
623,534 as of October 1, 1967, or 13.4%.

Airmen medically certified within the past 3
years, as of October 1, 1966 totaled 646,319 of which
96,432 had effectively become inactive by allowing
their medical certificate to lapse into the time period
from 25 to 36 months since last FAA medical
examination. As of October 1, 1967, airmen medically
certified within the past 3 years totaled 728,080.
Of this total, 104,546 airmen had allowed their
medical certification to lapse into an inactive status.
Inactivity, therefore, remained relatively constant
as measured at 12-month intervals (14.9% in
October 1966 and 14.4% in October 1967).

Whatever the motivation, approximately 30%
of the active airman population initially obtain
higher medical certification than is required by
regulation. Part of this “over certification” is
attributed to industry requirements but a large
percentage of general aviation pilots also obtain
higher medical certification than is required. In the
study population, 29.7% of the medically certified
first class airmen were apparently engaged in private
or student pilot activity and 55.3% of the medically
certified second class airmen were engaged in private


Frere 2. Classification of Airman/Medical
Certification Usage

. Airline Transport Pilot Purposes (Excluding Co-Pilots).

” Commercial Pilot Purposes (Including Air Traffic Con-
trollers, Flight Engineers, Flight Navigators, Flight
Instructors, Co-Pilots, and Military Pilot personnel).

. Private or Student Pilot Purposes.

"Unknown Purposes.

pe

raced

The proportions mentioned at the beginning of
this section were subsequently defined by considera-
tion of the factors mentioned above and the derived
usage classification indicated for each sample
member.

Certain assumptions are inherent in this approach
to estimating the population by usage. First, given
the screening factors, the classification by usage is
static and reflects the most recent certification data
available concerning the airman. Anticipation of
airman rating upgrades were not considered, except
to the extent that records of application for airman
rating were searched on three separate occasions at.
3-month intervals to reduce the proportion of air-
men in the “unknown” category. This is not,
however, a serious limitation as any approach
must, of necessity, be of a static nature as workload
time factors and certainty as concerns such variables
as anticipated upgrades are not measurable. Further,
the absence of certification data, either previous
medical factors or airman rating factors, required
a dependence upon the remaining known factors
to define usage. Supplemental research was required
in these rare instances but some minute error is
categorically recognized in this respect. It is doubt-
ful whether any of the aforementioned limitations
amount to the problems presented by nonresponse
and other bias-producing considerations normally
associated with a typical questionaire sample
directed to members of the population.

The estimation of the proportions mentioned
previously, with their complements, were applied
to the known medical certification status of the
active airman population by class of medical certifi-
cation, with the results yielding population estimates
according to the usage classifications defined in
Figure 2.

B. Sample Members. From a population of 56,611
medically certified active first class airmen, 1,476 air-
man records were randomly selected and extracted
from magnetic tape for purposes of estimating the
proportional usage classifications. Likewise, from

3 For a discussion of the problems of “nonresponse” see Sampling Tech-
niques, W. G, Cochran, Chapter 13.

a population of 160,682 medically certified active
second class airmen, 1,047 airman records were
considered in the estimation of the proportional
usage classifications. Only 73 medically certified
active third class airman records from a population
of 332,594 were considered in estimating the usage
proportions among third class airmen because
minimal usage alternatives exist for this class. As
mentioned previously, appropriate sample size
statistical methodology dictated the sample size
for each class of medical certification. (See the
Appendix for a discussion of sample size determina-
tion and sample design.)

C. An Example of Usage Classification Applied to
Sample Members. The most recent medical record
of each sample member was reviewed to determine
usage criteria from elements of data supplied by the
airman on FAA Form 1004 (Application for Airman
Medical Certificate). These data and additional
computer assigned data were combined with cur-
rent airman rating information, i.e., student, pri-
vate, commercial, airline transport ratings, etc., to
arrive at an appropriate usage classification.t
Questionable cases or instances of multiple airman
ratings were given more detailed review considering
previous medical records, statements reflecting
occupation and employer, and indications of business
or pleasure flying. Most cases, however, were class-
ified by usage according to class of medical certif-
icate issued, current airman rating, and length of
time since last FAA medical examination. Example
cases are presented below to illustrate usage classifi-
cations.

