U.S. Department of Education

NCES 2006–605

User’s Guide to 

Computing High School 

Graduation Rates

Volume 2

Technical report: Technical 

Evaluation of Proxy Graduation 

Indicators

U.S. Department of Education

NCES 2006–605

User’s Guide to 

Computing High School 

Graduation Rates

Volume 2

Technical report: Technical 

Evaluation of Proxy Graduation 

Indicators

August 2006

Marilyn M. Seastrom

Chris Chapman

National Center for Education Statistics

Institute of Education Sciences 

Robert Stillwell

Daniel McGrath

Pia Peltola

Rachel Dinkes

Zeyu Xu 

Education Statistics Services Institute
U.S. Department of Education

Margaret Spellings 

Secretary

Institute of Education Sciences

Grover J. Whitehurst

Director

National Center for Education Statistics

Mark Schneider

Commissioner

The National Center for Education Statistics (NCES) is the primary federal entity for collecting, analyzing, 

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August 2006

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Suggested Citation

Seastrom, M., Chapman, C., Stillwell, R., McGrath, D., Peltola, P., Dinkes, R., and Xu, Z. (2006). User’s 

Guide to Computing High School Graduation Rates, Volume2: Technical Evaluation of Proxy Graduation 

Indicators (NCES 2006-605). U.S. Department of Education, National Center for Education Statistics. 

Washington, DC: U.S. Government Printing Office.

For ordering information on this report, write to

U.S. Department of Education

D Pubs

P.O. Box 1398

Jessup, MD 20794-1398

or call toll free 1-877-4ED-Pubs or order online at http://www.edpubs.org. 

Content Contact

Marilyn Seastrom

(202) 502-7303

Marilyn.Seastrom@ed.gov
 

 

iii 

Executive Summary 

The increased focus on accountability in education in recent years has resulted in a growing 

interest in the accurate measurement of an on-time high school graduation rate. In fact, the No 

Child Left Behind Act of 2001 included an on-time graduation rate as an accountabilityreporting requirement. The accurate reporting of such a rate requires student record data on 

student progression from grade to grade, data on graduation status, and data on students who 

transfer in and out of a school, district, or state during the high school years, or in other words 

cohort data (National Institute of Statistical Sciences (NISS) 2004 Task Force, NCES 2005-

1105). At the time the on-time graduation rate reporting requirement was enacted, few states 

had data collection systems adequate to support the calculation of an accurate on-time 

graduation rate. 

Absent the required cohort data, existing measures of high school completion have been 

considered and a number of new proxy graduation indicators have been proposed. The existing 

high school completion measures rely on cross-sectional data, but do not focus uniquely on ontime graduation and thus are not adequate for a measure of on-time graduation. Each of the 

newly proposed proxy measures can be calculated using existing cross-sectional data, but each 

requires a set of assumptions to bridge the gap from cross-sectional data to the desired cohort 

rate. Recognizing the need for an interim measure to use while individual states develop 

student record systems, the leadership in the Department of Education asked NCES to evaluate 

the array of current and proposed graduation indicators. This two-volume report describes that 

effort. 

The first volume of this report examines the existing measures of high school completion and 

the newly proposed proxy measures. This includes a description of the computational 

formulas, the data required for each indicator, the assumptions underlying each formula, the 

strengths and weaknesses of each indicator relative to a true cohort on-time graduation rate, 

and a consideration of the conditions under which each indicator does or does not work. 

The second volume of this report provides documentation of the technical work that the 

Department leadership used to select an interim graduation rate. The analysis in volume 2 

draws upon the student record data from two states to compute the true cohort on-time 

graduation rate for each of those states, to compute the proxy graduation measures for each of 

these states, and to compare the performance of each proxy indicator to that of the true cohort 

rate. State and school district level rates were computed for three graduating classes in State 1 

and four graduating classes in State 2. A combination of descriptive univariate statistics and 

regression analyses were employed. Although each of the four proxy measures of on-time 

graduation rates— the Freshman Graduation Rate (FGR) indicator, the Averaged Freshman 

Graduation Rate (AFGR) indicator, the Green Graduation Indicator (GGI), and the Swanson 

Cumulative Promotion Indicator (SCPI), perform well relative to the true cohort rate (EACGI) 

in one or more of the analyses, AFGR is the only measure that is consistently among the best 

performing indicators in each analysis. 
 

 

iv 

Building on the performance of the Averaged Freshman Graduation Rate in the student record 

data comparisons from States 1 and 2, this rate was taken as the standard for comparison and 

the performance of this rate was compared to that of the other three proxy graduation rate 

measures using cross-sectional data for the 50 states and the District of Columbia for rates 

computed at the national and state levels. First, it was shown that in States 1 and 2 each of the 

four proxy measures computed using cross-sectional data correlate strongly with the same 

proxy measures computed using student record data and that the four proxy measures 

computed using cross-sectional data show the same patterns of correlation with the true cohort 

on-time graduation rate that were observed with the proxy measures computed using the 

student record data. Next, the analyses that compared the performance of each proxy 

graduation measure to the true cohort-on-time graduation rates in States 1 and 2 were repeated 

at the national and state levels comparing the performance of the other three proxy graduation 

rate measures to that of the Averaged Freshman Graduation Rate. The relative performance of 

each of the proxy measures repeated the patterns observed in the two states, with the 

performance of the Freshman Graduation Rate most closely approximating that of the 

Averaged Freshman Graduation Rate, and with weaker associations with the Greene 

Graduation Indicator and then with the Swanson Cumulative Promotion Indicator. 
 

 

v 

Preface 

The fact that graduation rates are an important indicator of students’ performance in American 

schools was highlighted by the inclusion of an on-time high school graduation rate in the 

monitoring requirements included in the 2001 No Child Left Behind Act. Unlike the 

assessment measures called out in the law, the calculation of an on-time graduation rate 

requires data that do not exist in most states. An on-time high school graduation rate requires 

data on student progression from grade to grade, data on graduation status, and data on students 

who transfer in and out of a school, district, or state during the four year period—in other 

words a student record system. 

Absent the data required to compute an accurate on-time cohort high school graduation rate, a 

number of researchers have proposed different formulations that rely on existing data to 

estimate proxy indicators of high school graduation rates. Each measure is unique with it’s own 

positive and negative attributes. In an attempt to sort out the various measures, the National 

Center for Education Statistics, on behalf of the Department of Education, asked the National 

Institute of Statistical Sciences (NISS) to convene a 2004 Task Force of experts to examine the 

array of measures and provide a recommendation for the calculation of graduation rates. The 

NISS Task Force concluded that the only way to accurately measure high school graduation 

rates in a mobile society like the United States is through the development and use of student 

record systems. They provided detailed specifications for the true cohort rate that will yield an 

accurate on-time graduation rate, and recommended that NCES work with the states to move 

the implementation forward (NCES 2005-105). 

At that time, seven states reported that they had statewide student record systems in place, and 

a number of other states were in the planning and early developmental stages. Recognizing 

that even if all 50 states were to start collecting the required data elements for the cohort ontime graduation rate in the 2005-06 school year, the country would still be 4 years away from 

having one consistent graduation rate measure across the states, leadership in the Department 

of Education asked NCES to further evaluate the array of current and proposed graduation 

indicators. This report describes that effort. 

This report consists of two volumes, the first takes an in-depth look at the various graduation 

indicators, with a description of the computational formulas, the data required for each 

indicator, the assumptions underlying each formula, the strengths and weaknesses of each 

indicator, and a consideration of the conditions under which each indicator does or does not 

work. In addition to the discussion in the body of the text, there is a summary description of 

each indicator and an accompanying spreadsheet that can be used to compute each indicator in 

appendix A. 

The second volume of this report is more technical in nature. The analysis presented in this 

volume of the report provided the technical basis that Department policy makers used to 

identify an interim graduation indicator. Thus, using the information from volume 1 as a 

backdrop, volume 2 uses the best available national and state data to provide estimates of the 
 

 

vi 

various indicators. While this provides some basis for drawing comparisons across the 

indicators, the comparative analysis relies most heavily on student record data from two 

individual states. The state data represent the universe of students enrolled in public schools in 

each state over a sufficient number of years to compute the true cohort rate. The NISS panel 

recommended the true cohort rate as the only rate that will yield an accurate on-time 

graduation rate. The true cohort rate is thus used as the “gold standard” for a comparison of 

the performance of the various graduation indicators for the two individual states. The analysis 

of the state student record data then served as a basis for a related analysis of proxy graduation 

indicators computed for all 50 states and the District of Columbia at the national and state 

levels using NCES Common Core of Data. 
 

 

vii 

Acknowledgments 

The authors wish to acknowledge the contribution of many individuals to the development of 

this report. Several staff members at NCES provided significant substantive contributions to 

the content of the report including Lee Hoffman, Jeff Owings, and Val Plisko. Staff at the 

Education Statistics Services Institute (ESSI) helped test and verify estimates in the report, and 

helped with the final report layout. Contributors from ESSI included Kevin Bromer, Aparna 

Sundaram, Janine Emerson, and Devin Carlson. We would also like to thank the careful 

review provided by Anne Ricciuti at the Institute of Education Sciences along with the 

comments provided by several anonymous reviewers. Their comments were thought 

provoking and greatly improved the report. Finally, we would like to thank Fiona Edler at 

Synergy Systems for her careful review of the release copy of the report. 
viii 

Contents 

Page 

Executive Summary....................................................................................................... iii 

Preface............................................................................................................................ v 

Acknowledgements........................................................................................................ vii 

List of Tables ................................................................................................................. ix 

List of Figures................................................................................................................ xii 

Chapter 1: Introduction.................................................................................................. 1 

Chapter 2: An Application of the Proxy Graduation Indicators and the True Cohort 

aaaRate Using Data From the Student Record System in State 1.................................. 5 

 2.1. State-Level Analysis ................................................................................... 5 

 2.2. School District-Level Analysis................................................................... 10 

 2.3. Summary..................................................................................................... 25 

Chapter 3: An Application of the Proxy Graduation Indicators and the True Cohort 

aaaRate Using Data From the Student Record System in State 2.................................. 27 

 3.1. State-Level Analysis ................................................................................... 27 

 3.2. School District-Level Analysis................................................................... 31 

 3.3. Summary..................................................................................................... 47 

Chapter 4: An Application of the Proxy Graduation Indicators Using Data From the 

 NCES Common Core of Data.................................................................................. 49 

 4.1. Using student record findings for the analysis of CCD data ...................... 52 

 4.2. Graduation indicators at the national level ................................................. 58 

 4.3. Graduation rates at the state level ............................................................... 62 

 4.4. Graduation rates at the district level ........................................................... 74 

 4.5. Summary..................................................................................................... 75 

Chapter 5: Conclusions.................................................................................................. 77 

References...................................................................................................................... 83 

Appendix A: Notes regarding analyses of student-tracking systems in two states........ A-1 

Appendix B: Analysis of Change Component of Greene Graduation Indicator ........... B-1 
ix 

List of Tables 

Table Page 

1.1. Formulas and definitions for the graduation rate proxy indicators ...................... 4 

2.1. Graduation indicators EACGI, CGI, IAGI, FGR, AFGR, GGI, GLI, and 

SCPI for State 1, by year: 2000-01 through 2002-03........................................... 7 

2.2a. Mean, standard deviation, minimum, 25th percentile, median, 75th 

percentile, and maximum of graduation indicators across school districts in 

State 1, by indicator and school year: 2000-01 through 2002-03 ....................... 11 

2.2b. Absolute difference relative to EACGI for mean, standard deviation, 

minimum, 25th percentile, median, 75th percentile, and maximum of 

graduation indicators across school districts in State 1, by indicator and 

school year: 2000-01 through 2002-03 ............................................................... 13 

2.3. Diagnostic statistics of the distribution of EACGI, FGR, AFGR, GGI, SCPI 

and GLI across school districts in State 1: 2000-01 through 2002-03 ................. 14 

2.4. Regression estimates of EACGI on proxy graduation indicators across 

school districts in state 1, by indicator and school year: 2000-01 through 

2002-03................................................................................................................. 19 

2.5. Regression estimates of school district-level graduation indicators in state 1, 

by indicator: 2000-01 through 2002-03 ............................................................... 24 

3.1. Graduation indicators EACGI, FGR, AFGR, GGI, and SCPI for state 2, by 

year: 1999-2000 through 2002-03....................................................................... 28 

3.2a. Mean, standard deviation, minimum, 25th percentile, median, 75th 

percentile, and maximum of graduation indicators across school districts in 

state 2, by indicator and school year: 1999-2000 through 2002-03 ..................... 32 

3.2b. Absolute differences relative to EACGI for mean, standard deviation, 

minimum, 25th percentile, median, 75th percentile, and maximum of 

graduation indicators across school districts in State 2, by indicator and 

school year: 1999-2000 through 2002-03 ............................................................ 33 

3.3. Diagnostic statistics of the distribution of EACGI, FGR, AFGR, GGI and 

 SCPI across school districts in State 2: 1999-2000 through 2002-03 .................. 35 
x 

List of Tables 

Table Page 

3.4 Regression estimates of the true cohort rate, EACGI, on proxy graduation 

indicators, across school districts in state 2, by indicator and school year: 

1999-2000 through 2002-03................................................................................. 40 

3.5 Regression estimates of school district-level graduation indicators in state 2 

across years, by indicator: 1999-2000 through 2002-03 ...................................... 47 

4.1. Regression estimates of State 1 student record school district estimates on 

State 1 CCD school district estimates for graduation indicators FGR, 

AFGR, GGI, and SCPI, by school year: 2000-01 and 2001-02 ........................... 53 

4.2. Regression estimates of State 1 student record school district estimates for 

EACGI on State 1 CCD school district estimates, by indicator and school 

year: 2000-01 through 2001-02............................................................................ 54 

4.3. Regression estimates of State 2 student record school district estimates on 

State 2 CCD school district estimates for FGR, AFGR, GGI, and SCPI, by 

school year: 1999-2000 through 2001-02 ............................................................ 55 

4.4. Regression estimates of State 2 student record school district estimates for 

EACGI on State 2 CCD school district estimates, by indicator and school 

year: 1999-2000 through 2001-02........................................................................ 56 

4.5. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, 

and SCPI with all indicators calculated using CCD data for State 1, by 

school year: 2000-01 and 2001-02 ....................................................................... 57 

4.6. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, 

and SCPI with all indicators calculated using CCD data for State 2, by 

school year: 1999-2000 through 2001-02 ............................................................ 58 

4.7. National graduation indicators, by year and indicator: 1995–96 through 

2001–02................................................................................................................ 59 

4.8. Graduation indicators, by indicator and state: School year 1995-96 ................... 64 

4.9. Graduation indicators, by indicator and state: School year 1996-97 ................... 65 

4.10. Graduation indicators, by indicator and state: School year 1997-98 ................... 66 

4.11. Graduation indicators, by indicator and state: School year 1998-99 ................... 67 
xi 

List of Tables 

Table Page 

4.12. Graduation indicators, by indicator and state: School year 1999-2000 ............... 68 

4.13. Graduation indicators, by indicator and state: School year 2000-01 ................... 69 

4.14. Graduation indicators, by indicator and state: School year 2001-02 ................... 70 

4.15. Minimum, maximum, range, and mean graduation indicator across years, by 

indicator and state: 1995-96 through 2001-02 ..................................................... 71 

4.16. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, 

and SCPI across states, by indicator and school year: 1995-96 through 

2001-02................................................................................................................. 73 

B-1. Number of freshmen students in the public schools in the United States: 

1990-91 through 2001-02..................................................................................... B-2 

B-2. Rate of change components of Greene graduation indicator and resulting 

estimates: 1995-96 through 2001-02.................................................................... B-2 
xii 

List of Figures 

Figure Page 

 

2.1. Estimates of graduation indicators EACGI, FGR, AFGR, GGI, GLI, SCPI 

in State 1: 2000-01 through 2002-03.................................................................... 8 

2.2. Distance, in percentage points, of each graduation indicator FGR, AFGR, 

GLI, GGI, and SCPI from the true cohort rate EACGI in State 1: 2000-01 

through 2002-03 ................................................................................................... 9 

2.3. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, GLI, and SCPI, by decile in State 1: 2000-01............................................ 15 

2.4. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, GLI, and SCPI, by decile in State 1: 2001-02............................................ 16 

2.5. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, GLI, and SCPI, by decile in State 1: 2002-03............................................. 17 

2.6. Distribution of the size of the absolute distance, in percentage points, 

between graduation indicators FGR, AFGR, GGI, SCPI, and the true 

cohort rate EACGI for school districts in State 1: 2000-01 ................................. 21 

2.7. Distribution of the size of the absolute distance, in percentage points, 

between graduation indicators FGR, AFGR, GGI, SCPI, and the true 

cohort rate EACGI for school districts in State 1: 2001-02 ................................. 22 

2.8. Distribution of the size of the absolute distance, in percentage points, 

between graduation indicators FGR, AFGR, GGI, SCPI, and the true 

cohort rate EACGI for school districts in State 1: 2002-03 ................................. 23 

3.1. Estimates of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI 

in State 2: 1999-2000 through 2002-03................................................................ 29 

3.2. Distance, in percentage points, of each graduation indicator FGR, AFGR, 

GGI, and SCPI from the true cohort rate EACGI in State 2: 1999-2000 

through 2002-03 ................................................................................................... 30 

3.3. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, and SCPI, by decile in State 2: 1999-2000 ................................................. 36 

3.4. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, and SCPI, by decile in State 2: 2000-01 ..................................................... 37 
xiii 

List of Figures 

Figure Page 

 

3.5. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, and SCPI, by decile in State 2: 2001-02 ..................................................... 38 

 

3.6. Percentile distribution of graduation indicators EACGI, FGR, AFGR, 

GGI, and SCPI, by decile in State 2: 2002-03 .................................................... 39 

3.7. Distribution of the size of the absolute distance, in percentage points, 

between FGR, AFGR, GGI, SCPI and the true cohort rate EACGI for 

school districts in State 2: 1999-2000 .................................................................. 42

3.8. Distribution of the size of the absolute distance, in percentage points, 

between FGR, AFGR, GGI, SCPI and the true cohort rate EACGI for 

school districts in State 2: 2000-01 ...................................................................... 43

3.9. Distribution of the size of the absolute distance, in percentage points, 

between FGR, AFGR, GGI, SCPI and the true cohort rate EACGI for 

school districts in State 2: 2001-02 ...................................................................... 44

3.10. Distribution of the size of the absolute distance, in percentage points, 

between graduation indicators FGR, AFGR, GGI, and SCPI and the true 

cohort rate EACGI for school districts in State 2: 2002-03 ................................. 45

4.1. National graduation rates for FGR, AFGR, SCPI, and GGI: 1995-96 

through 2001-02 ................................................................................................... 61 

 

1 

Volume 2 

Technical Evaluation of Proxy Graduation Indicators 

Chapter 1 

The first volume described the data elements included in each proxy graduation indicator, 

illustrated how to calculate each indicator, and discussed potential limitations. This 

volume of the report provides the technical information base used by Department policy 

makers in identifying an interim graduation indicator to use in monitoring progress under 

the No Child Left Behind Act. With the information from Volume 1 as a backdrop, this 

volume evaluates the performance of the subset of proxy indicators that can be calculated 

using existing public school data. 

The National Institute of Statistical Sciences (NISS) Task Force on graduation and 

dropout rates, convened by NCES on behalf of the Department of Education, identified 

the true cohort on-time graduation rate—that is, the Exclusion-Adjusted Cohort 

Graduation Rate (EACGI) as the most accurate graduation rate. Taking the true cohort 

on-time graduation rate as the gold standard, the goal of the analyses in this volume is to 

determine which proxy graduation indicator best approximates the true cohort on-time 

graduation rate. This evaluation is done first using data from the student record systems 

of two states to compare the performance of the proxy indicators with the true cohort ontime graduation rates computed for those states, and second, looking more broadly at the 

performance of the proxy graduation indicators for the nation and individual states. 

The recommended true cohort on-time graduation indicator, the EACGI, uses data from 

an individual student record system to take all possible changes in status into account, 

following the movement of students from one entering class of first-time 9th-graders (i.e., 

a cohort), new entrants to that class, and exits from that class over time as the students 

progress towards graduation (table 1.1). This indicator requires counts of first-time 9thgraders; counts of students who leave the 9th grade and each successive grade during the 

high school years due to documented transfers, imprisonment, or death (i.e., exclusions); 

counts of transfers in to the 9th grade and each successive grade during the high school 

years; and counts of graduates for the first-time 9th-graders who started in the class and 

for students who transferred in to the class. 