Case 1. Fifty-five-year-old male airman issued

first class medical certification on July 29, 1966.

Currently airline transport rated. Date of previous

FAA medical examination, January 1966. Em-

ployed by United Airlines. USAGE CLASSIFI-

CATION: Airline Transport Pilot Purposes.

Case 2. Forty-eight-year-old male airman issued

first class medical certification August 31, 1966.

Current airman ratings include airline transport

rating, flight instructor, and commercial ratings.

Date of previous FAA medical examination,

August 1965. Indicates occupation as business

or executive pilot. USAGE CLASSIFICATION:

Commercial Pilot Purposes.

Case 8. Twenty-three-year-old male airman issued

first class medical certification July 19, 1966.

«Airman ratings were obtained from records maintained by the Airman
Certification Branch of the Flight Standards Technical Division.



Both the airman certification and medical certi-
fication systems are automated and the obvious
solution, which would involve matching the two
tape files and categorizing the airman by rating
and medical certification status, would greatly
simplify the problem. However, this solution is not
feasible due to lead/lag considerations, workload
considerations and backlogs, incompatibility of
input control data under the separate systems,
differences in the degree of automation, and further
magnification of discrepancies between the two
tape systems due to input-errors. In short, a signifi-
cant error factor is recognized in a match procedure
involving these working files and the error is not
measurable.

This study, via usage of statistical methodology
described later, is an effort to estimate the active
airman population by apparent or effective airman
usage of required certification and considers both
airman rating and the medical certification factors.

II. Methodology

A. The Problem Statement. The problem of
estimating the active airman population by usage of
certification is reducible to one of estimating popu-
lation parameters via sampling techniques for the
following unknowns:!

1. The proportion of medically certified first class

airmen utilizing the medical certification for:

a. airman purposes requiring first class
medical certification,

b. airman purposes requiring second class
medical certification,

¢. airman purposes requiring third class
medical certification, or

d. other purposes, unknown or unrecognized
as requiring medical certification of any
class.

2. The proportion of medically certified second
class airmen utilizing the medical certifi-
cation for:

a. airman purposes requiring second class
medical certification,

b. airman purposes requiring third class
medical certification, or

¢. other purposes, unknown or unrecognized
as requiring medical certification of any
class.

” for a maximum of
e., regardless of the
‘lass purposes for

1 A medically certified airman is consider:
25 months after his last FAA Physical Examination,
class of medical certificate issued, it is valid for thi
a period of time up to 25 months,

3. The proportion of medically certified third
class airmen utilizing the medical certifi-
cation for:

a, airman purposes requiring third class
medical certification, or .

b. other purposes, unknown or unrecognized
as requiring medical certification of any
class,

A systematic random sampling procedure con-
sidering the three classes of medically certified air-
men as the respective subdivisions of the active
airman population was utilized to extract sample
members. Within each class of medical certification,
sufficient members were extracted for a predeter-
mined accuracy in view of the number of proportions
to be estimated within each class of medical certifi-
cation, i.e., more possible combinations reflecting
utilization are possible in the medically certified
first class subdivision, thus requiring a larger
sample size for the desired accuracy with respect
to proportional estimates. Reference to the Appendix
is recommended for a further detailed discussion of
statistical methodology. Suffice it to say here that
a sample from active members (medical examination ©
and issuance within the past 25 months) of each
class of medical certification was extracted from the
working magnetic tape files by computer program
means for purposes of estimating the proportions
defined in II.A.1, 2, and 3.2

As discussed in the introductory remarks, numer-
ous combinations of airman/medical certification
can legally exist and, if taken at face value, do not
serve to define the usage classification of the com-
bined certification in all instances. All members of
the sample were screened considering the known
factors of airman rating, class of medical certifi-
cation, current effective status of medical certifi-
cation (as indicated by the time lapse since the
most recent FAA medical examination) and previous
effective status of medical certification (as indicated
by the time lapse between the previous FAA medical
examination and the current FAA medical examina-
tion). The purpose and effect of this screening
procedure was to categorize the airmen by apparent
or effective usage considering combined airman/
medical certification factors. These usage classifi-
cations are defined in Figure 2.