The array of proxy graduation indicators described in volume 1 uses different 

combinations of aggregate counts of year- and grade-specific enrollments (grades 8-12), 

year-specific graduates, and in the case of the Common Core of Data Graduation Leaver 

Indicator (CCD GLI), year- and grade-specific dropouts (grades 9-12). The formulas for 

the proxy graduation indicators are included in table 1.1. 

The data required to compute the true cohort on-time graduation rate are not currently 

available at the national level. However, the best way to evaluate the performance of the 

proposed proxy graduation indicators is to compare the estimates computed for the proxy 

indicators with the values of the true cohort rate computed for the same population. In 

order to conduct such an analysis, NCES staff identified states that have had student 
 

2 

record systems in place for enough years to have the data elements needed to compute the 

recommended true cohort on-time graduation rate for several years—the cohort 

graduation indicator (EACGI). 

Two states meeting these criteria agreed to provide their data. NCES then worked with 

staff in the state education departments for the two states to acquire the data, and used the 

state data to compute the true cohort rate and the proxy indicators. Since the proxy 

measures are each designed to estimate the true cohort on-time graduation rate, the 

individual proxy indicators computed for these two states can be compared to their true 

cohort rates to evaluate how well each of the proxy indicators performs relative to the 

true cohort rate. This is done by comparing the distributional characteristics of the 

various indicators to those of the true cohort rate, by examining the correlations between 

each proxy indicator and the true cohort rate, by examining the amount of variation in 

each proxy measure that is explained by its association with the true cohort rate, and by 

examining the amount of error in each indicator measured as the distance from the true 

cohort estimate for the same population. 

The computation of the true cohort on-time graduation rate from the available data in the 

two states was informative. While the effort succeeded in yielding estimates of the 

cohort rate for these two states, the processes required to manipulate the data helped 

identify the level of specificity required in record keeping and data documentation to 

successfully use student-record system data. In particular, different approaches to student 

record keeping were used in each of the states. One state utilizes a centralized state-level 

system with unique records for individual students, whereas the other state utilizes a more 

decentralized system in which the records are maintained at the district level and 

consolidated for reporting at the state level. 

Both systems presented definitional problems concerning how to define first-time 

freshmen and how to define regular graduates. They also raised questions about which 

year’s cohort to assign transfers to when it is not known if transfer students had been 

retained since first enrolling in the 8th grade, or in what high school grades they have 

been retained; which year’s cohort to assign students to when they switched grades 

within a year; and how to assign students who transfer or otherwise leave a state when 

their records are inconsistent. In addition, there were some difficulties with multiple 

identifiers for individual students in the state with the decentralized student record 

system. In each case, decisions were reached and the data were processed consistently in 

light of the decisions. (See appendix A for additional details on the specific problems and 

their resolutions.) 

The analytic results from the state with the centralized individual student record system, 

State 1, are presented in chapter 2 and those for the state with the decentralized districtbased individual student record system are presented in chapter 3. 

Chapter 4 includes a broader look at the performance of the proxy graduation indicators 

for the nation and individual states. Here, currently available data from the Common 

Core of Data are used to compute the proxy graduation rates for the nation and states over 

the 7-year period from 1995-96 through 2001-02. This analysis draws upon the findings 
 

3 

from Chapters 2 and 3, by comparing the Averaged Freshman Graduation Rate (AFGR) 

indicator that was identified as the closest approximation of the true cohort rate 

performance to the other proxy graduation indicators—Freshman Graduation Rate (FGR) 

indicator, Greene Graduation Indicator (GGI), and Swanson Cumulative Promotion 

Indicator (SCPI). These comparisons are done at the national, state, and school district 

levels. 
 

4 

Formula:

Where: S9 = Number of first-time 9th-graders

C =

G =

TI =

E =

Formula:

Where: G =

Y =

S'9,y-3 =

Where:

S'9,y-3 = Smoothed estimator for first-time 9th-grade enrollment

Formula:

Where: G =

Y =

S*

9 =

Formula:

Where: ( 1 + ∆PHS ) * ( S'9,y-3 )

Where: G = Number of graduates receiving a regular diploma

Y = School Year

Sgrade = Number of students enrolled in a specific grade

∆PHS = High school population change over 4-year period

S'9,y-3 = Smoothed estimator for first-time 9th-grade enrollment

Formula:

S11,y+1 S12,y+1 Gy

S10,y S11,y S12,y

Where: Sgrade =

Y =

G =

Exclusion-Adjusted Cohort Graduation Indicator (EACGI)

EACGI=

 S9,cGc+3+TI9,cGc+3+TI10,c+1Gc+3+TI11,c+2Gc+3+T12,c+3Gc+3 

(S9,c - Ec,c+1,c+2, c+3) + (TI9,c - Ec,c+1,c+2, c+3) + (TI10,c+1 - Ec+1,c+2, c+3) + (TI11,c+2 - Ec+2,c+3) + (TI12,c+3 - Ec+3)

Cohort school year (i.e., the school year a student entered high school)

Number of graduates receiving a regular diploma

Number of students transferring into a grade level

Number of students excluded (documented transfers to state-designated diploma 

granting programs, death, or imprisonment)

Number of graduates receiving a regular diploma

School Year

Averaged Freshman Graduation Indicator (AFGR)

Freshman Graduation Indicator (FGR)

UGI =

Gy 

S9,y-3

S8,y-4 + S9,y-3 + S10,y-2

3

Swanson's Cumulative Promotion Indicator (SCPI)

UGI0 = Gy 

S

*

9,y-3

Number of graduates receiving a regular diploma

GGI =

Gy 

S'12,y

School year

Number of all 9th-grade students

Greene's Graduation Indicator (GGI)

S'9,y-3 = S8,y-4 + S9,y-3 + S10,y-2

3

S'12,y =

∆PHS = ( S9,y + S10,y + S11,y + S12,y ) - ( S9,y-3 + S10,y-3 + S11,y-3 + S12,y-3 )

( S9,y-3 + S10,y-3 + S11,y-3 + S12,y-3 )

Table 1.1. Formulas and definitions for the graduation rate proxy indicators 

School year

Number of graduates receiving regular diplomas

* *

S9,y

Number of students in a specified grade

SCPI = 

S10,y+1 *
 

5 

Chapter 2

An Application of the Proxy Graduation Indicators and the True 

Cohort Rate Using Data From the Student Record System in State 1 

Student records from State 1 were used to compute the true cohort on-time graduation 

rate (EACGI) and each of the other school based measures—Freshman Graduation Rate 

based on all freshmen (FGR), Averaged Freshman Graduation Rate based on first-time 

freshmen (AFGR), Greene’s Graduation Indicator (GGI), Swanson’s Cumulative 

Promotion Indicator (SCPI), and CCD Graduation Leaver Indicator (GLI). 

The individual student record system data were used to compute rates for EACGI at the 

state and school district levels for school years 2000-01, 2001-02, and 2002-03. Then, the 

individual student record data were aggregated to the school district and state levels and 

the five school-based indicators described in volume 1 (FGR, AFGR, SCPI, GGI, and 

GLI) were computed.1

 It is essential that the proxy indicators were computed using the 

aggregated measures described in volume 1 because the goal of this analysis is to 

evaluate the proxy indicators computed using the aggregated cross-sectional data that are 

currently available for most states. For example, the estimate for first-time freshmen was 

computed using average of the numbers of 8th-, 9th-, and 10th-graders in consecutive 

school years, rather than substituting the true estimate of first-time 9th-graders, and the 

annual counts of graduates were used rather than substituting the true estimate of on-time 

graduates. 

2.1. State-Level Analysis 

In State 1, the available student record data were used to track individual students 

enrolled in regular school districts over time—first-time freshmen were identified, 

adjustments were made for cohort exclusions and transfers in and out of the state over the 

high school years, and on-time graduates from these students were counted. The resulting 

number of on-time graduates was divided by the number of students in the exclusion- and 

transfer-adjusted cohort of freshmen that started high school 4 years earlier. This yielded 

true cohort on-time graduation rates of 60.5 in 2000-01, 62.6 in 2001-02, and 63.0 in 

2002-03—for an average rate of 62.1 percent. Thus, about 62 percent of the cohort of 

freshmen classes in this state graduated on time (table 2.1). 

As indicated above, data from student records can be used to compute both the 

recommended true cohort rate and the set of proxy graduation indicators to provide a 

basis for evaluating the performance of each of the proxy measures relative to the true 

 

1

 Consideration was given to extending this analysis to the school level, however there were two constraints 

that led to a decision to not pursue this analysis at the school level. First, approximately two-thirds of the 

students in grades 9-12 in State 1 attended schools that did not include the 8th grade. As a result, because 

the calculation of the estimated number of freshmen that is used to compute AFGR and GGI requires a 

count of the number of students enrolled in grade 8, it is not possible to compute these proxy indicators for 

two-thirds of the high school students in State 1. Second, at this lower level of disaggregation, the 

indicators are more sensitive to year-to-year changes in the population resulting from transfers in and out of 

individual schools. 
 

6 

cohort on-time graduation rate. Thus, estimates for the five proxy measures, FGR, 

AFGR, GGI, GLI, and SCPI, were computed using data aggregated from the student 

records with the formulas described and used in volume 1. 

In State 1, the estimates for GLI are higher than any of the other graduation indicators 

(figure 2.1). The estimates for GGI are the second highest in each year. Conversely, the 

estimates of FGR are lowest in each year. Estimates of AFGR and SCPI fall between 

those of GLI and FGR, with similar estimates in 2000-01 and 2001-02, but with SCPI 

dropping in 2002-03. A comparison of these proxy indicators to the EACGI shows that 

the GLI and GGI are highest and the true cohort rate falls between the lower estimate for 

FGR and the higher estimates for AFGR and SCPI in the first 2 years and between the 

lower estimates for FGR and SCPI and the higher estimate for AFGR in the third year. 

To further quantify the differences between each of the state-level proxy indicators and 

the true cohort rate, the difference between each graduation indicator and EACGI was 

computed for each year. Figure 2.2 shows that in State 1 AFGR, GGI, and GLI are each 

consistently higher than EACGI. In contrast, SCPI straddles EACGI, ranging from 5 

percentage points above EACGI to 3 percentage points below; and FGR is consistently 

lower than EACGI. One use of the various proxy graduation measures is to track year-toyear changes in graduation rates, to do this it is important to look at differences relative to 

EACGI within individual years and at the average of the absolute differences over the 

years of available data (table 2.1). The averaged absolute difference gives an indication 

of the average amount of error in a specific measure relative to the true cohort rate for the 

same period. GLI has absolute differences of 7 to 13 percentage points from EACGI, 

with an average absolute difference of 9 percentage points; and the absolute differences 

between GGI and EACGI range from 6 to 9 percentage points, with an average absolute 

difference of 7 percentage points. In contrast, AFGR, SCPI, and FGR each have absolute 

differences relative to EACGI ranging from 2 to 5 percentage points, with averaged 

absolute differences of 3.0 percentage points for AFGR, 3.2 for SCPI, and 3.5 for FGR. 
 

7 

Table 2.1. Graduation indicators EACGI, FGR, AFGR, GGI, GLI, and SCPI for State 1, by year: 

Table 2.1. 2000-01 through 2002-03 

 Indicator1

 

School year EACGI FGR AFGR2

 GGI2 GLI SCPI

2000-01 60.5 58.2 65.1 69.7 73.2 65.0 

2001-02 62.7 58.8 65.4 69.7 71.1 64.8 

2002-03 63.0 58.5 64.6 69.0 69.9 59.9 

 Absolute difference from EACGI 

2000-01 † 2.3 4.6 9.3 12.7 4.5 

2001-02 † 3.8 2.7 7.0 8.4 2.2 

2002-03 † 4.5 1.6 6.0 6.9 3.1 

Average † 3.5 3.0 7.4 9.3 3.2 

† Not applicable 

1

 EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, 

all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's 

Graduation Indicator; GLI = CCD Graduation Leaver Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator. 

2

 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts 

SOURCE: Data from a state 1 student record system. 
8

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InLeaver Indicator; SCPI = Swanson's Cumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator. SOURCE: Data from state 1 student record system.

405060708090

100

2000-01 2001-02 2002-03

Figure 2.1. Estimates of graduation indicators EACGI, FGR, AFGR, GGI, GLI, SCPI in State 1: 2000-01 through 2002-

Percent

Year

 0
9

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InLeaver Indicator; SCPI = Swanson's Cumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator. SOURCE: Data from state 1 student record system.

-3.1

6.0

6.9

1.6

-4.5

2.1

7.0

8.4

2.7

-3.9

4.5

9.2

12.7

4.6

-2.3

-30 -20 -10 0 10 20 

GLIGGI1

SCPI

Percentage points

Figure 2.2. Distance, in percentage points, of each graduation indicator FGR, AFGR, GLI, GGI, and SCPI from the trueFigure 3.2. cohort rate EACGI in State 1: 2000-01 through 2002-03

-100 

FGRAFGR1

Indicator

Lower than true cohort rate Higher than true cohort rate
 

10 

2.2. School District-Level Analysis 

The graduation indicators can also be computed at the school district level using the 

student-record-system data. In this case, first-time freshmen were identified, adjustments 

were made for cohort exclusions and transfers in and out of the school district over the 

high school years, and counts of on-time graduates from these students were tallied. 

These data were used to compute the true cohort on-time graduation rate for each regular 

school district in State 1. As was the case in the state-level analysis, data from the student 

record system were aggregated to form the cross-sectional estimates needed to compute 

the five proxy graduation indicators. The six graduation indicators were then analyzed to 

further evaluate the performance of the five proxy indicators relative to the true cohort 

on-time graduation rate for regular school districts in State 1. 

Looking first at the distributional properties of each of the school district-level indicators, 

table 2.2a displays the mean rate computed across school districts, along with the 

minimum, 25th percentile, median (50th percentile), 75th percentile, maximum values, 

and standard deviations across the regular school districts for each of the six graduation 

indicators in school years 2000-01 through 2002-03. 

Over the 3-year period, the lowest district rate for the true cohort on-time graduation rate 

occurred in 2000-01 with one district having a rate of 28 percent. The minimum rates for 

the other 2 years were 45 percent in 2001-02 and 49 percent in 2002-03. Conversely, the 

highest maximum rate was 88 percent, and it occurred in both 2001-02 and 2002-03. The 

maximum in 2000-01 was 79 percent. 

In 2000-01, the minimum estimates across the proxy indicators ranged from 22 for GLI 

to 55 percent for GGI. In 2001-02, the minimum estimates ranged from approximately 30 

percent for FGR to 51 percent for GGI, and in 2002-03, they ranged from 37 percent for 

SCPI to 54 percent for GLI and GGI. In 2000-01, the maximum estimates ranged from 

about 81 percent for FGR and AFGR to about 90 percent for GGI, GLI, and SCPI. In 

2001-02, the maximum rates for FGR and AFGR were approximately 80 percent, while 

those for GGI, GLI, and SCPI were approximately 88 percent or above. In 2002-03, the 

maximum for values ranged from 84 percent for SCPI to 91 percent for GLI. 
 

11 

Table 2.2a. Mean, standard deviation, minimum, 25th percentile, median, 75th percentile, and 

Table 2.2a. maximum of graduation indicators across school districts in State 1, by indicator 

Table 2.2a. and school year: 2000-01 through 2002-03 

Indicator1

 

Statistic EACGI FGR AFGR2

 GGI 2 GLI SCPI

2000-01 

Mean rate3 62.5 59.5 65.9 71.3 75.7 65.5

Standard deviation 8.6 8.9 7.5 7.3 9.9 10.7

Minimum 28.3 26.8 33.6 53.8 22.2 35.7

25th percentile 56.7 53.9 62.3 65.5 70.5 62.1

Median 61.9 60.1 66.6 70.3 77.8 66.4

75th percentile 68.2 65.3 70.7 75.6 81.6 69.2

Maximum 78.9 81.1 80.9 90.5 89.1 93.2

 

2001-02 

Mean rate3

 65.2 60.5 66.5 71.0 74.3 65.7

Standard deviation 8.3 9.5 7.7 7.5 9.1 9.4

Minimum 45.1 29.5 39.4 50.8 33.1 35.9

25th percentile 60.0 54.6 61.0 66.5 71.5 60.2

Median 65.8 61.3 67.6 71.1 74.7 66.9

75th percentile 69.6 65.9 71.2 75.6 79.4 71.3

Maximum 87.8 80.1 80.5 90.9 92.3 88.0

 

2002-03 

Mean rate3

 65.6 60.4 66.2 70.6 73.4 62.4

Standard deviation 9.3 9.7 8.1 7.8 8.4 10.9

Minimum 48.9 40.9 42.2 54.5 54.4 37.1

25th percentile 59.0 52.2 61.1 64.1 67.5 55.9

Median 65.5 60.5 66.0 70.3 74.0 63.9

75th percentile 71.4 67.5 72.0 76.8 78.8 68.7

Maximum 87.7 88.5 85.3 88.9 90.6 84.1

1

 EACGI = Exclusion-adjusted cohort graduation indicator; FGR = Freshman graduation rate, all 

freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = Greene's 

graduation indicator; GLI = CCD graduation leaver indicator; SCPI = Swanson's cumulative 

promotion indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

3

 The mean rate is the mean of the means across school districts. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from a state 1 student record system. 

To further quantify the differences between each of the school district-level proxy 

indicators and the true cohort rate, the difference between each graduation indicator and 

EACGI was computed for each year (table 2.2b), and averaged absolute differences were 

computed to provide an indication of the average amount of error in each specific 

measure relative to the true cohort rate for the same period. As was the case in the statelevel analyses, the differences between the estimates for GLI and EACGI are largest with 

an average absolute difference of 10 percentage points. Once again, GLI is followed by 
 

12 

GGI, which has an averaged absolute difference relative to EACGI of 6.5 percentage 

points. Taken across the individual differences, the comparisons of the performance of 

FGR relative to EACGI do not fare as well as was observed in the aggregate state-level 

data, with FGR exhibiting an averaged absolute difference relative to EACGI of 4.3 

percentage points. As was the case in the state-level data AFGR and SCPI have average 

absolute differences that show that on average they yield district-level results that are 

closest to the observed true cohort rates (i.e., EACGI) with averaged absolute differences 

of 1.8 percentage points for AFGR and 2.2 percentage points for SCPI. 

A comparison of the means and medians of each indicator in each of the 3 years shows 

differences up to 1 percentage point for EACGI, FGR, AFGR, and GGI; and differences 

up to 2 percentage points for SCPI and up to 3 percentage points for GLI. Given that 

differences between means and medians for a population can be an indication of skew in 

the distribution, additional diagnostic statistics were examined for each of these six 

indicators. 

For each indicator measures of skewness, kurtosis, and the Shapiro-Wilk W measure of 

normality were examined along with stem-and-leaf, box, and normal probability plots. 

For school years 2001-02 and 2002-03 these diagnostic statistics support the conclusion 

that the rates are distributed normally for EACGI, FGR, AFGR, and GGI (W is greater 

than .95, and there is no marked skewness (less than + 1) or kurtosis (less than + 1.7) 

(table 2.3). In the case of GLI, although the rates are distributed normally in 2002-03, 

there is reason for concern in 2001-02—where there is reason to question normality 

(W=.91), a peaked distribution (kurtosis=5.28), and evidence of a negative skew 

(skewness=-1.42). In school year 2000-01, the district with the lowest rates showed up in 

the box plots as an extreme outlier. The rate for that district was removed and the six 

graduation indicators were recomputed for 2000-01. The resulting diagnostics improved 

with support for normality (W=.94 to .99), absence of skew (+ 0.01 to 0.36) and little or 

no kurtosis (+ 0.08 to 1.71).2

 With this deletion, the minimum value in 2000-01 for 

EACGI was 51 percent and the minimum values for the proxy indicators in 2000-01 

ranged from 36 for SCPI to 59 percent for GLI. 

 

2

 One indicator, SCPI also had three additional extreme values, the removal of those items improved the 

distributional properties but did not change the analytic results described below. In the interest of 

preserving cases these three districts were retained in the data set. 
 

13 

Table 2.2b. Absolute difference relative to EACGI for mean, standard deviation, minimum, 25th 

Table 2.2b. percentile, median, 75th percentile, and maximum of graduation indicators across 

Table 2.2b. school districts in State 1, by indicator and school year: 2000-01 through 

Table 2.2b. 2002-03Table 2.2. 

Indicator1

 

Statistic EACGI FGR AFGR2 GGI2

 GLI SCPI

2000-01 

Mean rate3 † 3.0 3.4 8.8 13.2 3.0

Standard deviation † .3 1.1 1.3 1.3 2.1

Minimum † 1.5 5.3 24.5 6.1 7.4

25th percentile † 2.8 5.6 8.8 13.8 5.4

Median † 1.8 4.7 8.4 15.9 4.5

75th percentile † 2.9 2.5 7.4 13.4 1.0

Maximum † 2.2 2.0 11.6 10.2 14.3

 

2001-02 

Mean rate3

 † 4.7 1.3 5.8 9.1 .5

Standard deviation † 1.2 .6 .8 .8 1.1

Minimum † 15.6 5.7 5.7 12.0 9.2

25th percentile † 5.4 1.0 6.5 11.5 .2

Median † 4.5 1.8 5.3 8.9 1.1

75th percentile † 3.7 1.6 6.0 9.8 1.7

Maximum † 7.7 7.3 3.1 4.5 .2

 

2002-03 

Mean rate3

 † 5.2 .6 5.0 7.8 3.2

Standard deviation † .4 1.2 1.5 .9 1.6

Minimum † 8.0 6.7 5.6 5.5 11.8

25th percentile † 6.8 2.1 5.1 8.5 3.1

Median † 5.0 .5 4.8 8.5 1.6

75th percentile † 3.9 .6 5.4 7.4 2.7

Maximum † .8 2.4 1.2 2.9 3.6

Average

Mean rate3

 † 4.3 1.8 6.5 10.0 2.2

Standard deviation † .6 1.0 1.2 1.0 1.6

Minimum † 8.4 5.9 12.3 7.9 9.5

25th percentile † 5.0 2.9 6.8 11.3 2.9

Median † 3.8 2.3 6.2 11.1 2.4

75th percentile † 3.5 1.6 6.3 10.2 1.8

Maximum † 3.6 3.9 5.3 5.9 6.0

† Not applicable 

1

 EACGI = Exclusion-adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = Greene's 

graduation indicator; GLI = CCD graduation leaver indicator; SCPI = Swanson's cumulative 

promotion indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

3

 The mean rate is the mean of the means across school districts. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from a state 1 student record system. 
 

14 

Table 2.3. Diagnostic statistics of the distribution of EACGI, FGR, AFGR, GGI, SCPI and 

Table 2.3. GLI across school districts in State 1: 2000-01 through 2002-03 

Indicator1 

Statistic EACGI FGR AFGR2

 GGI2 SCPI GLI

2000-01 

Skewness -0.68 -0.66 -1.16 0.06 -0.28 -2.53

Kurtosis 2.56 2.02 4.32 -0.15 1.64 12.15

Shapiro-Wilk's W 0.95 0.97 0.93 0.99 0.94 0.82

 

2001-02 

Skewness 0.12 -0.64 -0.83 0.49 -0.49 -1.42

Kurtosis 0.26 1.02 1.57 0.03 0.91 5.28

Shapiro-Wilk's W 0.99 0.97 0.96 0.98 0.98 0.91

 

2002-03 

Skewness 0.27 0.26 -0.19 0.05 -0.26 -0.09

Kurtosis -0.28 -0.04 0.18 -0.30 -0.31 -0.36

Shapiro-Wilk's W 0.98 0.99 0.99 0.99 0.98 0.99

1

 EACGI = Exclusion-adjusted cohort graduation indicator; FGR = Freshman graduation rate, all 

freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = Greene's 

graduation indicator; SCPI = Swanson's cumulative promotion indicator; GLI = CCD graduation 

leaver indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from state 1 student record system. 

To better understand the overall distributions of these six graduation indicators, figures 

2.3 through 2.5 display the decile cut points of EACGI and each of the proxy graduation 

indicators. Three patterns emerge from these figures. First, the overall pattern of increase 

shows relatively smooth patterns between the 10th and 90th deciles, with somewhat 

larger changes at the extremes of the distribution. Second, as was the case at the state 

level, the rates for GLI are consistently high relative to the other five indicators. Third, 

the other four proxy indicators—FGR, AFGR, GGI, and SCPI are relatively close to 

EACGI, particularly between the 10th- and 90th-deciles. 
15 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; GLI=Graduation Leaver Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 1 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 

Figure 2.3. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, GLI, and SCPI, by decile in Sta

Percent

Percentile
16 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; GLI=Graduation Leaver Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 1 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 

Percent

Percentile

Figure 2.4. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, GLI, and SCPI, by decile in Sta
17 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; GLI=Graduation Leaver Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 1 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 

Figure 2.5. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, GLI, and SCPI, by decile in StatFigure 2.5. 2002-03

Percent

Percentile
 

18 

Since the goal of this analysis is to identify the proxy measure that best approximates the 

values of the true cohort on-time graduate rate (EACGI), at this point GLI is dropped 

from further analysis for two reasons. First, by definition, it is not an estimate of an ontime rate because students still enrolled in high school after the 4th year are excluded 

from the denominator. Second, related to this, the smaller denominator for GLI results in 

rates that are higher than EACGI in almost all instances. As a result, the remaining 

analyses will focus on comparisons between EACGI and FGR, AFGR, GGI, and SCPI. 

Ordinary least squares regression analyses were used to evaluate which of the remaining 

four proxy measures best approximates the true cohort on-time graduation rate. The 

Pearson product-moment correlation coefficients (r) between AFGR and EACGI range 

from .77 to .87 across the three years (table 2.4). The results for FGR are similar, but 

slightly lower in 2 of the 3 years, with correlation coefficients between FGR and EACGI 

ranging from .74 to .85. By comparison, over the 3 years, the correlation coefficients 

between GGI and EACGI range from .54 to .67 and the correlation coefficients between 

SCPI and EACGI range from .48 to .59.3

 

The slope of the regression line indicates the magnitude of change in the true cohort ontime graduation rate for a unit change in each proxy graduation indicator. In this case, 

since both variables in each regression equation are rates that are expressed as 

percentages, the slope represents the percentage point change in the true cohort rate 

associated with a 1-percentage point increase in the proxy graduation indicator under 

consideration. The regression results from AFGR and EACGI indicate that in 2000-01, a 

1-percentage point increase in AFGR is associated with a .91 percentage point increase in 

EACGI, for 2001-02 the slope is .85 and for 2002-03 a slope of 1 indicates that a 1 

percentage point change in AFGR is associated with a 1 percentage point increase in the 

true cohort rate. The slopes for the regression lines between FGR and EACGI over the 3 

years range from .70 to .81, indicating a 1 percentage point increase in FGR yields 

approximately seven- to eight-tenths of a percentage point increase in the true cohort rate. 

The slopes for the regression lines between GGI and EACGI range from .60 to .80. In 

contrast, the slopes for the regression line between SCPI and EACGI range from .34 to 

.51. Thus, a 1 percentage point increase in SCPI is associated with a smaller increase in 

the true cohort rate than is the case for AFGR, FGR or GGI. 

The square of the correlation coefficient ( r2

 ) is an indication of how well the regression 

line between a proxy graduation indicator and the true cohort on-time graduation 

indicator explains the variation in the true cohort on-time graduation rate.4

 The regression 

results indicate that across the three years between 60 and 77 percent of the variation in 

EACGI is explained by AFGR, and in the case of FGR the range in variation explained in 

EACGI is from 55 to 72 percent. By comparison, between 29 and 46 percent of the 

variation in EACGI is explained by GGI, and between 23 and 35 percent of the variation 

in EACGI is explained by SCPI. 

 

3

 For 2000-01, the extreme outlier was excluded from the results reported here; however, when the analyses 

included the outlier, the pattern of the strength of the correlation between EACGI and each proxy was the 

same with AFGR and FGR having the strongest correlations, with lower correlations for GGI and SCPI. 4

 In this simple regression, the r2 is the same as R2. 
 

19 

Table 2.4 Regression estimates of EACGI on proxy graduation indicators across school 

Table 2.4 districts in State 1, by indicator and school year: 2000-01 through 2002-03 

Indicator1

Statistic FGR AFGR3 GGI3

 SCPI

2000-012 

Correlation coefficient .74 .77 .60 .48 

R square .55 .60 .36 .23 

Slope .70 .91 .62 .34 

Standard deviation 5.08 4.80 6.07 6.64 

2001-02 

Correlation coefficient .83 .79 .54 .50 

R square .69 .62 .29 .25 

Slope .73 .85 .60 .44 

Standard deviation 4.71 5.17 7.08 7.29 

2002-03 

Correlation coefficient .85 .87 .67 .59 

R square .72 .77 .46 .35 

Slope .81 1.01 .80 .51 

Standard deviation 5.02 4.56 6.95 7.61 

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene’s graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2

 One district was excluded. 

3

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from state 1 student record system. 

The r2 is equivalent to the explained sum of squares divided by the total sum of squares, 

thus 1 minus r2 is an estimate of the amount of variation in the true cohort rate that is not 

explained by the proxy graduation indicator under consideration (i.e., the unexplained 

sum of squares divided by the total sum of squares). Related to this, the unexplained sum 

of squares can also be used to compute s2

, the variance about the least squares regression 

line (unexplained sum of squares divided by the degrees of freedom). The square root of 

the variance is then, the standard deviation about the least squares regression line. Over 

the 3 years, these standard deviations ranged from approximately 4.6 to 5.2 for AFGR 

and FGR and from approximately 6.1 to 7.6 for GGI and SCPI. 

In summary, while AFGR is not an exact approximation of EACGI, it is strongly 

correlated with EACGI. The variance in EACGI that is explained by the various 

regression analyses is highest in the case of AFGR; similarly, looking across the four 

proxy graduation indicators, the size of a unit of change in AFGR is closest to being the 
 

20 

same as a unit of change in EACGI. The AFGR is a better predictor of the true cohort 

rate than either GGI or SCPI in each of the three years. On the other hand, the 

performance of AFGR and FGR is relatively close, with AFGR performing somewhat 

better in 2 of the 3 years used in this analysis. Taken together, these analyses indicate that 

AFGR, followed closely by FGR, offers the best approximation of the four proxy 

graduation indicators under consideration.5

 

To better understand the magnitude of the errors in each proxy indicator, the absolute 

difference between each proxy indicator and the true cohort on-time graduation rate was 

computed for each regular school district in State 1. This gives an estimate of the size of 

the error in each proxy indicator. For each proxy graduation indicator the data for the 

individual school districts were compared to those from EACGI and aggregated in 5 

percentage point intervals from 0 to 15 and 15 percentage points or more from EACGI 

(figures 2.6 – 2.8). Across the 3 years, AFGR has the largest percentage of districts that 

are within 5 percentage points of the true cohort rate (55 percent in 2000-01, 59 percent 

in 2001-02, and 71 percent in 2002-03) and the smallest percentage of districts with large 

errors, with only 10 percent or fewer of the districts with proxy estimates that are 10 

percentage points or more from the true cohort rate. The results are similar for FGR, with 

estimates for approximately 50 percent of the districts within 5 percentage points of the 

true rate (47, 50, and 50 percent) and 16 percent or fewer of the districts have proxy 

estimates that are 10 percentage points or more from the true cohort rate. In contrast, 

SCPI has estimates that are within 5 percentage points of the true cohort rates for 41 to 47 

percent of the districts, but 30 to 32 percent of the school districts have proxy estimates 

that are 10 percentage points or more from the true cohort rate. Similarly, GGI has 

between 30 to 44 percent of the districts within 5 percentage points of the true cohort 

rate, but 20 to 38 percent of the school districts have proxy estimates that are 10 

percentage points or more from the true cohort rate. These findings are consistent with 

the correlation results, with smaller errors and higher correlations between AFGR and 

FGR and the true cohort rate and larger errors and lower correlations between SCPI and 

GGI and the true cohort rate. 

 

5

 FGR performs almost as well in its’ correlation coefficients, in the amount of variation explained in 

EACGI, and in the portion of the standard deviation in EACGI that is unaccounted for; in addition, FGR is 

a close second in the analyses of slopes and the amount of variance left unexplained. 
21 

# Rounds to zero.

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InCumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 1 student record system.

50

55

30

44

41

35

32

24

8

11

17

20

2

21

0

102030405060708090

100

FGR AFGR GGI SCPI

Figure 2.6 Distribution of the size of the absolute distance, in percentage points, between graduation indicators FG AFGR, GGI, SCPI, and the true cohort rate EACGI for school districts in State 1: 2000-01 

Percent

#

1 1

Indicator
22 

# Rounds to zero.

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InCumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 1 student record system.

50

59

41

47

36

33

30

23

9 8

15

21

5

14

0

102030405060708090

100

FGR AFGR GGI SCPI

Figure 2.7 Distribution of the size of the absolute distance, in percentage points, between graduation indicators FG AFGR, GGI, SCPI, and the true cohort rate EACGI for school districts in State 1: 2001-02 

Percent

#

Indicator

1 1
23 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InCumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 1 student record system.

47

71

44

41

38

26

36

29

11

2

9

20

5

2

11 

0

102030405060708090

100

FGR AFGR GGI SCPI

Figure 2.8 Distribution of the size of the absolute distance, in percentage points, between graduation indicators FG GGI, SCPI, and the true cohort rate EACGI for school districts in State 1: 2002-03 

Percent

Indicator

1 1
 

24 

States, school districts, and schools frequently use measures like graduation rates or 

dropout rates to report on educational progress. Thus, in addition to evaluating how each 

of the proxy indicators performs relative to the true cohort rate at the school district level 

in single years, it is also informative to evaluate the performance of each of the indicators 

over time within individual school districts. To do this, the correlation between the rates 

for individual school districts was calculated across adjacent school years for each 

graduation indicator. Taking EACGI as the standard, the correlations between school 

years 2000-01 and 2001-02 and school years 2001-02 and 2002-03 were both .82 (table 

2.5). The true cohort on-time graduation rates showed evidence of a reasonably strong 

correlation between the year-to-year estimates, with two-thirds of the variation in the true 

rate in one year explained by the true rate in the previous year. A 1 percentage point 

increment in EACGI in one year is associated with approximately nine-tenths of a 

percentage point increment in the true cohort rate in the next year. This suggests that 

while there is year-to-year variation over the 3-year time period, the rates within 

individual districts were more likely to be similar than to show large differences. 

Table 2.5 Regression estimates of school district-level graduation indicators in State 1, by 

Table 2.5 indicator: 2000-01 through 2002-03 

Indicator1

Statistic EACGI FGR AFGR3 GGI3

 SCPI

2000-01 vs. 2001-022

Correlation coefficient .82 .81 .78 .76 .48

R square .67 .66 .60 .57 .23

Slope .87 .90 .85 .80 .42

Standard deviation 4.65 5.15 4.45 4.99 8.40

2001-02 vs. 2002-03 

Correlation coefficient .82 .76 .72 .59 .64

R square .67 .58 .52 .35 .41

Slope .91 .77 .76 .62 .74

Standard deviation 5.40 6.38 5.69 6.35 8.46

1

 EACGI = Exclusion-adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene’s graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2 One district was excluded. 

3

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from state 1 student record system. 

For a proxy indicator to serve as a reasonable approximation of the true cohort rate, 

similar results should be evident over the same time period. For AFGR, the correlation 

between the first 2 years was .78 and the correlation between the second two years was 

.72; between 52 and 60 percent of the variation in AFGR in one year is explained by 

AFGR in the previous year; and a 1 percentage point increment in AFGR in one year is 

associated with an increment of about eight- to nine-tenths percentage point percent in 
 

25 

the previous year. For FGR, the correlation between 2000-01 and 2001-02 was .81 and 

between 2001-02 and 2002-03 it was .76, approximately 58 to 66 percent of the variation 

in FGR in one year is explained by the FGR in the previous year; and a 1 percentage 

point increment in FGR in one year is associated with an increment of approximately 

eight- to nine-tenths of a percentage point in the previous year. By comparison, the 

correlations for GGI were .59 and .76; with approximately 35 to 57 percent of the 

variation in GGI in one year explained by GGI in the previous year; and the slopes (i.e. a 

measure of the change in one year associated with a unit of change in the previous year) 

were .62 and .80. The correlations for SCPI were .48 and .64, as a result only 20 to 40 

percent of the variation in SCPI in one year is explained by SCPI in the previous year; 

and the slopes were .42 and .74. The correlations across years within each indicator add 

further support to the evidence that AFGR and FGR are the closest approximations to the 

true cohort rate. 

2.3. Summary 

The student record data in State 1 were used to compute the true cohort on-time 

graduation rate at the school district and state level. The same data were aggregated to 

create the cross-sectional enrollment, graduate, and dropout variables needed to compute 

the cross-sectional proxy graduation indicators. The distributional properties of all six 

graduation indicators were analyzed, and diagnostics procedures were used to examine 

the distributions for deviations from normality. An examination of the data resulted in a 

decision to focus the analysis on the four proxy indicators that most closely resemble the 

true cohort rate—AFGR, FGR, GGI, and SCPI. Then, correlation and ordinary leastsquares regression were used to compare the proxy indicators FGR, AFGR, GGI, and 

SCPI to the true cohort on-time graduation rate, and to examine the amount of variability 

over time in each of the indicators. In addition, the distance between the proxy indicator 

and the true cohort rate was examined for each school district to measure the amount of 

error in the proxy indicators. 

At the state level, the rates for AFGR, SCPI and FGR were the closest to the true cohort 

rates, with average absolute differences relative to EACGI across the 3 years of 3.0, 3.2, 

and 3.5 percentage points, respectively. GGI had an average absolute difference with 

EACGI of 7.4 points and GLI had an average absolute difference of 9.3 percentage 

points. 

Analyses at the district level showed that AFGR and FGR (with AFGR taking the lead in 

2 of the 3 years) have the strongest correlations with the true cohort on-time graduation 

rate and the smallest errors relative to the true cohort rates. Furthermore, the examination 

of the year-to-year correlations within each indicator showed strong associations over 

time for the true cohort on-time graduation rate and for AFGR and FGR. 

 

27 

Chapter 3 

 

An Application of the Proxy Graduation Indicators and the True 

Cohort Rate Using Data From the Student Record System in State 2 

This chapter extends the analysis of the true cohort on-time graduation rate (EACGI) to 

data from a second state. The student record system in State 2 differs from that in State 1. 

The system in State 2 is built and maintained at the school district level and reported up 

to the state education office, in contrast to the centralized system used in State 1. The 

staff in the state education office of State 2 provided a cleaned cohort file that was used 

to compute the EACGI at the state and school district levels for school years 1999-2000, 

2000-01, 2001-02, and 2002-03.6 

Given that the goal of this analysis is to determine how the different cross-sectional proxy 

graduation indicators perform when individual student record data are not available, the 

data from the student records and cross-sectional estimates provided by staff in State 2, 

were used to produce the equivalent of cross-sectional estimates of grade-by-grade 

enrollments in school years 1995-96 through 2002-03 and of all graduates from school 

years 1999-2000 through 2002-03. These estimates differ from those used to compute the 

true cohort on-time graduation rate, in that the enrollments include all students in a 

specific grade—not just first-time students—and the graduates include all graduates, not 

just on-time graduates. These data were then used to compute the Freshman Graduation 

Rate based on all freshmen (FGR), the Averaged Freshman Graduation Rate based on an 

estimate of first-time freshmen (AFGR), the Greene Graduation Indicator (GGI), and the 

Swanson Cumulative Promotion Indicator (SCPI). 

3.1. State-Level Analysis 

The recommended true cohort on-time graduation indicator for regular school districts, 

EACGI, was 58.4 percent in State 2 in 1999-2000, some 60.0 in 2000-01, some 63.1 in 

2001-02 and 64.5 in 2002-03. The average over these 4 years was 61.5 percent (table 

3.1). Thus, on average, 62 percent of the students in the entering freshman classes of 

1996-97, 1997-98, 1998-99, and 1999-2000 completed high school in 4 years and 

graduated on time. 