2 Aeromedical Certification working tape files as of October 1, 1966,
were used in this study,


Tapun L—Medically certified first class airmen by usage classification

Medical Estimated Estimated Percent
‘Usage Classification Certificate Population Population of
Required Oct. 1, 1966 Oct. 1, 1967 Total
Airline Transport Pilot Purposes (Excluding

Co-Pilots). 13,926 17,750 24.6
Commercial Second 24, 286 30,955 42.9
Private or Student Pilot Purposes. Third 16,814 21,430 29.7
Unknown Purposes. None 1,585 2,020 2.8
Total (Actual)._..----------------------- -------- 56,611 72,155 100.0

Includes Air Traffic Controllers, Flight Engineers, Flight Navigators, Flight Instructors, Co-Pilots, and Military

Pilot personnel.

2. The Medically Certified Second Class Popula-
tion: 160,682 medically certified second class
airmen were included in the study population;
the current population totals 182,654. Per-
centages derived from sample results were
applied to the medically certified second class
airmen in the study population and the current
population. The estimates by usage classifi-
cation are presented in Table II.

3. The Medically Certified Third Class Popula-
tion: The study population included 332,594
medically certified third class airmen; the third
class population now totals 368,725. The
percentage relationships realized through anal-
ysis of sample members and subsequent usage
classifications were applied to the study and
current populations to arrive at the estimates
given in Table III.

Tanue IL.—Medically certified second class airmen by usage classification

Medical Estimated Estimated Percent
‘Usage Classification Certificate Population Population of
Required Oct. 1, 1966 Oct. 1, 1967 Total
Commercial Pilot Purposes*. Second 67,165 76,349 1.8
Private or Student Pilot Purposes - Third 88,857 101, 008 55.3
Unknown Purposes_ None 4,660 5,297 2.9
‘Total (Actual)...----------------~----- ------ 160,682 182,654 100.0

*Includes Air Traffic Controllers, Flight Engineers, Flight Navigators, Flight Instructors, Co-Pilots, and Military

Pilot personnel.

Tasun UI.—Medically certified third class airmen by usage classification

Medical Estimated Estimated Percent
Usage Classification Gertifieate Population Population of
Required Oct. 1, 1966 Oct. 1, 1967 Total
Private or Student Pilot Purposes. Third 314,301 348,445 94.5
Unknown Purposes...--.----- None 18,293 20,280 5.5
Total (Actual). _ wane 332,594 368,725 100.0

C. Total Population Estimates by Usage Classifi-
cation. Without regard to the type of medical
certificate held, this section is concerned with
estimates, by usage classification, of the total
population at the time of the study (October 1,
1966) and the total current population as of October
1, 1967. Utilizing the total population estimation
models described in the “Summary”, the populations
were further defined as described below:

1. The Study Population: Applying sample
proportions to the total study population
yields the following estimates by usage classifi-
cations (see Table IV).

The Current Population: In the same manner
described above, the current total population
was estimated by usage classification. Results
are presented in Table V.



AM 68-5

USAGE OF COMBINED AIRMAN CERTIFICATION
BY ACTIVE AIRMEN:
AN ACTIVE AIRMAN POPULATION ESTIMATE

Charles F. Booze, Jr., M.A.

Approved by Released by

J. Rosert Diz, M.D. Pp. V. Srecei, M.D.

Curer, Crviz ApromepicaL Institute Frprrat Air SURGEON
March 1968

DEPARTMENT OF TRANSPORTATION
FEDERAL AVIATION ADMINISTRATION
Office of Aviation Medicine



Wi=X1(0.246)

Na=X2(0.418)-+X,(0.429)

Ns=Xs(0.945) + X1(0.297) + X2(0.553)

‘No=X1(0.028) + X2(0.029) + X3(0.055) or

No= Xt Xt Xe— (Nit Net Ne)
Where,

A

Ni=The estimated number of medically certified
active airmen usage classified under Airline
Transport Purposes.

N= The estimated number of medically certified

active airmen usage classified under Com-
mercial Purposes.

A

Na=The estimated number of medically certified
active airmen usage classified under Pri-
vate or Student Purposes.