State-level estimates of the cross-sectional proxy graduation indicators show patterns 

similar to those described for State 1. AFGR yielded the highest estimates among these 

four proxy indicators, with estimates ranging from 62 percent in 1999-2000 and 2000-

01to 67 percent in 2002-03 (figure 3.1). FGR estimates were consistently lower than the 

true cohort rates and the estimates for AFGR, ranging from 56 percent in 2000-01 to 58 

percent in 2001-02 and 2002-03. GGI was between FGR and AFGR in the last 3 of the 4 

years. SCPI was lower than FGR in 1999-2000 and 2000-01(51 percent and 54 percent), 

but higher than FGR in 2001-02 and 2002-03 (58 and 59 percent). 

 

6

 The analyses included in this report do not include school-level analyses for two reasons. First, a large 

number of schools that do not include the 8th grade so it is not possible to compute the estimate of first-time 

freshmen that is used in AFGR and GGI. Second, at this lower level of disaggregation, the indicators are 

more sensitive to year-to-year changes associated with transfers in and out of individual schools. 
 

28 

Table 3.1. Graduation indicators EACGI, FGR, AFGR, GGI, and SCPI for State 2, by year: 

Table 3.1. 1999-2000 through 2002-03 

Indicator1

Year EACGI FGR AFGR2 GGI2

 SCPI

1999-2000 58.4 56.3 62.3 56.0 50.8

2000-01 60.0 55.8 62.4 56.5 54.2

2001-02 63.1 57.5 65.4 58.9 58.5

2002-03 64.5 57.6 67.4 60.5 58.8

 Absolute Difference 

1999-2000 † 2.1 3.8 2.4 7.7

2000-01 † 4.2 2.4 3.5 5.8

2001-02 † 5.6 2.3 4.3 4.6

2002-03 † 6.9 2.9 4.0 5.8

Average † 4.7 2.8 3.5 6.0

† Not applicable 

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR= Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene's graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from State 2 student record system. 

A comparison of each of the proxy indicators to the true cohort rate shows that AFGR 

ranged from 4 to 6 percentage points higher than the true rate over this 4-year time period 

(figure 3.2). GGI was 1 to 3 percentage points below the true rate. FGR had rates that 

were 2 to 3 points below the true rate from 1999-2000 through 2001-02, and 5 percentage 

points lower in 2002-03. SCPI was also lower than the true cohort rate, with differences 

ranging from 1 to 7 percentage points. 

As was done in the analysis of data from State 1, the absolute difference between each 

graduation indicator and EACGI was computed for each year, and then averaged across 

the years of available data (table 3.1) to give an indication of the average amount of error 

in each measure relative to the true cohort rate over the time period. SCPI has an average 

absolute difference of 6 percentage points; the average absolute difference between FGR 

and EACGI is close to 5 percentage points; and the averaged absolute difference for GGI 

is 3.5 percentage points. In contrast, AFGR has an averaged absolute difference relative 

to EACGI of 2.8 percentage points. 
29 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman GraduatGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion Indicator.SOURCE: Data from state 2 student record system.

405060708090

100

1999-2000 2000-01 2001-02 2002-03

Year

Figure 3.1. Estimates of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI in State 2: 1999-2000 through 20

Percent

0
30 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator.SOURCE: Data from state 2 student record system.

-4.2

-2.5

4.4

-5.4

-1.3

-0.9

5.6

-2.3

-4.1

-1.9

4.1

-7.0

-1.8

4.5

-1.5

-2.5

-30 -20 -10 0 10 20 

SCPI

GGI

AFGR

FGR

Indicator

Percentage Points

Lower than true cohort rate Higher than true cohort rate

Figure 3.2. Distance in percentage points, of each graduation indicator FGR, AFGR, GGI, and SCPI from the true coFigure 3.2. EACGI in State 2: 1999-2000 through 2002-03

1

1

-100 
 

31 

3.2. School District-Level Analysis 

The data from the student records in State 2 were also used to compute estimates for 

EACGI and the four proxy indicators for each school district in the state. The summary 

data in table 3.2a show the distributional properties of each of the indicators. Over the 4-

year period, the minimum values of the school district level true cohort on-time 

graduation rates ranged from 46 percent in 2000-01 to 50 percent in 2002-03. During this 

period, the highest values of the true cohort on-time rate ranged from 78 percent in 1999-

2000 to 87 percent in 2002-03. 

In 1999-2000, the minimum estimates across the proxy indicators ranged from 22 percent 

for SCPI to 45 percent for AFGR. In 2000-01, the minimum estimates ranged from 27 

percent for SCPI to 47 percent for AFGR. In 2001-02, the minimum estimates ranged 

from 31 percent for SCPI to 51 percent for GGI. In the fourth year, 2002-03, the 

minimum estimates ranged from 32 percent for FGR and SCPI to 43 percent for GGI. In 

1999-2000, the maximum estimates ranged from 77 percent for AFGR, FGR, and GGI to 

84 percent for SCPI. In 2000-01, the maximum estimates ranged from 77 percent for 

FGR to 88 percent for AFGR. The 2001-02 maximum rates ranged from 78 percent for 

GGI to 84 percent for AFGR. In 2002-03, the maximum rates were 87 percent for SCPI 

and 96 percent for GGI, with rates in excess of 100 percent for both FGR and AFGR.7

The school district analysis of absolute differences between each graduation measure and 

the rates observed for EACGI is repeated for State 2 (table 3.2b). Specifically, averaged 

absolute differences were computed to provide an indication of the average amount of 

error in each specific measure relative to the true cohort rate for the same period. The 

differences between the estimates for FGR and EACGI are largest with an average 

absolute difference of 5.7 percentage points. SCPI results are more similar to those for 

EACGI at the school district level than was the case at the state level in this state, with an 

averaged absolute difference of 2.5 percentage points. However, the district level results 

for GGI and AFGR are even closer to those observed for EACGI, with averaged absolute 

differences relative to EACGI of 1.9 percentage points for GGI and 1.5 percentage points 

for AFGR. 

A comparison of the means and medians for each graduation indicator across the 4 years 

shows differences of up to 2 percentage points. Since differences between means and 

medians for a population can be an indication of skew in the distributions, additional 

diagnostics were examined for each of the six indicators. 

 

7

 There were only two estimates that exceeded 100%, and they were both in the same school district. For 

that district the number of graduates in 2002-03 exceeded both the total number of freshmen 4 years earlier 

and the averaged freshman estimate for the same year. 
 

32 

Table 3.2a. Mean, standard deviation, minimum, 25th percentile, median, 75th percentile, and 

maximum of graduation indicators across school districts in State 2, by indicator 

and school year: 1999-2000 through 2002-03 

Indicator1

Statistic EACGI FGR AFGR2 GGI2

 SCPI

1999-2000 

Mean 3 61.3 57.1 63.1 59.2 54.0

Standard deviation 7.0 8.3 6.6 6.5 11.4

Minimum 48.3 35.0 44.5 44.3 22.3

25th percentile 56.7 51.3 59.3 55.0 47.0

Median 59.7 56.2 62.5 58.6 54.6

75th percentile 65.4 63.1 68.0 62.5 60.8

Maximum 77.9 76.8 77.1 76.7 83.7

2000-01 

Mean 3

 61.3 56.9 63.2 60.3 56.7

Standard deviation 8.1 8.6 7.8 7.7 9.6

Minimum 45.8 38.1 47.3 43.8 26.8

25th percentile 56.0 50.1 57.5 55.8 50.5

Median 59.9 57.0 63.5 59.2 56.0

75th percentile 66.0 63.0 68.3 62.5 62.8

Maximum 81.2 76.9 87.7 85.7 80.4

2001-02 

Mean 3

 64.9 58.2 65.9 62.5 62.1

Standard deviation 7.3 9.0 7.5 6.1 10.0

Minimum 48.0 35.4 47.2 50.9 31.1

25th percentile 61.0 52.3 60.0 58.2 56.6

Median 64.2 56.9 66.2 61.7 61.7

75th percentile 69.9 63.8 70.7 66.0 68.9

Maximum 83.5 81.4 84.2 77.9 79.8

2002-03 

Mean 3

 67.0 59.5 68.4 64.2 62.5

Standard deviation 7.4 11.3 10.3 8.7 11.4

Minimum 50.0 31.5 41.6 43.0 31.7

25th percentile 62.0 52.4 61.1 59.1 56.5

Median 66.3 59.3 67.8 62.3 63.4

75th percentile 71.2 66.1 73.2 68.7 70.1

Maximum 86.5 103.5 113.8 96.0 86.9

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR= Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene's graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts use Greene's smoothed 9th-grade estimate. 

3

 Mean is the mean of the district means. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from State 2 student record system. 
 

33 

Table 3.2b. Absolute differences relative to EACGI for mean, standard deviation, minimum, 

25th percentile, median, 75th percentile, and maximum of graduation indicators 

across school districts in State 2, by indicator and school year: 1999-2000 through 

2002-03 

Indicator1

Statistic EACGI FGR AFGR2 GGI2

 SCPI

1999-2000 

Mean 3 † 4.2 1.8 2.1 7.3

Standard deviation † 1.3 0.4 0.5 4.4

Minimum † 13.3 3.8 4.0 26.0

25th percentile † 5.4 2.6 1.7 9.7

Median † 3.5 2.8 1.1 5.1

75th percentile † 2.3 2.6 2.9 4.6

Maximum † 1.1 0.8 1.2 5.8

2000-01 

Mean 3

 † 4.4 1.9 1.0 4.6

Standard deviation † 0.5 0.3 0.4 1.5

Minimum † 7.7 1.5 2.0 19.0

25th percentile † 5.9 1.5 0.2 5.5

Median † 2.9 3.6 0.7 3.9

75th percentile † 3.0 2.3 3.5 3.2

Maximum † 4.3 6.5 4.5 0.8

2001-02 

Mean 3

 † 6.7 1.0 2.4 2.8

Standard deviation † 1.7 0.2 1.2 2.7

Minimum † 12.6 0.8 2.9 16.9

25th percentile † 8.7 1.0 2.8 4.4

Median † 7.3 2.0 2.5 2.5

75th percentile † 6.1 0.8 3.9 1.0

Maximum † 2.1 0.7 5.6 3.7

2002-03 

Mean 3

 † 7.5 1.4 2.8 4.5

Standard deviation † 3.9 2.9 1.3 4.0

Minimum † 18.5 8.4 7.0 18.3

25th percentile † 9.6 0.9 2.9 5.5

Median † 7.0 1.5 4.0 2.9

75th percentile † 5.1 2.0 2.5 1.1

Maximum † 17.0 27.3 9.5 0.4

See notes at end of table 
 

34 

Table 3.2b. Absolute differences relative to EACGI for mean, standard deviation, minimum, 

25th percentile, median, 75th percentile, and maximum of graduation indicators 

across school districts in State 2, by indicator and school year: 1999-2000 through 

2002-03—continued 

Indicator1

Statistic EACGI FGR AFGR2 GGI2

 SCPI

Average 

Mean 3 † 5.7 1.5 2.1 4.8 

Standard deviation † 1.9 1.0 0.9 3.2 

Minimum † 13.0 3.6 4.0 20.1 

25th percentile † 7.4 1.5 1.9 6.3 

Median † 5.2 2.5 2.1 3.6 

75th percentile † 4.1 1.9 3.2 2.5 

Maximum † 6.1 8.8 5.2 2.7 

† Not applicable

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR= Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene's graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts use Greene's smoothed 9th-grade estimate. 

3

 Mean is the mean of the district means. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from State 2 student record system. 

For each indicator measures of skewness, kurtosis, and the Shapiro-Wilk W measure of 

normality were examined along with stem-and-leaf, box, and normal probability plots. 

For school years 1999-2000, 2000-01, and 2001-02, the diagnostic statistics support the 

conclusion that the rates are distributed normally for EACGI, FGR, AFGR, and SCPI (W 

is greater than .95), and there is no marked skewness (less than + 1) or kurtosis (less than 

+ 1) (table 3.3). The same is true for GGI in 1999-2000 and 2001-02, however, in 2000-

01, there is a possibility that the distribution is not normal (W=.94). In 2002-03, there is 

some concern over the normality of the distributions for GGI, FGR, and AFGR (W=.92 

to.96) and there is evidence of kurtosis (2.5 to 5.1), suggesting a peaking in the 

distribution. 
 

35 

Table 3.3. Diagnostic statistics of the distribution of EACGI, FGR, AFGR, GGI and SCPI 

Table 3.3. across school districts in State 2: 1999-2000 through 2002-03 

Indicator1 

Statistic EACGI FGR AFGR2

 GGI 2 SCPI

1999-2000 

Skewness 0.55 0.07 0.18 0.36 0.09

Kurtosis -0.33 0.14 0.30 0.68 0.34

Shapiro-Wilk's W 0.96 0.99 0.99 0.98 0.99

2000-01 

Skewness 0.60 0.09 0.41 0.92 0.00

Kurtosis -0.04 -0.29 0.31 1.26 0.80

Shapiro-Wilk's W 0.96 0.99 0.98 0.94 0.99

2001-02 

Skewness 0.11 0.17 0.03 0.34 -0.59

Kurtosis -0.06 0.23 0.20 -0.26 0.74

Shapiro-Wilk's W 0.99 0.99 0.99 0.98 0.97

2002-03 

Skewness 0.17 0.83 1.06 1.07 -0.34

Kurtosis 0.28 2.70 5.14 2.55 0.19

Shapiro-Wilk's W 0.99 0.96 0.92 0.93 0.99

1

 EACGI = Exclusion-adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GGI = 

Greene’s graduation indicator; SCPI = Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from state 2 student record system. 

To further understand the overall distributions of these five graduation indicators, figures 

3.3 through 3.6 display the decile cut points of EACGI and each of the four proxy 

graduation indicators. As was the case in State 1, there are relatively smooth patterns 

between the 10th and 90th deciles, with somewhat larger changes at the extremes of the 

distribution. 
36 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 2 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 100

Percentile

Percent

Figure 3.3. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI, by decile in State 2
37 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 2 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 100

Percentile

Percent

Figure 3.4. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI, by decile in State 2: 
38 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator. SOURCE: Data from state 2 student record system.

0

102030405060708090

100

0 10 20 30 40 50 60 70 80 90 100

Percentile

Percent

Figure 3.5. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI, by decile in State 2: 
39 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: EACGI = Exclusion-Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman GraduatiGGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator.SOURCE: Data from state 2 student record system.

0

102030405060708090

100110120

0 10 20 30 40 50 60 70 80 90 100

Percentile

Percent

Figure 3.6. Percentile distribution of graduation indicators EACGI, FGR, AFGR, GGI, and SCPI, by decile in State 2: 
 

40 

To better quantify the relationships between each of the four proxy graduation indicators 

and the true cohort on-time graduation rate, correlations and ordinary least squares 

regression analyses were used to evaluate which of the four proxy measures best 

approximates the true cohort rate. 

The correlations between AFGR and EACGI range from .64 to .72 across the 4 years 

(table 3.4). The results for FGR range from .61 to .74, but the correlations between FGR 

and EACGI are lower than those between AFGR and EACGI in 3 of the 4 years. The 

correlations between GGI and the true cohort rate are lower than those for AFGR and 

FGR in 3 of the 4 years, ranging from .58 to .66. SCPI has the lowest of the four 

correlations in 3 of the 4 years, with correlations ranging from .52 to .61, but the 

correlation of .69 for SCPI is higher than those for the other three proxy indicators in 

1999-2000. 

Table 3.4. Regression estimates of the true cohort rate, EACGI, on proxy graduation 

indicators, across school districts in State 2, by indicator and school year: 1999-

2000 through 2002-03 

Indicator1

Statistic FGR AFGR2 GGI2

 SCPI

1999-2000 

Correlation coefficient .61 .64 .66 .69 

R square .37 .41 .43 .48 

Slope .52 .69 .71 .43 

Standard deviation 5.62 5.44 5.35 5.12 

2000-01 

Correlation coefficient .66 .71 .63 .52 

R square .43 .51 .39 .27 

Slope .62 .74 .66 .44 

Standard deviation 6.17 5.74 6.36 7.00 

2001-02 

Correlation coefficient .62 .66 .58 .56 

R square .39 .44 .34 .32 

Slope .50 .64 .69 .41 

Standard deviation 5.72 5.49 5.93 6.04 

2002-03 

Correlation coefficient .74 .72 .62 .61 

R square .54 .52 .39 .38 

Slope .48 .52 .53 .40 

Standard deviation 5.04 5.14 5.82 5.89 

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; SCPI = 

Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts use Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from State 2 student record system.
 

41 

The regression results indicate that approximately one-half of the variation in EACGI is 

explained by AFGR in 2 of the 4 years (r2

 = .51 and .52), with 44 percent and 41 percent 

of the variation in explained EACGI by AFGR in the other 2 years. Some 54 percent of 

the variation in EACGI in 2002-03 is explained by FGR and approximately 40 percent is 

explained in the other 3 years (.37 to .43). While 40 to 50 percent of the variation in 

EACGI in 1999-2000 is explained by SCPI (.48) and GGI (.43), the variation explained 

in the other 3 years ranges from approximately 30 to 40 percent (.27 to .39). 

In summary, although the relationships between the true cohort on-time graduation rate 

and the proxy indicators AFGR and FGR are not as strong in State 2 as those evident in 

State 1, the same patterns prevail, with AFGR and FGR showing stronger correlations 

with the true cohort rate than the other two proxy indicators. 

 

To continue the analysis of the error in each proxy indicator relative to the true cohort 

rates, figures 3.7 through 3.10 display the distributions of the absolute differences 

between the proxy indicators for individual school districts and the true rate for each 

year. For each proxy graduation indicator, the data for the individual school districts were 

aggregated in 5 percentage point intervals from 0 to 15 and 15 percentage points or more 

from EACGI. Across the 4 years, AFGR consistently has a majority of school districts 

with rates close to their true rates, with 58 to 64 percent of the estimates within 5 

percentage points of the true cohort rates. The performance of GGI is similar on this 

dimension, with 52 to 66 percent of the district rates within 5 percentage points of their 

true rates. SCPI yields estimates that are within 5 percentage points of their true cohort 

rates for 37 and 43 percent of the districts. The pattern for FGR is less consistent, in the 

first 2 years (1999-2000 and 2000-01) approximately one half of the districts (52 and 46 

percent) had estimates that were within 5 percentage points of their true rates, but in the 

last 2 years (2001-02 and 2002-03), only 27 percent of the district estimates were within 

this 5 percentage point margin of error. The patterns are, for the most part, reversed when 

the percentage of districts with error of 10 percentage points or higher are examined. 

AFGR has the smallest percentage of districts with large errors, with only 8 to 11 percent 

of the district estimates 10 or more percentage points from their true cohort rates. GGI is 

more variable with the percent of districts with large errors ranging from 6 to 18 

percentage points. SCPI yields large errors for 23 to 45 percent of the districts. FGR 

yields estimates with large errors in 21 to 24 percent of the districts in the first 2 years 

and large errors in 34 to 40 percent of the districts in the last 2 years. Thus, although the 

correlations with the true cohort rate for FGR and AFGR were similar across the 4 years 

and were stronger than the correlations with the true cohort rate and SCPI and GGI, this 

analysis of the magnitude of the errors in each indicator relative to the true cohort rate 

shows that in this state AFGR outperforms the other three proxy indicators. 
42 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InCumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 2 student record system.

52

64 63

37

27 28

18

15

7 7

27

6

1 1

27

0

102030405060708090

100

FGR AFGR GGI SCPI

Indicator

Percent

Figure 3.7. Distribution of the size of the absolute distance, in percentage points, between FGR, AFGR, GGI, SCPI a

Figure 3.7cohort rate EACGI for school districts in State 2: 1999-2000

1 1
43 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation InCumulative Promotion indicator; EACGI = Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 2 student record system.

46

58

66

43

30

33

19

28

15

7

12

19

9

1 3

0

102030405060708090

100

FGR AFGR GGI SCPI

Indicator

Percent

Figure 3.8. Distribution of the size of the absolute distance, in percentage points, between FGR, AFGR, GGI, SCPI a

Figure 3.8.cohort rate EACGI for school districts in State 2: 2000-01

1 1
44 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR=Freshman Graduation Rate; AFGR=Averaged Freshman Graduation Rate; GGI=Greene Graduation Indicator; SCPI=Swanson's Cumulative EACGI=Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 2 student record system.