No=The estimated number of medically certified
active airmen usage classified as unknown
or not requiring medical certification of
any class.

And,

Xi=The actual number of medically certified
First Class airmen.

X2=The actual number of medically certified
Second Class airmen.

X3=The actual number of medically certified
Third Class airmen.


or student pilot activity. Several possible reasons
exist for obtaining higher medical certification.
Certainly, anticipated upgrade in airman rating
provides motivation for obtaining a higher class of
medical certification. More significant, however, is
probably the belief that a more thorough exami-
nation is obtained by making application for first
or second class medical certification. Lastly, some

“status” benefit is recognized as motivating airmen
to obtain higher medical certification than required.

The same analogy can be made with reference to
airman ratings. Airmen obtain higher technical
qualifications than required for their intended use.

In the final analysis, whatever the motivation,
these factors contribute to the enhancement of
aviation safety.

"Tasue VI.—Medically certified airman population summary—October 1, 1966

‘Time Lapse Since Date of Last Examination

Medical Certificate Active Airmen Tnactive Tote!
‘Airmen
<7Mo. <13Mo.  <25Mo, Subtotal © (25-36 Mo,
First Class. 39,109 13,275 4,227 56,611 1,773 58,384
Second Class. 65,760 48,945 45,977 160,682 22,352 183 , 034
Third Class_ - 108,739 73,983 149,872 332,594 72,307 404,901
Total____---- 213,608 136,203 200,076 549,887 96,432 646,319
Tain VII.—Medically certified airman population summary—October 1, 1967
‘Time Lapse Since Date of Last Examination
Medical Certificate Active Airmen Ingetive Total
Airmen
<7 Mo, <13 Mo. <25 Mo. ‘Subtotal 25-36 Mo.
First Class. .- 42,656 18,580 10,919 72,155 2,477 74,632
Second Class - 71,526 56,891 54,237 182,654 22,968 205 , 622
Third Class. - 119,311 80,048 169,366. 368,725 79,101 447,826
‘Total___-.--- 233,493 155,519 234,522 623,584 104,546 728,080
V. Summary “Private or Student Pilot Purposes” category

Assuming regulatory requirements and motiva-
tional factors to remain relatively constant with
respect to airman certification and its subsequent
usage by the airman population, the study has
provided a tool by which future populations may be
broadly defined. The only significant foreseeable
adjustment to this method of estimation occurs
with respect to the “Unknown Purposes” category.
The impact of the recently initiated program of
combined student pilot and medical certificate
issuance is likely to have the effect of reducing the
“Unknown Purposes” category to insignificant
proportions. However, when it is recognized that
this category is largely made up of airmen who have
not yet soloed, (some airmen who do not require
medical certification are also included, i.e., para-
chutists, glider pilots, etc.) little description is lost
by adding this proportional representation to the

within the respective classes of medical certification.
Conversely, this “Unknown Purposes” category
could still be used to estimate the number of airmen
in future populations who have not yet soloed.

The general aviation population appears to be
much larger than conventional statistical summaries
would indicate (approximately 75-80% of the total
active population). Likewise, the professional,
occupationally related population estimates indicate
a smaller total representation than would be
recognized by conventional summary data. The
active airman population increased rather dramati-
cally (13.4% in the time period observed) while
inactivity remained relatively constant.

The estimation model is presented below and
assumes the availability of medical certification
input:



Currently holds private airman rating. No

previous FAA medical examination, Indicates

nonaeronautical occupation. USAGE CLASSIFI-

CATION: Private or Student Pilot Purposes. -

Case 4. Thirty-nine-year-old male airman issued

second class medical certification May 23, 1966.

Currently holds commercial rating, Previous

FAA medical examination, May 1965. Indicates

occupation as commercial pilot, not self-employed.

USAGE CLASSIFICATION: Commercial Pilot

Purposes.

Case 5. Twenty-four-year-old male airman issued

second class medical certification on June 18, 1965.

Currently holds private airman rating. Previous

FAA medical examination, June 1963. Indicates

nonaeronautical occupation. USAGE CLASSII'I-

CATION: Private or Student Pilot Purposes.

Case 6. Twenty-nine-year-old female issued third

class medical certification September 8, 1966.