27

58 60

37 39

31

34

39

22

7

3

16

12

3 3

0

102030405060708090

100

FGR AFGR GGI SCPI

Indicator

Percent

Figure 3.9. Distribution of the size of the absolute distance, in percentage points, between FGR, AFGR, GGI, SCPI a

Figure 3.9.true cohort rate EACGI for school districts in State 2: 2001-02

1 1
45 

1 First-time 9th-grade counts were estimated using Greene's smoothed 9th-grade estimate.

NOTE: FGR=Freshman Graduation Rate; AFGR=Averaged Freshman Graduation Rate; GGI=Greene Graduation Indicator; SCPI=Swanson's Cumulative EACGI=Exclusion-Adjusted Cohort Graduation Indicator.SOURCE: Data from state 2 student record system.

27

58

52

37

33

30 30 31

24

10 12

19

16

1

6

0

102030405060708090

100

FGR AFGR GGI SCPI

Indicator

Percent

Figure 3.10. Distribution of the size of the absolute distance, in percentage points, between graduation indicators FFigure 3.10. GGI, and SCPI and the true cohort rate EACGI for school districts in State 2: 2002-03

1 1
 

46 

To this point, the analysis of the district data in State 2 has focused on the performance of 

each proxy indicator relative to the true cohort rate in individual years. However, because 

graduation rates are frequently used to monitor the performance of individual school 

districts over time it is also informative to evaluate the performance of each of the 

indicators over time within individual school districts. To do this, the correlation between 

the rates for individual school districts was calculated across adjacent school years for 

each graduation indicator. Taking EACGI as the standard, the correlations between 

school years 1999-2000 and 2000-01 and between 2000-01 and 2001-02 were both .79 

and the correlation between school years 2001-02 and 2002-03 was .80 (table 3.5). The 

true cohort on-time graduation rate showed evidence of a strong correlation between the 

year-to-year rates. This suggests that over the 4-year time period the true cohort rates 

within individual districts were more likely to be similar than to show large year-to-year 

differences. For a proxy indicator to serve as a reasonable approximation of the true 

cohort rate, similar relatively high correlations should be evident over the same time 

period. For FGR, the correlation was .75 between 1999-2000 and 2000-01, .80 between 

2000-01and 2001-02, and .82 between 2001-02 and 2002-03. For AFGR, the correlation 

between the first 2 years was .69, however, the between year correlations were higher in 

the last 3 years of the data—.76 between 2000-01 and 2001-02 and .78 between 2001-02 

and 2002-03. The year-to-year correlations for GGI and SCPI were lower, with 

correlations between .63 and .69. 
 

47 

Table 3.5 Regression estimates of school district-level graduation indicators in State 2 across 

years, by indicator: 1999-2000 through 2002-03 

Indicator1

Statistic EACGI FGR AFGR2 GGI2

 SCPI

1999-2000 vs. 2000-01 

Correlation coefficient .79 .75 .69 .68 .63

R square .63 .56 .47 .46 .40

Slope .92 .75 .81 .81 .53

Standard deviation 4.96 5.74 5.69 5.71 7.51

2000-01 vs. 2001-02 

Correlation coefficient .79 .80 .76 .63 .63

R square .63 .64 .57 .40 .40

Slope .71 .84 .73 .50 .66

Standard deviation 4.44 5.46 4.96 4.77 7.82

2001-02 vs. 2002-03 

Correlation coefficient .80 .82 .78 .69 .66

R square .64 .68 .61 .48 .43

Slope .82 1.03 1.07 .98 .75

Standard deviation 4.41 6.46 6.49 6.30 8.69

1

 EACGI = Exclusion adjusted cohort graduation indicator; FGR = Freshman graduation rate, 

all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; SCPI = 

Swanson's cumulative promotion indicator. 

2

 First-time 9th-grade counts use Greene's smoothed 9th-grade estimate. 

NOTE: Estimates are based on regular school districts. 

SOURCE: Data from State 2 student record system. 

3.3. Summary 

At the state level, the rates for AFGR and GGI were closest to the true cohort rates, with 

average absolute differences from EACGI of 2.8 and 3.5 percentage points. The student 

record data were used to compute the true cohort on-time graduation rate at the school 

district level. The same data were aggregated to create the cross-sectional enrollment, 

graduate, and dropout variables needed to compute the cross-sectional proxy graduation 

indicators. The distributional properties of all five graduation indicators were analyzed, 

and diagnostics procedures were used to examine the distributions for deviations from 

normality. An examination of the data resulted in a decision to focus the analysis on the 

four proxy indicators that most closely resemble the true cohort rate. That done, 

correlation and ordinary least squares regression were used to compare the proxy 

indicators FGR, AFGR, GGI, and SCPI to the true cohort on-time graduation rate, and to 

examine the amount of variability over time in each of the indicators. In addition, the 

distance between the proxy indicator and the true cohort rate was examined for each 

school district to measure the amount of error in the proxy indicators. 
 

48 

The analyses comparing the school district level data for each proxy indicator to the true 

cohort rate showed that although each proxy measure had a stronger association with 

EACGI than AFGR in one of the 4 years, AFGR has the most consistent pattern. More 

specifically, AFGR exhibits stronger correlations with EACGI than FGR in 1999-2000, 

2000-01, and 2001-02, and stronger than GGI or SCPI in 2000-01, 2001-02 and 2002-03. 

Thus overall, at the school district level in State 2, AFGR shows the strongest pattern of 

correlation with the true cohort on-time graduation rate. Similarly, the analysis of the 

distribution of the size of the differences between each graduation measure and the true 

cohort rate showed that in State 2, AFGR had the smallest errors relative to the true 

cohort rates. Furthermore, the examination of the year-to-year correlations within each 

indicator showed strong associations over time for the true cohort on-time graduation rate 

and for AFGR and FGR. 
 

49 

Chapter 4 

An Application of the Proxy Graduation Indicators Using Data From 

the NCES Common Core of Data 

The analyses of chapters 2 and 3 provided a basis for comparing the proxy indicators 

with the true cohort on-time graduation rate for two states. In order to consider how the 

graduation indicators perform more broadly, the findings from the analyses in the two 

states are considered using the available cross-sectional data for the nation and individual 

states. Absent student record system data for all students in the nation, the true cohort 

rate cannot be computed at the national or state levels. Instead, current national and cross 

state analyses are limited to those proxy graduation indicators that can be computed using 

existing cross-sectional data from the Common Core of Data (CCD). 

Recall that among the proxy graduation indicators under consideration in the analyses in 

chapters 2 and 3, the Averaged Freshman Graduation Rate was the most consistent 

among the best performing measures across levels of aggregation in both states. More 

specifically at the state level in State 1, AFGR, SCPI, and FGR were, on average across 

the 3 years, closest to EACGI, with AFGR exhibiting a slight “edge.” Then at the state 

level in State 2, AFGR and GGI were, on average across the 4 years, closest to EACGI, 

with AFGR in the lead. At the district level in state 1, AFGR and SCPI were the closest 

to EACGI when the values for the mean of means were compared; however, when 

regression analysis between the proxy measures and EACGI were examined, AFGR was 

more strongly correlated with EACGI and more of the variation in EACGI was explained 

by AFGR, especially relative to SCPI. At the district level in State 2, AFGR and GGI 

were closest to EACGI when the values for the mean of means were compared; however, 

in the regression analysis, while the results were more mixed, AFGR was again the most 

consistent in both correlations with EACGI and in the amount of variation explained. 

The outcome of the results was similar in the other two sets of district level analyses in 

both states, with AFGR emerging as one of the two best indicators in each analysis and as 

the only indicator that held that position across all analyses. As a result, AFGR is taken as 

the standard in the analyses of the cross-sectional data in this chapter. 

 

Prior to conducting the analysis, it is important to review the sources and types of 

available cross-sectional data, and to consider any limitations in the data. The CCD is the 

source of the available school-based data on high school graduation, completion, and 

enrollment. By way of background, the CCD is an annual survey of the state-level 

education agencies that provides data about all public elementary and secondary schools, 

all local education agencies, and all state education agencies throughout the United 

States. The CCD’s goal is to provide comparable education data across all states. The 

CCD is a set of five surveys that are sent to state education departments: Public School 

Universe, Local Education Agency (School District) Universe, State Aggregate Nonfiscal 

Data, State Aggregate Fiscal Data, and School District Fiscal Data. The first three of 

these surveys include cross-sectional data that can be used to compute the proxy 

graduation indicators. 
 

50 

 

The Freshman Graduation Rate (FGR), the Averaged Freshman Graduation Rate 

(AFGR), the Swanson Cumulative Promotion Indicator (SCPI), and the Greene 

Graduation Indicator (GGI) can each be computed for the nation and for all states and 

districts using data from the annual CCD data files—State Nonfiscal Survey of Public 

Education, the Public School Universe, and the Local Education Agency (School 

District) Universe surveys. The state universe file can be used at the national and state 

levels, while school and agency universe files are needed at the district level. In contrast, 

the Graduation Leaver Indicator (GLI) requires data from the CCD Dropout Component 

of the Local Education Agency Universe data file, and these dropout data are not yet 

available for all states and the District of Columbia.8

 

The analysis in this chapter starts with the five proxy graduation indicators that can be 

calculated with currently available data: FGR, AFGR, SCPI, GGI, and GLI. Before 

starting the analysis, it is important to note that a review of the work done to date on 

graduation rates by NCES (2004, 2003), Swanson (2003), Greene (2002), and others 

makes it apparent that there are different data sources to be used for different graduation 

indicators, and in some cases multiple data sources that can be used to calculate the same 

graduation indicators. 

In particular, the number of students by grade at the school level from the Public School 

Survey, and the number of diploma recipients,9

 other high school completers, and 

dropouts from each of grades 7 through 1210 from the Local Education Agency (School 

District) Universe Survey, include the data required to compute the GLI—this indicator 

can be computed using these data aggregated to the district or state level. In addition, the 

school-level data for the number of students by grade can be aggregated to the district 

level, and combined with district-level data for the numbers of diploma recipients to 

produce district-level estimates of the FGR, AFGR, SCPI, and GGI. These district-level 

data can then be aggregated to the state level to produce state-level estimates of FGR, 

AFGR, SCPI, and GGI and ultimately national estimates of the same graduation 

indicators. 

It is also possible to compute state and national estimates for the same four graduation 

indicators using state-level aggregates of the number of students by grade level in the 

current school year and diploma recipients and other completers in the previous year 

using data from the State Aggregate Nonfiscal Data. Thus, state- and national estimates 

for FGR, AFGR, SCPI, and GGI can be calculated from two different data files. Because 

the state data file frequently includes students and graduates from special programs that 

are not included in any district- or school-level data files, the same state level graduation 

 

8

 While GLI was dropped from the analyses in chapters 2 and 3, it is included again here to confirm 

whether the pattern observed in State 1 is repeated across states. 9

 Prior to 1998-99 data were reported separately for regular diploma recipients and other diploma 

recipients. Starting in 1998-99, these two categories were combined in the data collection. 

10 The dropout data, although collected within the Local Education Agency (School District) Universe 

survey, are released separately as the “Dropout Component of the Local Education Agency Universe 

Survey.” 
 

51 

indicator computed using state data in one instance and school and district data 

aggregated to the state level in another, will not necessarily yield identical results. 

Given this range of options to choose from, more information is needed about the details 

of each dataset. For example, a comparison of the proxy graduation indicators suggested 

that the population coverage of each data set, the treatment of nonresponse, and the 

treatment of ungraded students must each be considered. 

Looking first at coverage for the 50 states and the District of Columbia, the district-level 

dropout data that are needed for the GLI are only available for states that are using the 

prescribed CCD definitions. For the 2000-01 school year, a total of 49 states submitted 

dropout data to the CCD. Of these, 45 reported using agreed-upon reporting definitions; 

those that did not were excluded from the CCD dropout data file. (Coverage is up from 

12 participating states when the collection was started in 1991-92.) In contrast, the 

indicators that only require data on enrollments and graduates can be calculated using 

data from files that include all 50 states and the District of Columbia (i.e., the State 

Nonfiscal file or the School and School District files combined). 

Considering nonresponse next, a review of the CCD file documentation found that nearly 

all state education offices in the 50 states and the District of Columbia provided counts of 

all students enrolled in grades 9 through 12 and of diploma recipients at both the state and 

school levels. In those few instances when these state-level data were not reported, they 

were imputed. Of course, in the absence of independent audits, there is no way of 

knowing with certainty whether all students in all schools are reported or whether all 

diploma recipients in all school districts are reported. Missing data at the school or 

district level are also missing in the state estimates, although it is not as apparent because 

the data are reported out as a group at the state level. The picture is not as clear for the 

other completer counts that are used in the GLI. For example, in 2002-03 there were three 

states that reported missing some or all of their data on other high school completers. In 

addition, there were 14 states that reported not having documentation on the other 

completer category. While this is not nonresponse per se on the part of these 14 states, it 

does highlight the fact that there are differences across states in the categorization and 

reporting of different types of high school completers. 

The third factor to consider is the treatment of ungraded students. The CCD Dropout 

Component includes these students by allocating them across the grades served by the 

schools they attend. However, these students are left in a separate category in the other 

CCD School District file, the CCD School file and the CCD State Nonfiscal file. Because 

ungraded students are enrolled in the school and can contribute to the population of high 

school completers, their exclusion from the denominator of graduation rates computed 

from these files serves to inflate the estimates of the indicators, FGR, AFGR, SCPI, and 

GGI, when they are computed using these data (e.g., rates published by Greene and 

Winters (2002) and Swanson (2003)). Alternatively, ungraded students can be allocated 

across the grades served by the schools they attend in order to provide a more realistic 

estimate of an on-time graduation rate. The data used in the analysis in this chapter 

include the ungraded students allocated across grades. 
 

52 

From this review of data limitations, it is evident that differences in the data elements that 

are used must be carefully considered in any analysis of graduation indicators. For these 

reasons, the data used for each indicator in this chapter are carefully defined. Wherever 

possible, comparisons across indicators are done based on indicators that are calculated 

using the same data files; and when this is not possible, differences are described. 

4.1. Using student record findings for the analysis of CCD data 

In addition to a descriptive comparison of the proxy graduation indicators computed 

using CCD data, the results from the analyses of student record data from States 1 and 2 

can be used as an analytic basis for further analysis of CCD based graduation indicators. 

Although the data required to calculate true cohort on-time graduation rates are not 

available for other states, since AFGR was identified across analyses at both the state and 

school district levels as the one proxy measure that was consistently among the best 

performing indicators relative to EACGI, it is used here as an approximation of the true 

cohort rate in States 1 and 2, and is taken as the standard for comparison in the analyses 

in this chapter. In particular, the relationships between AFGR and each of the other 

proxy graduation indicators are examined to determine if the relative comparison of the 

indicators across all states is the same as that observed in States 1 and 2. 

This analysis is based on a set of assumptions. First, that rates computed using CCD data 

are strongly correlated with the rates computed using the student record data from States 

1 and 2. Second, that the relationships observed between the indicators in the analysis of 

the student record data are repeated in the CCD data for States 1 and 2. Third, that these 

assumptions can be generalized to all states. 

District-level data are used to test the first two assumptions. Specifically, FGR, AFGR, 

GGI, and SCPI were computed across school districts using the student record data from 

State 1 for 2000-01 and 2001-02 and were then correlated with the same rates computed 

across school districts using CCD data for State 1.11 This analysis yielded correlations 

across the graduation measures of .93 to .96 in 2000-01 and of .95 to .96 in 2001-02 for 

State 1 (table 4.1). Next, the CCD school district rates for FGR, AFGR, GGI, and SCPI in 

State 1 were regressed against the true cohort rate EACGI from the student record data 

for each school district in State 1. Regression of each of the rates against EACGI 

provided information on how each proxy graduation indicator computed with CCD data 

correlated with EACGI across school districts in State 1, how much of the variance in 

EACGI could be explained by each CCD proxy graduation indicator, and how much 

EACGI changes with a 1 percentage point change in each CCD proxy graduation 

indicator. This analysis showed consistent results within each indicator across the 2 years, 

with the strongest relationships evident between EACGI and AFGR and EACGI and 

FGR, and with weaker relationships between EACGI and both GGI and SCPI (table 4.2). 

 

11 Because district level rates are more subject to population changes, and because errors in reporting can 

have a profound impact on district level rates, the Districts with CCD rates above 100 percent or below 25 

percent were trimmed from the regression analysis. 
 

53 

Table 4.1. Regression estimates of State 1 student record school district estimates on State 1 

CCD school district estimates for graduation indicators FGR, AFGR, GGI, and SCPI, 

by school year: 2000-01 and 2001-02 

Indicator1

Statistic FGR AFGR2 GGI2 SCPI

2000-013 

Correlation coefficient .96 .93 .95 .93

R square .91 .87 .91 .87

Slope .98 .94 .96 .86

Standard deviation 2.37 2.30 2.25 3.90

2001-02 

Correlation coefficient .96 .96 .96 .95

R square .93 .92 .92 .90

Slope .99 0.96 .95 .91

Standard deviation 2.55 2.15 2.11 2.99

1

 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Rate, first-time 

freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion 

Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

3

 One district was excluded. 

NOTE: Cases with estimates of less than 25 percent or over 100 percent on any indicator were 

excluded. 

SOURCE: Data from State 1 student record system; U.S. Department of Education, National 

Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary 

School Universe Survey" school years 1996-97 through 2002-03 and “Local Education Agency 

Universe Survey” school years 2001-02 through 2002-03. 

Recall that table 2.3 in chapter 2 showed the relationships between the true cohort ontime graduation rate and each of the proxy graduation indicators when all rates were 

calculated using student record data. A comparison of the results in tables 4.2 and 2.3 

shows that the relative positions of the proxy graduation indicators compared to the true 

cohort rates are the same using either CCD data or student record data. That is to say, the 

relationships with EACGI are stronger for AFGR and FGR and weaker for GGI and 

SCPI. 
 

54 

Table 4.2. Regression estimates of State 1 student record school district estimates for EACGI on 

State 1 CCD school district estimates, by indicator and school year: 2000-01 through 

2001-02 

Indicator1

Statistic FGR AFGR2 GGI2

 SCPI

2000-013

Correlation coefficient .77 .80 .62 .48

R square .60 .65 .38 .23

Slope .75 .96 .65 .31

Standard deviation 4.80 4.50 5.97 6.64

2001-02 

Correlation coefficient .82 .78 .55 .45

R square .67 .61 .30 .20

Slope .74 .84 .60 .38

Standard deviation 4.82 5.27 7.03 7.53

1

 EACGI = Exclusion Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation 

Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = 

Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

3

 One district was excluded. 

NOTE: Cases with estimates of less than 25 percent or over 100 percent on any indicator were 

excluded. 

SOURCE: Data from State 1 student record system; U.S. Department of Education, National 

Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary 

School Universe Survey" school years 1996-97 through 2002-03 and “Local Education Agency 

Universe Survey” school years 2001-02 through 2002-03. 
 

55 

The analysis for State 2 showed that the proxy graduation indicators computed across 

school districts using student record data were strongly correlated with the same rates 

computed across school districts using CCD data (.92 to .98) (table 4.3). The analysis in 

table 4.4 shows that although the relationships are weaker, the relative positions between 

the proxy measures as compared to the true cohort rates are repeated in State 2 (tables 4.4 

and 3.3). 

Table 4.3. Regression estimates of State 2 student record school district estimates on State 2 CCD 

school district estimates for FGR, AFGR, GGI, and SCPI, by school year: 1999-2000 

through 2001-02 

Indicator1

Statistic FGR AFGR2 GGI2 SCPI

1999-2000 

Correlation coefficient .97 .93 .92 .97

R square .94 .86 .85 .95

Slope .95 .90 .95 .99

Standard deviation 2.01 2.31 2.46 2.47

2000-01 

Correlation coefficient .97 .96 .95 .98

R square .94 .92 .91 .96

Slope 1.02 1.03 1.09 1.03

Standard deviation 2.09 2.23 2.38 2.05

2001-02 

Correlation coefficient .97 .94 .92 .97

R square .94 .88 .85 .94

Slope .99 .95 .88 .97

Standard deviation 2.29 2.65 2.41 2.50

1

 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation 

Rate, first-time freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Cases with estimates of less than 25 percent or over 100 percent on any indicator were 

excluded. 

SOURCE: Data from State 2 student record system; U.S. Department of Education, National 

Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary 

School Universe Survey," school years 1995-96 through 2002-03 and “Local Education Agency 

Universe Survey” school years 2000-01 through 2002-03. 
 

56 

Table 4.4. Regression estimates of State 2 student record school district estimates for EACGI 

on State 2 CCD school district estimates, by indicator and school year: 1999-2000 

through 2001-02 

Indicator1

Statistic FGR AFGR2 GGI2

 SCPI

1999-2000 

Correlation coefficient .58 .62 .67 .67

R square .34 .38 .44 .45

Slope .49 .65 .74 .42

Standard deviation 5.78 5.59 5.29 5.26

2000-01 

Correlation coefficient .63 .68 .61 .48

R square .40 .47 .38 .23

Slope .63 .77 .73 .43

Standard deviation 6.33 5.97 6.46 7.16

2001-02 

Correlation coefficient .60 .62 .52 .51

R square .35 .39 .27 .26

Slope .49 .61 .59 .37

Standard deviation 5.87 5.73 6.25 6.27

1

 EACGI = Exclusion Adjusted Cohort Graduation Indicator; FGR = Freshman Graduation 

Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = 

Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Cases with estimates of less than 25 percent or over 100 percent on any indicator were 

excluded. 

SOURCE: Data from State 2 student record system; U.S. Department of Education, National 

Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary 

School Universe Survey," school years 1995-96 through 2002-03 and “Local Education 

Agency Universe Survey” school years 2000-01 through 2002-03. 

Finally, the relationships comparing AFGR to FGR, GGI, and SCPI were examined in 

both the state student record data for State 1 and the CCD data. The estimates based on 

student record data are displayed in table 4.5; a comparison of the estimates with 

comparable estimates using CCD data for State 1 showed that the results were similar 

across the two sets of estimates.12 In both analyses the correlations between AFGR and 

FGR for 2000-01 and 2001-02 were strong (r greater than .90) and more than 84 percent 

of the variation in AFGR was explained by FGR in both sets of data. In both sets of 

comparisons GGI outperforms SCPI, but the relationships between AFGR and GGI or 

SCPI are weaker than the relationship between AFGR and FGR. Again, the same analysis 

conducted using data from State 2 showed a stronger relationship between AFGR and 

FGR than between AFGR and GGI or SCPI (table 4.6). 

 

12 The CCD analysis for States 1 and 2 are not displayed here to protect the identities of the States. 
 

57 

Table 4.5. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, and SCPI 

with all indicators calculated using student record data for State 1, by 3 school 

year: 2000-01 and 2001-02 

Indicator1

Statistic FGR GGI2

 SCPI

2000-013

Correlation coefficient4 .92 .71 .48

R square .84 .50 .23

Slope .74 .63 .29

Standard deviation 2.55 4.52 5.63

2001-02 

Correlation coefficient .93 .65 .46

R square .87 .42 .21

Slope .76 .66 .38

Standard deviation 2.81 5.95 6.94

1

 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation 

Rate, first-time freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

3 One district was excluded. 

SOURCE: Data from State 1 student record system. 
 

58 

Table 4.6. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, and SCPI 

with all indicators calculated using student record data for State 2, by school year: 

1999-2000 through 2001-02 

Indicator1

Statistic FGR GGI2

 SCPI

1999-2000 

Correlation coefficient .92 .78 .79

R square .84 .61 .62

Slope .73 .78 .45

Standard deviation 2.65 4.13 4.06

2000-01 

Correlation coefficient .90 .77 .70

R square .81 .59 .50

Slope .81 .77 .57

Standard deviation 3.41 5.00 5.55

2001-02 

Correlation coefficient .92 .59 .66

R square .84 .35 .43

Slope .76 .72 .49

Standard deviation 3.03 6.11 5.70

1

 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation 

Rate, first-time freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

NOTE: Districts 68 and higher were excluded. 

SOURCE: Data from State 2 student record system. 

While it would, of course, be preferable to have student record system data from a larger 

subset of states, these analyses lend support to the use of AFGR as the standard in 

evaluating the performance of the proxy measures across states. 

4.2. Graduation indicators at the national level 

The FGR, AFGR, GGI and SCPI can all be calculated at the national level using state 

data. This section focuses on how widely the proxy graduation indicators vary over a 7-

year period, the relative position of the indicators over that period, the stability and 

direction of trends for each indicator, and the relationship between each indicator and 

underlying demographic changes in the population during the 7 years. 

The FGR, AFGR, GGI, and SCPI proxy indicators were estimated using data from the 

CCD state nonfiscal data file.13 However, because ungraded students are reported 

separately in this data file, the ungraded students in grades 9 through 12 were allocated 

proportional to each state’s enrollment in those grades and then added to the grade-

 

13 Because missing state-level data are imputed in this data file, the national- and state-level analyses in this 

chapter are based on data for all states in all years. 
 

59 

specific enrollments. The resulting state-level data for 1995-96 through 2001-02 were 

aggregated to the national level, and these data were used to compute annual rates for the 

four indicators (table 4.7).14 

Table 4.7. National graduation indicators, by year and indicator: 1995–96 through 2001–02 

Indicator1

 1995-96 1996-97 1997-98 1998-99 1999-

2000 2000-01 2001-02

FGR 66.5 66.4 66.6 66.0 66.3 66.3 67.0

AFGR2 71.0 71.3 71.3 71.1 71.7 71.7 72.6

GGI2

 66.6 66.4 66.7 67.3 68.8 69.2 69.7

SCPI 66.1 65.4 65.3 65.7 66.6 67.9 69.8

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation 

Rate, first-time freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator. 

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common 

Core of Data (CCD), "State Nonfiscal Survey of Public Elementary/Secondary Education," 

school years 1991-92 through 2002-03. 

The national average for the AFGR ranged from a low of 71 percent to a high of 73 

percent over the 7-year period, with an average rate of 72 percent. The national FGR 

ranged from a low of 66 percent to a high of 67 percent, with an average rate of 66 

percent. The national GGI ranged from a low of 66 to a high of 70, with an average of 68 

percent. The national average computed for the SCPI ranged from a low of 65 percent to 

a high of 70 percent, with an average of 67 percent. As was the case in the analysis of 

data from States 1 and 2, the AFGR yields a higher estimate than the other three 

measures. In any given year, the point spread between AFGR and lowest of the proxy 

graduation indicators is approximately 5 to 6 percentage points. 

When the proxy graduation indicators are examined over the 7 years, the patterns for the 

FGR and AFGR were similar (figure 4.1). After a decline from 1995-96 to 1996-97, 

there was little change between 1996-97 and 2000-01, with a 1 percentage point increase 

in the indicator based on all freshmen (FGR) and a 2 percentage point increase in the 

indicator based on first-time freshmen (AFGR). Thus, the difference between the two 

indicators increased by one percentage point—from just under 5 to just under 6 

percentage points. In contrast, the Swanson Cumulative Promotion Indicator and the 

Greene Graduation Indicator are both on a par with the graduation rate, based on all 

freshmen (FGR) in 1995-96 and 1996-97. Then after a decrease between 1995-96 and 

1996-97, both the Swanson cumulative promotion indicator and the Greene graduation 

indicator increased gradually between 1996-97 and 2001-02, with the Swanson indicator 

gaining 5 percentage points and the Greene indicator gaining 4 percentage points over the 

6 years. Because the Greene and Swanson indicators increased more than the rate based 

on all freshmen, the Greene and Swanson indicators end up half way between the 

freshman graduation rate based on all freshmen and the averaged freshman graduation 

 

14 There is no national estimate for GLI because not all states report the required data elements. 
 

60 

based on first-time freshmen in 2001-02 (approximately 3 percentage points from each 

unadjusted indicator). 

Each of these proxy graduation indicators is influenced by underlying changes in the 

populations used in the denominators of the indicators. For example, an examination of 

CCD enrollment data by grade shows that the patterns over time for FGR and AFGR are 

affected by the fact that the school populations in their denominators are driven by a 

population that is increasing in size, albeit at a decreasing rate of increase over time (data 

not shown). CCD enrollment data by grade also show that for SCPI, the estimates are 

influenced by grade-to-grade differences in the rates of growth between the freshman 

classes and enrollments in the other grades.15 Finally, in the case of GGI, an examination 

of the CCD enrollment data by grade over time shows that the pattern is affected by both 

the slowing rate of growth in the size of the population entering high school and the size 

of the population adjustment that is applied to the estimated number of first-time 

freshmen. 

Comparisons of data across the rates reveal that in most cases the all freshmen 

denominator in FGR is larger than the estimated first-time freshmen denominator in 

AFGR (data not shown). The difference between estimates of all freshmen and that for 

first-time freshmen is driven by 9th-grade retention patterns. The averaging across 

consecutive years’ enrollments in grades 8, 9, and 10 is intended to dampen the impact of 

9th-grade retentions, thus yielding an estimate of on-time freshmen. Year-to-year 

changes in the rates of population increase vary by grade and introduce another source of 

difference between AFGR and FGR over time. 

In the same vein, comparisons of data across the rates show that the only difference 

between AFGR and GGI is in the size of the population adjustment that is applied to the 

estimate of first-time freshmen to get an estimate of the potential seniors 4 years later for 

GGI. In GGI, this population adjustment is the ratio of the difference between 

enrollments in grades 9 through 12 in the senior year and enrollments in grades 9 through 

12 four years earlier in the freshman year to enrollments in grades 9 through 12 four 

years earlier in the freshman year. The application of this ratio is intended to adjust for 

changes due to migration over the high school years to produce an estimate of the 

potential number of seniors 4 years later. At the national level during this time period, 

this adjustment yields an estimate of GGI that is lower than the estimate of AFGR, 

suggesting that the estimated number of potential seniors enrolled 4 years later is larger 

than the number of freshmen 4 years earlier. The Greene estimate suggests that there 

were more potential seniors than the starting number of freshmen in each of the 7 years in 

the analysis (appendix B). The assumption that this adjustment accounts for the net effect 

of migration between the freshman and senior years leads to the conclusion that there was 

a net increase in the size of each high school class in each year between 1996-97 and 

2001-02—with the potential for more ending seniors than beginning freshmen in each 

successive cohort. This is not a realistic assumption.

 

15 Important here is the fact that differential rates of change in 9th-grade enrollments relative to enrollments 

in grade 10-12 impact year to year changes in this proxy graduation rate, independent of the number of 

graduates. 
61 

school years 1991-92 through 2002-03.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Public Elementary/Secondary EducatNOTE: FGR=Unadjusted Graduation Indicator, All Freshmen; AFGR=Unadjusted Graduation Indicator, First-Time Freshmen; SCPI=Swanson's Cumulative Promotion IGraduation Indicator. 

Figure 4.1. National graduation rates for FGR, AFGR, SCPI, and GGI: 1995-96 through 2001-02

405060708090

100

1995-96 1996-97 1997-98 1998-99 1999-00 2000-0

Year

Percent

FGR AFGR SCPI GGI

0
 

62 

In 2001-02, for example, the GGI adjustment calculation yields a rate of change of 4.1 

percent. An examination of data for the freshman classes that make up the student 

population in grades 9-12 in 2001-02 shows that the freshman class increased in size each 

year, contributing to one half of the 4 percent increase measured by the Greene 

approach.16 In ignoring the growth in the size of the incoming freshman classes, the 

Greene indicator attributes too much of the change to migration. As a result the GGI 

artificially inflates the size of the denominator and decreases the graduation indicator. 

When the Greene Graduation Indicator is adjusted to control the impact of population 

growth in the incoming freshmen classes, it yields graduation rates that range from 1 to 4 

percentage points higher than the current GGI estimates. Thus, instead of rates ranging 

from 66 to 70 percent, the rates that have been adjusted to reflect only growth in the 

population between grades 9 and 12 are in the range of 69 to 72 percent. These new 

estimates are much closer to the estimates of 71 to 73 percent from the Averaged 

Freshman Graduation Rate. 

 

4.3. Graduation rates at the state level 

Analyses similar to the national analyses can be performed at the state level for FGR, 

AFGR, GGI, SCPI, and in some states GLI. Again, the proxy graduation indicators are 

compared in terms of their variation over a 7-year period, their relative positions, and the 

stability and direction of trends over 7 years. In addition, the state level data allow 

statistical analyses of the relationships between AFGR and the other indicators across the 

population of states and years. In this analysis, AFGR is taken as the standard because it 

was found to be the most consistent among the best performing measures in comparisons 

to the true cohort rate in chapters 2 and 3. 

The FGR, AFGR, GGI, and SCPI were computed for all 50 states and the District of 

Columbia for each of the 7 school years from 1995-96 through 2001-02. Data from the 

state nonfiscal data files that were used in the national-level analysis were also used for 

the state-level analysis of these four proxy graduation indicators; as a result any missing 

data have been imputed and the ungraded students have been allocated to specific grades. 

The dropout data required for computing the GLI are not available for all states; thus, the 

GLI was computed for the subset of 30 states that had the needed district- and schoollevel data available for at least 5 of the 7 years.17 These data for GLI have the ungraded 

students allocated, but missing state data have not been imputed. 

The national graduation indicators for the four proxy measures that can be computed for 

all 50 states and DC were around 70 percent (ranging from 65 to 73 percent in individual 

years) (table 4.7). Looking across all states over the 7 years, it is evident that there is 

more variability at the state level in each of the proxy measures than there was at the 

 

16 Since the grade 9-12 population in 2001-02 is comprised of the incoming freshman class for that year and 

the 3 previous years, the observed value compared to an estimate holding the freshman class size to 

observed count in 1998-99 shows a 2 percent increase in the size of the incoming population. 

17 GLI is included in this initial analysis of CCD data as a reference because a number of states are 

currently using GLI as an annual yearly progress (AYP) measure. 
 

63 

national level (tables 4.8-4.14). In particular, over the 7-year period AFGR ranged from 

yearly lows between 50 and 84 percent to yearly highs between 61 and 89 percent (table 

4.15). The rates from FGR ranged from yearly lows between 48 and 84 percent to yearly 

highs between 54 and 91 percent. The GGI estimates ranged from yearly lows between 

53 and 81 percent to yearly highs of 58 to 89 percent. In the case of SCPI, the yearly 

minimums ranged from 36 to 83 percent and the yearly high estimates ranged from 53 to 

102 percent. Finally in the case of GLI, the yearly minimums ranged from 59 to 89 

percent between 1997-98 and 2001-02 and the yearly maximums over those 5 years 

ranged from 66 to 93 percent.18

 

18 1995-96 and 1996-97 were not included here because of the relatively small number of reporting states in 

those years. 
 

64 

Table 4.8. Graduation indicators, by indicator and state: School year 1995-96 

 Indicator1

 

State FGR AFGR2 GGI2 SCPI GLI

Alabama 57.8 62.7 59.5 56.6 —

Alaska 64.7 68.3 61.6 65.6 —

Arizona 57.9 60.8 54.8 63.6 —

Arkansas 74.4 74.2 70.3 71.8 80.6

California 64.0 67.6 63.4 66.5 —

Colorado 71.6 74.8 68.0 71.6 —

Connecticut 72.0 76.1 73.2 70.7 —

Delaware 65.8 70.4 63.5 64.9 —

District of Columbia 50.4 49.7 54.5 47.8 —

Florida 57.8 62.3 56.6 55.4 —

Georgia 55.0 61.9 56.6 53.4 —

Hawaii 70.0 74.5 67.9 57.5 —

Idaho 79.2 80.5 73.2 79.1 —

Illinois 72.2 75.2 72.0 76.1 —

Indiana 69.2 73.6 71.0 68.1 —

Iowa 82.6 84.3 77.4 81.3 —

Kansas 74.3 77.1 70.9 73.7 —

Kentucky 66.9 71.3 68.9 62.2 —

Louisiana 55.2 61.7 58.9 53.4 —

Maine 71.4 73.7 77.0 75.8 —

Maryland 72.5 78.3 71.3 71.4 —

Massachusetts 75.1 78.0 74.8 73.7 82.9

Michigan 66.6 71.4 69.6 74.5 —

Minnesota 85.3 86.1 77.6 85.5 —

Mississippi 54.7 59.7 58.2 51.9 69.1

Missouri 70.7 75.0 70.1 70.6 74.4

Montana 82.2 83.9 76.4 77.4 —

Nebraska 82.9 85.6 79.0 83.8 81.2

Nevada 65.2 65.8 54.9 65.6 62.8

New Hampshire 74.6 77.5 71.1 72.8 —

New Jersey 78.1 82.8 81.6 79.8 —

New Mexico 59.8 63.7 57.6 54.3 67.1

New York 58.1 63.6 60.8 54.8 —

North Carolina 61.3 66.5 64.6 57.8 —

North Dakota 89.0 89.5 83.1 89.0 —

Ohio 69.4 74.5 70.8 66.9 —

Oklahoma 72.8 75.6 70.2 70.7 —

Oregon 66.3 68.3 65.0 68.4 —

Pennsylvania 74.7 80.0 75.4 74.1 83.1

Rhode Island 69.5 72.7 69.6 67.5 81.0

South Carolina 54.1 60.9 57.8 51.9 —

South Dakota 85.6 84.5 71.8 74.4 —

Tennessee 62.1 66.6 64.1 60.3 —

Texas 58.4 66.1 60.5 58.6 —

Utah 76.8 76.9 69.0 75.3 —

Vermont 89.3 85.3 70.4 77.0 —

Virginia 73.5 76.2 71.5 71.0 —

Washington 72.2 75.5 66.8 71.3 —

West Virginia 74.6 77.0 79.0 75.4 —

Wisconsin 80.0 83.6 75.4 77.9 —

Wyoming 77.8 77.7 71.6 76.2 —

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation Indicator; 

SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1991-92 through 1996-97 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1991-92 through 1995-96. 
 

65 

Table 4.9. Graduation indicators, by indicator and state: School year 1996-97 

 Indicator1 

State FGR AFGR2 GGI2 SCPI GLI

Alabama 57.3 62.4 59.6 56.5 —

Alaska 63.8 67.9 61.8 64.3 —

Arizona 61.7 65.3 56.5 58.1 —

Arkansas 69.4 70.6 67.2 70.9 79.9

California 64.9 68.8 62.9 66.4 —

Colorado 72.1 74.7 66.2 69.7 —

Connecticut 72.6 76.7 72.3 70.7 80.7

Delaware 66.7 71.7 63.7 63.2 79.6

District of Columbia 54.4 54.6 60.1 50.7 —

Florida 57.6 62.7 55.9 54.6 —

Georgia 54.8 62.0 56.6 54.5 —

Hawaii 62.8 69.1 65.5 62.6 —

Idaho 78.4 80.1 73.6 74.5 —

Illinois 73.0 76.1 71.6 70.3 —

Indiana 69.7 74.0 72.0 69.7 —

Iowa 82.5 84.6 78.5 80.9 92.7

Kansas 73.6 76.9 71.1 73.4 —

Kentucky 66.5 71.1 70.4 70.5 —

Louisiana 52.3 59.3 57.9 50.1 —

Maine 71.2 75.2 78.5 76.8 —

Maryland 70.0 76.6 70.1 72.4 —

Massachusetts 75.2 78.4 74.0 74.3 84.6

Michigan 68.1 73.5 68.2 62.3 —

Minnesota 77.3 78.6 71.0 78.7 —

Mississippi 54.4 59.6 58.4 54.7 69.3

Missouri 70.2 74.7 71.0 70.7 74.4

Montana 80.6 83.2 77.2 77.9 —

Nebraska 82.4 84.8 77.7 82.9 82.1

Nevada 72.8 73.2 59.8 67.0 63.3

New Hampshire 74.5 77.3 69.8 73.8 —

New Jersey 80.0 83.9 79.5 79.5 —

New Mexico 56.4 62.5 58.6 53.7 66.5

New York 59.2 65.3 63.0 55.7 —

North Carolina 60.2 65.5 62.8 58.4 —

North Dakota 86.9 87.8 81.0 82.5 89.7

Ohio 70.8 76.4 72.2 69.7 —

Oklahoma 71.8 74.8 69.6 71.6 80.9

Oregon 67.1 69.1 65.1 65.0 —

Pennsylvania 74.3 79.8 75.3 74.9 83.4

Rhode Island 69.4 72.9 68.9 66.6 79.6

South Carolina 52.4 59.6 56.9 51.6 —

South Dakota 80.7 84.2 77.3 77.2 —

Tennessee 57.1 61.6 59.2 49.2 —

Texas 58.9 67.0 60.4 59.5 —

Utah 80.7 81.1 74.5 81.1 —

Vermont 81.8 83.6 76.0 78.3 —

Virginia 73.3 76.6 71.1 70.8 —

Washington 71.4 74.0 65.9 70.6 —

West Virginia 73.5 76.7 79.0 76.0 —

Wisconsin 79.5 83.7 75.9 77.5 —

Wyoming 77.7 78.4 72.9 74.2 —

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation Indicator; 

SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator. 2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1992-93 through 1997-98 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1992-93 through 1996-97. 
 