Currently holds private airman rating. Date of

previous FAA medical examination, August

1964. USAGE CLASSIFICATION: Private or

Student Pilot Purposes.

The example cases cited serve to illustrate the
technique of usage classification as applied to sample
members within each class of medical certification.
Usage classifications, within each medical class, were
then totaled and the proportions by usage classifi-
cation estimated for each sample class.

Extrapolation to the total study and current
populations was subsequently accomplished to
arrive at estimates, by usage of combined certifi-
cation, of the number of airmen in these populations.

IH. Results

A. Sample Results. The analysis of combined
airman certification factors with respect to sample
members resulted in the following usage relation-
ships within the respective subdivisions:

1. Medically Certified First Class Sample Mem-

bers.

Medically certified first class airmen deter-
mined to be utilizing their medical certifi-
cate for airman purposes requiring a first
class medical certificate amounted to 363 of the
1,476 sample members, or 24.6%. Medically
certified first class airmen usage classified as
requiring only second class medical certifi-
cation totaled 634 of the 1,476 sample mem-
bers, or 42.9%. Medically certified first class
airmen defined as using their certification for

third class purposes amounted to 438 of the
1,476 sample members, or 29.7%. The re-
maining 41 airmen making up the sample
from the first class population could not be
classified as requiring medical certification of
any class. This latter group represents 2.8%
of the 1,476 medically certified first class
airmen sampled.

2. Medically Certified Second Class Sample

Members.

From the sample of 1,047 medically certified
second class airmen, 438 or 41.8% were classi-
fied as utilizing their medical certificate for
airman purposes requiring the second - class
medical certificate. Medically certified second
class airmen usage classified as requiring
third class medical certification totaled 579
of the 1,047 sampled, or 55.3%. The 30
airmen comprising the remainder of those
sampled from this class of medically certified
airmen could not be usage classified as requir-
ing any class of medical certification. These
latter airmen represent 2.9% of the 1,047
sample members.

3. Medically Certified Third Class Sample Mem-

bers.

Sixty-nine of the 73 medically certified
third class airmen comprising the sample were
found to be utilizing their certification for
purposes requiring a third class medical
certificate. This total represents 94.5% of the
73 sample members. The remaining 4 airmen
(5.5%) could not be usage classified as re-
quiring any class of medical certification.

B. Sample Results Extrapolated to the Study
Population and Current Airman Population.5 Apply-
ing the percentages obtained from the sample yields
the following estimates by usage classification with
respect to the three classes of medical certification:

1. The Medically Certified First Class Popu-

lation: The population from which the sample
was drawn included 56,611 medically certified
first class airmen; the current total is 72,155.
Application of the percentage relationships
described in III.A.1 to this subdivision of the
total study and the current populations yield
estimates by usage classification as follows:

|} The reader is reminded that the precision of any estimate from a sample

depends on statistical methodology and ‘sampling error’ as defined in the

sampling plan, Such estimates should thus be viewed as point estimates

within an. acceptable range of accuracy. Reference the Appendix for a
further discussion of desired accuracy. Further reference concerning

“point estimates” is provided in Chapter 1 of Statistical Methods by

George W. Snedecor,




And,
, ’
ay a A
, , ,
=———__ or p' =— =P?
PP Gd Fag Fad mn
,
as a A
, , ,
= =—=P/=
Ps =O Fay) bau! Pets by
a
, ,
a or py == Py! =
ay a3! +40
And,
” ”
ay as” A
” ” ”
= or p3" =——~= P3'
Ps ay’ Fay” BP: Ze
” O
ao A
—* or py! = = 0"
a bay” Po 3

Given these estimates of P and their standard
errors, estimated values for A1, Ae, As, Ao, Ay’, ete.,
were determined. Where A; is the population value
estimated by a;.

In the population,

Ni=Ai= Xi(P1)

No= Ag+ Ad! = X2(P2!) +Xi(P2)
Ng=AgtAs' + As" = Xa(Ps") +Xi(Ps) +X2(Ps’)
No=Ao+Ao’+ Ao” = Xi(Po) +X2(Po’) +Xa(Po")

Or using the estimated proportions, the estimation
model becomes:

A A
Mi=Xi(Pi)
A A A
Nox Xi(Pr) + Xi(Ps) a
A
N 3=X: (Ee) +X; (Ps) +X; o(Ps)
f= xuPo + XP) +KAP = Kit Xot Xs
= (WAN. +N)

Where N ; and py are estimates of population param-
eters.