66 

Table 4.10. Graduation indicators, by indicator and state: School year 1997-98 

 Indicator

1

State FGR AFGR2 GGI2 SCPI GLI

Alabama 59.8 64.4 62.3 57.8 70.8

Alaska 65.0 68.9 62.9 69.4 —

Arizona 61.1 65.6 58.5 62.0 —

Arkansas 72.7 73.9 70.6 71.0 75.0

California 66.0 69.6 62.8 67.4 —

Colorado 71.3 73.9 65.5 67.9 —

Connecticut 72.7 76.9 72.0 72.2 80.8

Delaware 68.0 74.1 67.0 62.1 79.0

District of Columbia 53.7 53.9 57.5 36.1 —

Florida 57.0 62.1 54.8 51.8 —

Georgia 51.3 58.2 53.6 51.3 62.0

Hawaii 62.0 68.8 64.5 60.1 —

Idaho 78.5 79.7 75.5 77.8 —

Illinois 73.3 76.8 74.0 70.4 71.0

Indiana 70.3 73.8 72.7 68.7 —

Iowa 81.9 83.9 79.7 80.9 86.7

Kansas 72.8 76.0 70.8 77.6 —

Kentucky 65.6 70.2 68.6 60.8 —

Louisiana 54.2 61.3 61.6 55.3 65.1

Maine 77.6 78.5 75.3 74.9 85.1

Maryland 69.5 76.2 69.9 74.0 79.8

Massachusetts 75.1 78.3 73.0 72.7 83.9

Michigan 69.1 74.6 71.1 70.9 —

Minnesota 83.9 85.0 76.8 82.8 73.9

Mississippi 54.5 59.8 59.5 54.9 70.2

Missouri 71.0 75.2 72.1 71.8 76.5

Montana 79.7 82.2 77.7 78.6 —

Nebraska 84.7 85.6 79.1 80.7 81.8

Nevada 69.7 70.6 59.4 69.0 62.9

New Hampshire 74.2 76.7 68.6 73.4 —

New Jersey 73.0 76.3 72.3 72.7 81.3

New Mexico 56.4 61.6 58.9 57.3 67.2

New York 58.2 63.9 61.4 52.7 —

North Carolina 59.6 65.6 62.7 57.5 —

North Dakota 85.4 86.7 81.3 82.5 89.3

Ohio 73.0 77.0 72.8 69.3 —

Oklahoma 71.9 75.1 70.1 72.9 78.2

Oregon 66.9 69.0 64.6 65.7 —

Pennsylvania 74.0 79.4 75.3 73.7 82.8

Rhode Island 68.5 72.5 69.0 68.3 80.1

South Carolina 52.2 59.3 57.1 49.1 —

South Dakota 75.0 77.7 72.8 61.9 83.9

Tennessee 53.8 58.4 58.9 55.9 77.5

Texas 61.0 69.4 62.7 60.5 —

Utah 80.6 80.7 76.6 81.4 78.9

Vermont 80.5 83.9 76.7 74.7 81.5

Virginia 72.4 76.6 72.2 72.4 80.2

Washington 70.9 73.3 65.5 67.8 —

West Virginia 74.6 77.4 79.9 74.7 83.8

Wisconsin 78.8 83.1 77.5 76.0 72.0

Wyoming 77.4 77.1 73.9 74.7 76.2

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation 

Indicator; SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator.

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1993-94 through 1998-99 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1993-94 through 1997-98. 
 

67 

Table 4.11. Graduation indicators, by indicator and state: School year 1998-99 

 Indicator1

State FGR AFGR2 GGI2 SCPI GLI

Alabama 55.5 61.3 61.7 55.3 71.3

Alaska 66.4 70.0 62.3 61.0 —

Arizona 59.9 62.3 53.7 54.3 —

Arkansas 72.2 73.7 72.4 73.8 74.9

California 67.1 71.1 64.1 68.4 —

Colorado 70.3 73.4 65.8 68.3 —

Connecticut 71.3 76.0 70.5 73.4 82.2

Delaware 64.1 70.4 66.4 58.5 79.2

District of Columbia 49.6 52.0 61.9 79.1 —

Florida 56.0 61.4 54.5 52.3 —

Georgia 50.4 57.5 53.4 50.7 62.2

Hawaii 59.7 67.5 65.2 59.5 —

Idaho 77.8 79.5 76.8 79.6 —

Illinois 71.8 76.0 73.9 70.6 70.4

Indiana 70.3 74.3 74.5 70.4 —

Iowa 81.1 83.3 81.6 80.6 87.1

Kansas 74.0 76.7 71.0 73.7 —

Kentucky 64.4 70.0 70.1 61.7 —

Louisiana 53.8 61.1 63.1 56.7 59.3

Maine 74.2 74.7 72.1 73.5 85.6

Maryland 70.5 76.6 69.8 70.5 80.6

Massachusetts 74.5 77.9 72.8 73.5 84.4

Michigan 69.4 73.9 70.0 68.7 —

Minnesota 84.7 86.0 79.4 84.9 75.1

Mississippi 54.0 59.2 60.5 57.3 70.0

Missouri 71.6 75.8 73.4 71.3 77.5

Montana 78.3 81.3 79.2 78.1 —

Nebraska 86.3 87.3 82.8 82.1 82.5

Nevada 70.5 71.0 60.1 68.9 64.1

New Hampshire 72.7 75.3 68.1 72.8 —

New Jersey 74.2 77.5 73.9 72.2 82.5

New Mexico 57.8 63.3 61.8 58.5 68.2

New York 56.1 62.5 61.4 53.5 —

North Carolina 58.6 65.4 62.2 58.7 —

North Dakota 84.5 85.6 82.8 84.8 89.6

Ohio 69.2 75.0 74.7 70.0 —

Oklahoma 72.9 76.4 72.2 72.2 78.7

Oregon 66.3 68.2 63.6 67.5 —

Pennsylvania 73.7 79.1 76.5 75.1 83.7

Rhode Island 67.2 72.2 68.1 67.8 81.7

South Carolina 51.8 59.1 57.7 45.6 —

South Dakota 71.2 74.2 77.1 76.6 84.7

Tennessee 53.9 58.5 59.2 64.5 71.7

Texas 60.6 69.2 63.7 60.6 —

Utah 81.4 81.6 79.9 82.5 78.7

Vermont 79.2 81.9 76.1 78.7 81.2

Virginia 71.6 76.3 72.1 70.3 79.6

Washington 70.6 73.2 67.0 70.2 —

West Virginia 75.1 77.9 81.4 71.5 83.1

Wisconsin 78.1 82.6 79.2 76.3 73.1

Wyoming 76.5 76.6 75.7 70.7 76.8

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation 

Indicator; SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator.

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1994-95 through 1999-2000 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1994-95 through1998-99. 
 

68 

Table 4.12. Graduation indicators, by indicator and state: School year 1999-2000 

 Indicator1

State FGR AFGR2 GGI2 SCPI GLI

Alabama 58.9 64.1 66.0 61.9 74.4

Alaska 62.3 66.7 61.1 58.0 —

Arizona 58.7 63.6 58.8 61.8 —

Arkansas 73.1 74.6 74.4 72.4 74.2

California 67.5 71.7 65.6 67.9 —

Colorado 70.4 74.1 68.4 72.3 —

Connecticut 76.7 81.9 75.4 80.4 84.5

Delaware 60.7 66.8 66.8 67.5 77.1

District of Columbia 52.0 54.5 55.4 37.5 —

Florida 55.2 61.0 54.8 49.7 —

Georgia 52.3 59.7 56.1 52.6 65.0

Hawaii 64.1 70.9 69.4 62.2 —

Idaho 76.9 79.4 78.9 76.0 —

Illinois 71.0 76.3 75.7 72.2 68.9

Indiana 67.9 71.8 72.8 67.6 —

Iowa 80.8 83.1 83.0 80.9 87.8

Kansas 73.7 77.1 72.8 74.6 —

Kentucky 64.7 69.7 69.9 69.2 —

Louisiana 54.9 62.2 64.9 57.3 61.0

Maine 76.0 75.9 72.8 74.7 85.5

Maryland 72.1 77.6 71.4 71.2 81.1

Massachusetts 74.3 78.0 72.6 74.6 84.5

Michigan 69.0 75.3 74.2 77.0 —

Minnesota 83.7 84.9 80.2 84.6 74.8

Mississippi 54.2 59.4 61.5 57.2 69.8

Missouri 72.3 76.3 73.9 72.7 79.2

Montana 77.9 80.8 80.6 78.7 —

Nebraska 83.8 85.7 83.7 81.3 84.0

Nevada 68.6 69.7 60.3 55.5 66.4

New Hampshire 73.6 76.1 69.2 73.8 —

New Jersey 79.7 83.6 80.9 84.6 83.4

New Mexico 58.6 64.7 64.8 61.3 70.8

New York 55.4 61.8 60.9 55.2 —

North Carolina 58.7 65.8 62.5 60.1 —

North Dakota 84.1 86.0 86.4 83.0 88.9

Ohio 69.3 75.2 75.9 71.2 —

Oklahoma 72.5 75.8 73.6 71.0 78.8

Oregon 67.2 69.6 65.9 66.5 —

Pennsylvania 73.8 78.7 76.8 74.0 83.9

Rhode Island 68.1 72.8 69.2 69.9 80.6

South Carolina 51.0 58.6 59.3 50.1 —

South Dakota 73.7 77.6 82.8 78.5 85.4

Tennessee 53.9 59.5 58.5 46.3 71.2

Texas 61.9 71.0 66.7 63.8 —

Utah 82.1 82.5 84.0 83.0 79.9

Vermont 77.7 81.0 76.6 74.5 81.0

Virginia 72.0 76.9 73.3 72.2 79.4

Washington 70.8 73.7 68.4 67.2 —

West Virginia 74.5 76.7 82.5 70.3 82.5

Wisconsin 78.0 82.7 80.5 78.8 71.0

Wyoming 75.0 76.3 79.5 76.4 77.4

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation Indicator; 

SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator. 2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1995-96 through 2000-01 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1995-96 through1999-2000. 
 

69 

Table 4.13. Graduation indicators, by indicator and state: School year 2000-01 

 Indicator

1

State FGR AFGR2 GGI2 SCPI GLI

Alabama 58.2 63.7 65.8 61.0 74.3

Alaska 63.8 68.0 63.7 61.4 —

Arizona 70.0 74.2 68.4 81.2 —

Arkansas 72.7 73.9 75.2 75.2 73.8

California 67.6 71.6 66.4 67.7 —

Colorado 69.2 73.2 67.8 68.9 —

Connecticut 72.6 77.5 70.3 73.3 85.4

Delaware 64.5 71.0 69.6 65.5 77.8

District of Columbia 54.5 60.2 68.5 61.1 —

Florida 54.6 61.2 55.7 53.2 —

Georgia 51.4 58.7 55.7 54.5 64.2

Hawaii 60.9 68.3 70.2 66.0 —

Idaho 78.0 79.6 80.5 81.8 —

Illinois 70.7 75.6 73.7 73.2 69.7

Indiana 67.6 72.1 74.1 69.6 —

Iowa 80.4 82.8 83.3 76.6 88.1

Kansas 74.0 76.5 73.2 74.7 —

Kentucky 63.3 69.8 70.0 51.4 —

Louisiana 57.1 63.7 69.1 63.6 63.2

Maine 75.3 76.4 73.6 77.2 85.9

Maryland 73.2 78.7 73.2 73.6 82.6

Massachusetts 74.9 78.9 73.4 68.6 —

Michigan 70.7 75.4 70.5 70.3 —

Minnesota 82.3 83.6 80.4 84.2 77.0

Mississippi 55.0 59.7 62.2 56.5 71.0

Missouri 71.7 75.5 73.5 70.9 80.8

Montana 77.1 80.0 81.2 79.0 —

Nebraska 80.0 83.8 84.1 81.7 82.9

Nevada 68.5 70.0 60.5 54.7 70.3

New Hampshire 75.0 77.8 71.5 74.4 —

New Jersey 81.9 85.4 81.3 94.8 85.0

New Mexico 61.0 65.9 66.3 62.3 72.4

New York 54.7 61.5 61.3 56.8 —

North Carolina 59.4 66.5 63.0 63.4 —

North Dakota 84.0 85.4 88.8 83.2 90.1

Ohio 70.6 76.5 77.3 73.2 —

Oklahoma 73.0 75.8 76.3 73.3 79.2

Oregon 65.9 68.3 65.5 71.1 —

Pennsylvania 74.1 79.0 77.5 77.3 83.8

Rhode Island 68.1 73.5 69.7 67.2 79.7

South Carolina 48.4 56.5 57.2 53.4 —

South Dakota 71.5 77.4 84.6 81.9 84.4

Tennessee 54.4 59.0 58.7 63.4 72.1

Texas 61.9 70.8 67.2 65.8 —

Utah 81.4 81.6 84.7 82.6 81.5

Vermont 76.6 80.2 79.2 81.4 80.7

Virginia 72.7 77.5 73.2 71.5 80.8

Washington 65.9 69.2 66.1 66.1 —

West Virginia 73.2 75.9 84.0 71.1 83.3

Wisconsin 78.2 83.3 81.4 79.6 72.8

Wyoming 72.6 73.4 77.6 73.7 76.4

— Not available. 

1 FGR = Freshman Graduation Rate, all freshmen; AFGR = Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation Indicator; 

SCPI = Swanson's Cumulative Promotion Indicator; GLI = CCD Graduation Leaver Indicator. 2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1996-97 through 2001-02 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1996-97 through 2000-01. 
 

70 

Table 4.14. Graduation indicators, by indicator and state: School year 2001-02 

 Indicator

1

State FGR AFGR2 GGI2 SCPI GLI

Alabama 57.2 62.1 63.4 64.0 73.5

Alaska 60.7 65.9 64.1 61.8 —

Arizona 69.2 74.7 67.3 88.6 —

Arkansas 73.9 74.8 75.5 74.5 74.2

California 68.5 72.7 68.0 70.6 —

Colorado 69.8 74.7 69.3 70.5 —

Connecticut 74.9 79.7 72.3 76.3 86.5

Delaware 62.0 69.5 67.6 62.0 79.7

District of Columbia 66.8 68.4 70.0 102.4 —

Florida 55.7 63.4 57.1 56.9 —

Georgia 53.6 61.1 57.4 56.7 66.1

Hawaii 64.8 72.1 73.1 65.9 —

Idaho 77.2 79.3 80.4 78.2 —

Illinois 72.1 77.1 73.6 73.5 77.7

Indiana 68.3 73.1 74.9 73.7 —

Iowa 81.0 84.1 86.3 83.0 88.4

Kansas 73.6 77.1 75.6 76.1 —

Kentucky 63.9 69.8 73.8 72.7 —

Louisiana 57.8 64.4 69.6 64.1 65.5

Maine 74.7 75.6 73.0 77.4 85.0

Maryland 73.5 79.7 75.0 75.3 83.1

Massachusetts 73.7 77.6 73.4 76.0 —

Michigan 67.6 72.9 68.2 72.2 —

Minnesota 82.3 83.9 81.3 84.0 78.2

Mississippi 57.3 61.2 63.5 59.8 74.0

Missouri 72.8 76.8 75.4 77.2 82.0

Montana 77.1 79.8 81.8 78.6 —

Nebraska 80.0 83.9 84.8 82.3 83.5

Nevada 70.0 71.9 62.3 59.6 72.0

New Hampshire 74.9 77.8 72.4 78.2 —

New Jersey 82.7 85.8 77.3 86.1 87.5

New Mexico 61.5 67.4 68.1 64.3 73.9

New York 58.7 66.4 65.6 62.5 —

North Carolina 60.6 68.2 63.4 64.7 —

North Dakota 83.7 85.0 90.7 84.7 90.3

Oklahoma 73.0 75.8 76.3 73.3 79.2

Oregon 65.9 68.3 65.5 71.1 —

Pennsylvania 74.1 79.0 77.5 77.3 83.8

Rhode Island 68.1 73.5 69.7 67.2 79.7

South Carolina 48.4 56.5 57.2 53.4 —

South Dakota 71.5 77.4 84.6 81.9 84.4

Tennessee 54.4 59.0 58.7 63.4 72.1

Texas 61.9 70.8 67.2 65.8 —

Utah 81.4 81.6 84.7 82.6 81.5

Vermont 76.6 80.2 79.2 81.4 80.7

Virginia 72.7 77.5 73.2 71.5 80.8

Washington 65.9 69.2 66.1 66.1 —

West Virginia 73.2 75.9 84.0 71.1 83.3

Wisconsin 78.2 83.3 81.4 79.6 72.8

Wyoming 72.6 73.4 77.6 73.7 76.4

— Not available. 

1 FGR = Freshman graduation rate, all freshmen; AFGR = Averaged freshman graduation rate, first-time freshmen; GLI = CCD Graduation leaver indicator; 

SCPI = Swanson's cumulative promotion indicator; GGI = Greene's graduation indicator.

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "State Nonfiscal Survey of Public 

Elementary/Secondary Education," school years 1997-98 through 2002-03 and "Local Education Agency Universe Survey Dropout and Completion Data 

File," school years 1997-98 through 2000-01. 
 