Sample Size.

The study is concerned with presenting estimates,
not only for the population as a whole, ie., the
proportion of airmen. who obtain medical certifi-
cation commensurate with that required by their
usage classification (P) and the proportion who
acquire medical certification for a higher level
than that dictated by their usage classification (Q)
but also with the presentation of estimates of P,
for the classes of medical certification and in expand-
ing Q; for the classes of medical certification to
indicate the proportions by classification (see for-

il

mulas on pages 10 and 11.) whoseusage classification
dictates another lower class of medical certification,

_ A A RK A A
ie, P2, Ps, Po, and Ps’, and Py’, which make up

é: and oy respectively.

Members of the medically certified airman popu-
lation are identifiable by class of medical certificate
issued. Further a desired variance (V) was defined
with respect to sample proportions (p,). Extracting
from sampling theory as presented by Cochran,
sample size was arrived at as follows: 7

n= Dees

Where ; refers to a subdivision within the popula-
tion. There are eight subdivisions within the active
airman population as indicated on pages 10 and 11
thus eight separate P Q relationships. This amounts
to computing a sample size for each subdivision
within a particular class of medical certification
Another way of expressing this is to say that the
total population may be viewed as three separate
subpopulations and that a sample size was computed
for each of the subdivisions of a class of medical
certification (subpopulation) and summed to get
the sample size from the particular class or sub-
population (n,).

Thus,

where i=0, 1, 2,3

where i=0, 2, 3

Or,
n=mtmtns

Calculations for 7; and n are as follows:

yao

desired variance of the sample proportion

* Coghran, William G... (1953), Sampling Techniques; John Wiley and
Sons, New York, Second Edition, Chapter



The random starting point in the interval 1-153
was 64, Therefore, starting with Second Class
medical record number 64, every koth item or every
153rd record was selected to comprise n2= 1,047.

For ns:

Jeg 3 = 382,594 _ 4 556.1 or 4,556

With a random start in the interval 1-4556 of
434, every 4556th record was selected to comprise
m= 73.

Simple random sampling theory as presented by
Cochran was utilized in a systematic sampling plan
since the alphabetic sequence of the file is unrelated
to the estimates sought by the procedure and since
systematic sampling is a more expeditious means of
sampling from a sequential tape file.

Conjidence Limits.

The normal approximation to the confidence
limits for P;, Ps’, and P;” are presented below as
dictated by the formula:

Pe ['v Tryp bm +39 |

Where f=n/N (the sample fraction) and ¢ is the
normal deviate corresponding to the confidence

probability.?

First Class Estimated Proportions:

A A
Pi=0.246 — Qi=0.754
1476
o.246-[1.064)/1 S6gT
{4 OH
1476-1" 2(1476)
0.18548, 1
o2s62[}. 96 1=0.02607 “475 +35]

0.2464 [1.96-/0.97393-V/ 0.000125 +.0.000339]
0.2464:[1.96 (0.987) (0.0112) +0.000339]
0.246-£[1.96 (0.011054) +0.000339]

* Cochran, William G. (1058), Sampling, Techniques; Jol Wiley and
Sons, New York, Second Edition, Chapter 4

13

0.246 +-[(0.021666 +0.000339)]

0.246 40.022 .
Pry=0.268 By =0.224
Second Class Estimated Proportions:
A nN
Px =0.418 Qe’ =0.582
1047
0.4184 | 1. Peaks
[1.064 160,682
y¥@ 418) (0.582), 1
1047-1 sao
————- {0.243276 , 1
0.4184] 1. = onay
+[1.06vi 0.00652 W546 +a

0.418+[1.96-/0.99348 0.000232 +-0.000478]

0.418+[1.96 (0.997) (0.0152) +-0.000478]

0.4184-[1.96 (0.015154) +0.000478]

0.418-+[ (0.029702 +-0.000478)]

0.4184:0.030
Py=0.448 Phe =0.388

Third Class Estimated Proportions:

=0.945 Qs" =0.055

Py
0.9454 [}: 964y1- js
332,504
V2 945) (0.055), _1
73-1 aH

0454 | 1.96-/T=0,0000T9 «| 2.051975 isl
o.045-+[ 1.96 1 0.000215 a3 Tae

0.945 +-(1.96-/0.999781 V/0.000722+ 0.006849]
0.945-£[1.96 (0.999) (0.0269) +0.006849]
0.945-£[1.96 (0.026873) +-0.006849}

0.9454 {(0.052671-+-0.006849)]

0.945 40.060

nN rN
Piy=1.000 Ph, = 0.885

CUS. GOVERNMENT PRINTING OFFICE: 1968 O—309-340



TABLE OF CONTENTS

Page
I. INTRODUCTION
II. METHODOLOGY
A. ‘The Problem Statement.
B. Sample Members_-..---.-
CG. An Example of Usage Classification Applied to Sample Members.

Wl. RESULTS....--
A. Sample Results -
B. Sample Results Extrapolated to the Study Population and Current Airman
Population.
C. Total Population Estimates by Usage Classification.

RR we

eNO

LIST OF TABLES

Table Page

I. Medically Certified First Class Airmen by Usage Classification.
Il. Medically Certified Second Class Airmen by Usage Classification.
III. Medically Certified ‘Third Class Airmen by Usage Classification
TV. Study Population Estimates by Usage Classification.
V. Current Population Estimates by Usage Classification -_
VI. Medically Certified Airman Population Summary (October 1, 1968)
VII. Medically Certified Airman Population Summary (October 1, 1967)

NI Beaan

LIST OF FIGURES

Figure Page
1 Minimum Medical Certification Required for Operational Usage of Airman Ratings. - 1
2 Classification of Airman/Medical Certification Usage



ACKNOWLEDGMENT

This study is from the Civil Aeromedical Institute, Medical Statistical Section,
Federal Aviation Administration, Oklahoma City, Oklahoma.

The author wishes to express his gratitude to John IF, MeCoy, Ph.D., and Mrs.
Margaret Shackelford, M.S., of the University of Oklahoma Medical Center,
Biostatistical Unit, for their appraisal and comments. Appreciation is also extended
to Miss Shirley Dark for her assistance in typing and preparation of this study.

The opinions and conclusions contained in this report are those of the author

and should not be construed as reflecting the views or endorsement of the Federal
Aviation Administration.

Qualified requesters may obtain Aviation Medical Reports from Defense Documentation Center.
The general public may purchase from Clearinghouse for Federal Scientific and Technical
Information, U.S. Dept. of Commerce, Springfield, Va. 22151.


APPENDIX

Statistical Methodology.

This appendix has been included to present further
details with respect to (1) the population estimation
model, (2) sample size determination, (3) sample
design as concerns the study, and (4) confidence
limits of estimated proportions. The estimation of
the proportions mentioned in ILA of the study
along with the known medical certification status
of active airmen resulted in the population estimates
presented in the “Results” portion of the study.
This appendix will provide the reader with further
insight as to the logic and methodology applied in
arriving at those estimates.

The Population Estimation Model by Usage Classifi-
cation.

The following definitive relationships exist. with
respect to the active airman population and propor-
tions mentioned above:

N=NitNot+NstNo

Where N equals the active airman population:
N, equals the number of airmen in the usage classifi-
cation of airline transport purposes; N2 equals the
number of airmen in the usage classification of
commercial purposes, including co-pilots, flight
engineers, flight navigators, flight instructors, con-
trol tower operators, and military pilot personnel;
N; equals the number of airmen in the usage classifi-
cation of private or student purposes; and No equals
the number of medically certified airmen whose
airman rating is unknown and, therefore, whose
usage classification is also unknown.

Also,
N=X+X2tXs

Where X; equals the number of medically certified
first class airmen; Xz equals the number of medically
certified second class airmen; and X; equals the
number of medically certified third class airmen.
Therefore,

NitNot+NstNo=XitX2tXs
X= Xi(Pit Pot Pot Po)

Where P; equals the proportion of medically
certified first class airmen who are usage classified
under airline transport purposes and, therefore,
require first class medical certification; P» equals
the proportion of medically éertified first class
airmen who are usage classified under commercial
purposes and, consequently, require second class
medical certification; P; equals the proportion of
medically certified first class airmen who are usage
classified under private or student purposes and thus
require third class medical certification; and Po
equals the proportion of other medically certified
first class airmen whose airman rating and usage
classification are unknown or who do not require
medical certification of any class, i.e., parachutists,
mechanics, ete.

X2=X2(P! + Ps’ +Po’)

Where P,! equals the proportion of medically
certified second class airmen who are usage classified.
under commercial purposes, thus requiring second
class medical certification; P;’ equals the proportion
of medically certified second class airmen who are
usage classified under private or student purposes
and, therefore, require third class medical certifi-
cation; and Py’ equals the proportion of other
medically certified second class airmen whose
airman rating and usage classification are unknown
or who do not require medical certification of any
class.

X= Xa(Ps!+Po')

Where P;’ equals the proportion of medically
certified third class airmen who are usage classified
under private or student purposes and, therefore,
require third class medical certification; and Po’
equals the proportion of other medically certified
third class airmen whose airman rating and usage
classification are unknown or who do not require
medical certification of any class.



Where,

d=5.0% (Sample Error)
t=1.96 (95% Confidence)
0.0025

V=—F eq = 0-000651

For m, (the sample size from medically certified

First Class airmen):

—P: Q_ (0.60) (0.40)
v 0.000651

mm = 368.7 or 369

tg = OO) (0-40) _ 368.7 or 369

= Ps Qs_ (0.60) (0.40) _
mag = age, 368.7 or 369
_ Po Qo_ (0.60) (0.40)
0.000651

Where my is the expected sample size from the
subdivision of First Class medically certified airmen

‘m9 = 368.7 or 369

who are represented by & =P, (See page 10).
1

M2, M13, and mo respectively indicate the expected
sample size from the remaining three classifications
possible among medically certified First Class

airmen. Remember here that By, Py and Py make up
A
Q: for this class.
Therefore,
m= 1476

For m2, (the sample size from medically certified
Second Class airmen):
Ps! Qe! _ (0.65) (0.35) _

a= = os BI = 349.4 or 349

_ Py Qs _ (0.65) (0.35) _
t= 7 000651 = 349.4 or 349

— Po! Qo’ _ (0.65) (0.35) _
T= ~D.000651 = 349.4 or 349

Where nz equals the expected sample size from
the subdivision of Second Class medically certified

fo A
airmen who are represented by et = P2/. Qo is made
A A °
up of Ps’ and Py’.

Therefore,
n= 1047

For ms, (the sample size from medically certified
Third Class airmen):

_ Pat Qs’ _ (0.95) (0.05) __ 0.0475
V ~~ 0.000651 0.000651

This situation differs from those presented for

Ns = 72.9 or 73

m and nz because By and Ov" are the only classifi-
cations present in third class medically certified
airmen for which the specified variance (V) was
required,

Summing for m, m2, and ns:

n= pei @i, pP!

Ql SPs" Qs"
+phi ot

Or,
n=mtntns
n=1476+1047+73
n= 2596

In effect, the eight subdivisions were summed to
realize n.

n; equals the sample size required from each class
of medical certification. Therefore, m equals 2,
ne equals x2, and ns equals 3, in terms of the notation
presented on pages 10 through 12.

Sample Design.

The sample size determined above considers that
a desired variance has been defined with respect
to the several proportions of interest among the
classes of medical certification.

Following a scheme of systematic sampling,
every kth item was selected as dictated by the
considerations set forth above with respect to
sample size among classes of medical certification.®

k, is defined as x,
ua

Therefore,
ky=— =" = 38.4 or 38

From a table of Random Numbers a starting
point of 2 was selected within the interval 1-38.
Hence, starting with the second First Class medical
record on the active master tape file, every 38th
record was selected for enclosure in the sample,
i.e., 2, 40, 78, 116, ete.

Similarly, for ne:

kg=— => = 153.4 or 153

* Neiswanger, William A, (1956). Elementary Statistical Methods; The
MacMillan Company, New York, Revised Edition, Chapter 4.