 71 

Min Max Range Mean Min Max Range Mean Min Max Range Mean Min Max Range Mean Min Max Range Mean

Alabama 55.5 59.8 4.3 57.8 61.3 64.4 3.1 63.0 59.5 66.0 6.5 62.6 55.3 64.0 8.8 59.0 70.8 74.4 3.6 72.9

Alaska 60.7 66.4 5.7 63.8 65.9 70.0 4.1 67.9 61.1 64.1 3.0 62.5 58.0 69.4 11.4 63.1 — — — —

Arizona 57.9 70.0 12.1 62.6 60.8 74.7 13.9 66.6 53.7 68.4 14.8 59.7 54.3 88.6 34.2 67.1 — — — —

Arkansas 69.4 74.4 5.1 72.6 70.6 74.9 4.3 73.7 67.2 75.5 8.3 72.2 70.9 75.2 4.3 72.8 73.9 80.6 6.7 76.1

California 64.0 68.5 4.5 66.5 67.6 72.7 5.1 70.4 62.8 68.0 5.2 64.8 66.4 70.6 4.1 67.8 — — — —

Colorado 69.2 72.1 2.9 70.7 73.2 74.8 1.6 74.1 65.5 69.3 3.8 67.3 67.9 72.3 4.4 69.9 — — — —

Connecticut 71.3 76.7 5.5 73.3 76.0 81.9 5.9 77.8 70.3 75.4 5.1 72.3 70.7 80.4 9.7 73.9 80.7 86.5 5.9 83.3

Delaware 60.7 68.0 7.3 64.5 66.8 74.1 7.3 70.6 63.5 69.6 6.1 66.4 58.5 67.5 9.0 63.4 77.1 79.7 2.6 78.7

District of Columbia 49.6 66.8 17.2 54.5 49.7 68.4 18.7 56.2 54.5 70.0 15.5 61.1 36.1 102.4 66.3 59.2 — — — —

Florida 54.6 57.8 3.2 56.3 61.0 63.4 2.4 62.0 54.5 57.1 2.6 55.6 49.7 56.9 7.2 53.4 — — — —

Georgia 50.4 55.0 4.6 52.7 57.5 62.0 4.5 59.9 53.4 57.4 4.0 55.6 50.7 56.7 6.0 53.4 62.0 66.1 4.1 63.9

Hawaii 59.7 70.0 10.3 63.5 67.5 74.5 7.0 70.2 64.5 73.1 8.6 67.9 57.5 66.0 8.5 62.0 — — — —

Idaho 76.9 79.2 2.2 78.0 79.3 80.5 1.2 79.7 73.2 80.5 7.3 77.0 74.5 81.8 7.3 78.2 — — — —

Illinois 70.7 73.3 2.6 72.0 75.2 77.1 1.9 76.2 71.6 75.7 4.1 73.5 70.3 76.1 5.8 72.3 68.9 77.7 8.8 71.6

Indiana 67.6 70.3 2.7 69.0 71.8 74.3 2.5 73.2 71.0 74.9 3.9 73.2 67.6 73.7 6.1 69.7 — — — —

Iowa 80.4 82.6 2.2 81.5 82.8 84.6 1.8 83.7 77.4 86.3 8.9 81.4 76.6 83.0 6.4 80.6 86.7 92.7 6.0 88.5

Kansas 72.8 74.3 1.5 73.7 76.0 77.1 1.2 76.8 70.8 75.6 4.7 72.2 73.4 77.6 4.3 74.8 — — — —

Kentucky 63.3 66.9 3.6 65.0 69.7 71.3 1.6 70.3 68.6 73.8 5.2 70.2 51.4 72.7 21.3 64.1 — — — —

Louisiana 52.3 57.8 5.6 55.0 59.3 64.4 5.1 62.0 57.9 69.6 11.7 63.6 50.1 64.1 13.9 57.2 59.3 65.5 6.2 62.8

Maine 71.2 77.7 6.5 74.3 73.7 78.5 4.7 75.7 72.1 78.5 6.3 74.6 73.5 77.4 3.9 75.8 85.0 85.9 0.9 85.4

Maryland 69.5 73.5 4.0 71.6 76.2 79.8 3.6 77.7 69.8 75.0 5.2 71.5 70.5 75.3 4.8 72.6 79.8 83.1 3.3 81.4

Massachusetts 73.7 75.2 1.5 74.7 77.6 78.9 1.3 78.1 72.6 74.8 2.2 73.5 68.6 76.0 7.3 73.3 83.0 84.8 1.8 84.3

Michigan 66.6 70.7 4.1 68.6 71.4 75.4 4.0 73.9 68.2 74.2 6.0 70.3 62.3 77.0 14.7 70.9 — — — —

Minnesota 77.3 85.3 8.0 82.8 78.6 86.1 7.5 84.0 71.0 81.3 10.4 78.1 78.7 85.5 6.8 83.5 73.9 78.2 4.3 75.8

Mississippi 54.0 57.3 3.3 54.9 59.2 61.2 2.0 59.8 58.2 63.5 5.3 60.6 51.9 59.8 7.9 56.0 69.1 74.0 4.8 70.5

Missouri 70.2 72.8 2.7 71.5 74.7 76.8 2.1 75.6 70.1 75.4 5.3 72.8 70.6 77.2 6.6 72.2 74.4 82.0 7.7 77.9

Montana 77.1 82.2 5.1 79.0 79.8 83.9 4.1 81.6 76.4 81.8 5.5 79.2 77.4 79.0 1.6 78.3 — — — —

Nebraska 80.0 86.3 6.3 82.9 83.8 87.3 3.4 85.3 77.7 84.8 7.1 81.6 80.7 83.8 3.1 82.1 81.3 84.0 2.7 82.6

Nevada 65.2 72.8 7.6 69.3 65.8 73.3 7.4 70.3 54.9 62.3 7.4 59.6 54.7 69.0 14.3 62.9 62.8 72.0 9.3 66.0

New Hampshire 72.8 75.0 2.2 74.2 75.3 77.8 2.5 76.9 68.1 72.4 4.3 70.1 72.8 78.2 5.4 74.2 — — — —

New Jersey 73.0 82.7 9.7 78.5 76.3 85.8 9.5 82.2 72.3 81.6 9.3 78.1 72.2 94.8 22.6 81.4 81.3 87.5 6.2 83.9

New Mexico 56.4 61.5 5.1 58.8 61.6 67.4 5.8 64.1 57.6 68.1 10.5 62.3 53.7 64.3 10.6 58.8 66.8 73.9 7.2 69.8

New York 53.5 59.2 5.8 56.5 60.5 65.3 4.8 62.7 59.7 63.0 3.3 61.2 52.7 56.9 4.2 55.1 — — — —

North Carolina 58.6 61.3 2.7 59.8 65.4 68.2 2.8 66.2 62.2 64.6 2.3 63.0 57.5 64.7 7.2 60.1 — — — —

North Dakota 83.7 89.0 5.3 85.4 85.0 89.5 4.5 86.6 81.0 90.7 9.8 84.9 82.5 89.0 6.5 84.2 88.9 90.3 1.4 89.6

Ohio 69.2 73.0 3.8 70.6 74.5 77.5 2.9 76.0 70.8 77.3 6.6 74.4 66.9 74.3 7.4 70.7 — — — —

Oklahoma 71.8 73.0 1.2 72.5 74.8 76.4 1.5 75.6 69.6 77.9 8.3 72.8 70.7 73.9 3.2 72.2 78.2 80.9 2.7 79.2

Oregon 65.9 68.5 2.6 66.9 68.2 71.0 2.8 69.1 63.6 68.2 4.6 65.4 65.0 72.1 7.2 68.0 — — — —

Pennsylvania 73.7 75.8 2.1 74.3 78.7 80.2 1.5 79.5 75.3 77.5 2.2 76.3 73.7 77.3 3.6 75.0 82.8 85.0 2.2 83.8

Rhode Island 67.2 70.4 3.2 68.7 72.2 75.7 3.5 73.2 68.1 72.1 4.0 69.5 66.6 73.3 6.8 68.7 79.6 81.7 2.1 80.6

South Carolina 48.4 54.1 5.7 51.3 56.5 60.9 4.4 58.8 56.9 59.3 2.4 57.6 45.6 53.4 7.8 50.3 — — — —

South Dakota 71.2 85.6 14.5 76.5 74.2 84.5 10.3 79.2 71.8 84.6 12.8 78.2 61.9 84.5 22.5 76.4 83.9 85.4 1.5 84.6

Tennessee 53.8 62.1 8.3 55.9 58.4 66.6 8.2 60.5 57.3 64.1 6.8 59.4 46.3 64.5 18.1 56.6 71.2 77.5 6.3 73.4

Texas 58.4 64.2 5.8 61.0 66.1 73.5 7.4 69.6 60.4 69.0 8.6 64.3 58.6 67.6 9.0 62.3 — — — —

Utah 76.8 82.1 5.3 80.5 76.9 82.5 5.6 80.7 69.0 84.7 15.7 78.9 75.3 83.0 7.7 81.1 78.7 83.4 4.7 80.5

Vermont 76.6 89.3 12.7 80.5 80.2 85.3 5.1 82.6 70.4 81.5 11.1 76.6 74.5 83.8 9.3 78.3 80.7 81.5 0.9 81.0

Virginia 71.6 73.5 1.9 72.4 76.2 77.5 1.3 76.7 71.1 73.3 2.1 72.2 70.3 72.6 2.3 71.5 79.4 81.7 2.3 80.3

Washington 65.9 72.2 6.4 70.0 69.2 75.5 6.3 73.0 65.5 69.7 4.2 67.1 66.1 71.3 5.2 69.1 — — — —

West Virginia 71.0 75.1 4.1 73.8 74.2 77.9 3.7 76.5 79.0 84.0 5.0 81.1 70.3 76.0 5.7 73.0 82.5 83.8 1.3 83.1

Wisconsin 78.0 80.0 2.0 78.8 82.6 84.8 2.2 83.4 75.4 82.3 6.9 78.9 76.0 80.6 4.6 78.1 71.0 75.8 4.8 72.9

Wyoming 72.6 77.8 5.2 75.7 73.4 78.4 5.0 76.3 71.7 80.2 8.5 75.9 70.7 76.4 5.7 74.1 76.2 77.4 1.2 76.7

Indicator1 

Table 4.15. Minimum, maximum, range, and mean graduation indicator across years, by indicator and state: 1995-96 through 2001-02

GLI3 GGI2 

State

AFGR2 FGR SCPI

— Not available.

2

 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate.

3 Data are from 1997-98 to 2001-02.

NOTE: In CCD State Non-fiscal data, grade-level enrollments were adjusted to include ungraded students.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "Local Education Agency Universe Survey," school years 1996-97 through 2002-03; "Local 

Education Agency (School District) Universe Survey Dropout and Completion Data" 1991-92 through 2001-02; and "Public Elentary/Secondary School Universe Survey," school years 1991-92 through 2002-03.

1 FGR = Freshman Graduation Rate, all freshmen; AFGR= Averaged Freshman Graduation Rate, first-time freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative Promotion indicator; GLI 

= CCD Graduation Leaver Indicator.
 

72 

In general, at the state level, when estimates for GLI are available they are higher than 

those from the other four indicators. Recall from chapter 2 that GLI was dropped from 

further analysis once it was determined that it was consistently higher than the true cohort 

on-time graduation rate and each of the other proxy rates. This can be attributed to the 

fact that GLI is a leaver rate, rather than an on-time estimate, and does not include 

students who do not complete on time in the denominator. This, taken together with the 

fact that GLI is only available for a subset of states, leads to a decision to drop GLI from 

further analysis here as well. 

 

Next, taking AFGR as the standard, a comparison of the state-level estimates from FGR 

with those from AFGR over the 7-year period shows that FGR and AFGR were highly 

correlated (r = .97 to .98); as a result some 95 to 97 percent of the variation in AFGR 

was explained by the variation in FGR (table 4.16). A 1 percentage point increase in FGR 

was associated with eight- to nine-tenths of a percentage point increment in AFGR. 

Approximately 80 percent of the standard deviation in AFGR was accounted for by FGR 

(the inverse of the coefficient of alienation). 

The same comparisons of the state-level estimates from GGI with those from AFGR 

showed correlations between .88 and .94, with 77 to 88 percent of the variation in AFGR 

explained by GGI. For the first 3 years of the 7-year period, a 1 percentage point increase 

in GGI was associated with a 1 percentage point increment in AFGR, but at the end of the 

following 4 years a 1 percentage point increase in GGI was associated with an increment 

in AFGR of approximately eight-tenths of a percentage point. 

The results of a comparison of the state level estimates from SCPI with those from AFGR 

were more variable. The correlation coefficients ranged from .77 to .96, with the amount 

of variation in AFGR that was explained by SCPI ranging from .60 to .92 percent. Over 

the 7 years the amount of increase in AFGR associated with a 1 percentage point 

increment in SCPI ranged from under six-tenths to eight-tenths of a percentage point. 

Although it is not possible to compare the available proxy measures for individual states 

directly with the true cohort on-time graduation rates for those states, this analysis 

compared the performance of FGR, GGI, and SCPI to that of AFGR at the state level to 

determine if the relative performance of the indicators is the same as that observed in 

states 1 and 2. The analysis showed that the relative positions of the measures are 

consistent with the analysis of the data from States 1 and 2. Using the available statelevel CCD data, FGR exhibited performance that was most similar to AFGR. GGI did not 

perform as well as FGR, but outperformed SCPI, and SCPI then had the weakest 

relationship with AFGR (table 4.16). 
 

73 

Table 4.16. Regression estimates of AFGR on proxy graduation indicators FGR, GGI, and SCPI across states, by 

indicator and school year: 1995-96 through 2001-02 

Indicator1

Statistic FGR GGI2

 SCPI 

1995-96 

Correlation coefficient .98 .91 .92 

R square .95 .83 .85 

Slope .86 1.03 .80 

Standard deviation 1.81 3.49 3.32 

1996-97 

Correlation coefficient .98 .92 .96 

R square .96 .84 .92 

Slope .87 1.01 .81 

Standard deviation 1.52 3.19 2.26 

1997-98 

Correlation coefficient .98 .94 .93 

R square .96 .88 .87 

Slope .86 1.03 .75 

Standard deviation 1.58 2.78 2.89 

1998-99 

Correlation coefficient .98 .90 .80 

R square .96 .82 .65 

Slope .85 .94 .70 

Standard deviation 1.59 3.55 4.91 

1999-2000 

Correlation coefficient .98 .92 .95 

R square .97 .85 .90 

Slope .85 .88 .72 

Standard deviation 1.51 3.11 2.52 

2000-01 

Correlation coefficient .98 .88 .87 

R square .96 .77 .77 

Slope .84 .82 .70 

Standard deviation 1.47 3.66 3.72 

2001-02 

Correlation coefficient .97 .88 .77 

R square .95 .77 .60 

Slope .83 .79 .57 

Standard deviation 1.63 3.49 4.64 

1 FGR = Freshman Graduation Rate, all freshmen; GGI = Greene's Graduation Indicator; SCPI = Swanson's Cumulative 

Promotion Indicator; AFGR = Averaged Freshman Graduation Rate, first-time freshmen. 

2 First-time 9th-grade counts estimated using Greene's smoothed 9th-grade estimate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), 

"Local Education Agency Universe Survey," school years 1991-92 through 2002; “Local Education Agency (School 

District) Dropout and Completion Data,” school years 1991-92 through 1996-97; "Local Education Agency (School 

District) Universe Survey Dropout and Completion Data," school years 1997-98 through 2001; and “State Nonfiscal 

Survey of Public Elementary/Secondary Education,” school years 1991-92 through 2002-03.
 

74 

4.4. Graduation rates at district level 

Missing data for individual schools and districts are not imputed in the school and district 

level CCD data files. As a result, in the data required for an analysis of the same 7 years 

at the district level, New Jersey was missing both enrollment and diploma counts in 1 

year and Arizona, Minnesota, and Washington were each missing diploma counts in 1 

year. There are also instances where the data are missing for some districts within 

reporting states. Over the 9 years of enrollment data required to calculate the proxy 

graduation indicators, there were 5 years with no additional missing enrollment data (i.e., 

beyond the states listed above) and the amount of missing district enrollment data ranged 

from 0.2 to 0.4 percent in the other 4 years. Over the 7 years of graduate data required to 

calculate the proxy graduation indicators, there was 1 year with no additional missing 

graduate data and the amount of missing graduate data in the other years ranged from 0.3 

to 1.9 percent. 

When the available data were used to compute FGR, AFGR, GGI, and SCPI for each 

district with available data for each of the 7 school years from 1995-96 through 2001-02 

a review of those rates showed that the maximum rates frequently exceed 100 percent, 

and the minimum rates are often as low as 0. This occurs for some of the districts for 

FGR, AFGR, GGI, and SCPI in each of the 7 years. Thus, although these rates produce 

results that are within the expected range of 0 to 100 percent at the national and state 

levels, this is not necessarily the case at the school district level. 

Two factors may contribute to the extreme values observed for some school districts—

incomplete reporting of either enrollment or graduate data at the district level and 

population changes. Either of these two factors is more likely to be masked as a result of 

aggregation when data are reported at the state or national levels, but are more evident at 

the school district level. For example, estimates over 100 percent arise when the estimate 

of freshman 4 years earlier is smaller than the number of graduates in the year in 

question.19 This could happen as a result of incomplete counting of freshmen in a school 

district 4 years earlier or could happen when the number of high school age students 

moving into the district during the 4 years between the freshman and senior years exceeds 

the number of high school age students moving out of the district during the same period, 

alternatively it could happen in the case of a merge of two school districts. 

On the other hand, graduation rates could be depressed by poor data quality or population 

changes. For example, graduation rates of zero can arise if all of the members of the 

senior class move out of the district, drop out and/or fail to graduate in a particular year. 

In a similar vein, if the number of high school age students moving out of the district 

during the 4 years between the freshman and senior years exceeds the number of high 

school age students moving into the district during the same period the resulting 

graduation rates would be unexpectedly low.20 

 

19 The percent of districts with one or more proxy graduation indicator over 100 percent was between 15 

and 16 percent over the 4 years from 1997-98 through 2000-01, the comparable value was 19 percent for 

1996-97 and 2001-02, and it was 21 percent in 1995-96. 

20 In each of the 7 years, between 0.5 and 1.0 percent of the districts had one or more proxy graduation 

indicators below 25 percent. 
 

75 

Of course, similar changes could also inflate or deflate graduation rates that are not at the 

extremes of the distribution of rates. While it is possible to review changes in reporting 

practices or changes in migration patterns of the high school age population at the district 

level, they are not documented in the national dataset. In general, the smaller the school 

district, the more sensitive the rates are likely to be to fluctuations in the relevant 

enrollment or graduation data. As a result, there is no context for evaluating the validity 

of these rates at the individual district level; this is most likely to be problematic in the 

case of small districts. Because of these data limitations, an analysis of the CCD data for 

school districts across the nation is not included in this report. 

4.5. Summary 

As described at the beginning of this chapter, before drawing comparisons across 

different proxy graduation indicators, it is important to understand and clearly describe 

the data elements and sources for those data since subtle differences in the data elements, 

the data sources, or both, can contribute to the size of observed differences across the set 

of proxy graduation indicators. Because of this, wherever possible, comparisons across 

indicators in this report are done based on indicators that are calculated using the same 

data files; and when this is not possible, differences are described. 

Annual data for school years 1995-96 through 2001-02 showed that the estimates from 

the four proxy graduation indicators that could be calculated using national data ranged, 

on average, from 65 to 73 percent. In terms of relative ranks, at the national level AFGR 

yielded the highest rates, with a denominator of only first-time freshmen. Conversely, 

FGR yielded the lowest rates, with a denominator of all freshmen. GGI includes a growth 

adjustment to the first-time freshman estimate in the denominator, and since that growth 

was positive for each of the years in this analysis, the GGI denominator is larger than that 

of AFGR, but smaller than that of FGR and as a result yielded rates intermediate to those 

for AFGR and FGR. Finally, SCPI yielded rates similar to those for FGR over the first 5 

of the 7 years, but grade-to-grade differences in growth rates brought the SCPI estimates 

closer to those for AFGR in the latest 2 years. 

The state-level analysis added estimates of the CCD Graduation Leaver Indicator (GLI) 

for the 30 states with available data, and where available, these estimates tended to be 

higher than those from the other indicators. This is by design in that the denominator of 

GLI consists solely of students who have left the system and thus is smaller than the 

denominators of the other proxy indicators—each of which also includes some estimate 

of students who are still enrolled. These definitional differences, coupled with the lack of 

data for all states, led to a decision to drop GLI from the detailed analysis in this chapter. 

It was noted that the underlying assumptions supporting the selection of those indicators 

must be carefully considered. To this end, the national analysis included a description of 

the unintended consequences that changes in the growth rates of the population in 

specific data elements can have on the estimates. In particular, the changes over time in 

AFGR, FGR, and GGI are driven by the fact that the denominator is increasing over time, 

albeit at a decreasing pace. The SCPI is driven by a set of grade-to-grade differences in 
 

76 

the rates of growth between the freshman classes and enrollments in the other grades. 

Finally, the GGI is further influenced by the assumption that differences in the sizes of 

the enrolled population of 9th- through 12th-graders in the freshman and senior years can 

be attributed to growth due to migration. The analysis showed that this assumption 

ignores the rate of growth in incoming freshmen classes and that as a result the GGI 

overestimates the pool of potential graduates from the first-time freshmen. The GGI 

adjusted to control the impact of population growth in the incoming freshman classes 

yields graduation rates that range from 1 to 4 percentage points higher than the current 

GGI estimates. 

The national patterns were repeated in the state level analysis. Since AFGR was 

identified in the analyses of data from States 1 and 2 as the proxy measure that was 

consistently among the best performing indicators relative to EACGI, it was used in this 

analysis as an approximation of the true cohort rate in States 1 and 2, and was used as the 

standard for comparison in the analysis of data for other state. In particular, regression 

analyses were used to compare the relative performance of AFGR, FGR, GGI, and SCPI. 

The patterns observed in the student record data from States 1 and 2 are repeated in the 

analyses of CCD cross-sectional data for states. The FGR exhibited the strongest 

correlations with AFGR, and although the correlations between AFGR and GGI were not 

as strong, they were stronger than the correlations between AFGR and SCPI. 
 

77 

Chapter 5 

Conclusions 

Graduation rates provide an indication of the overall success of the educational system in 

providing a high school education to young adults. As essential an indicator as this is in modern 

society, the detailed data required to accurately measure high school entry, progression, and 

successful timely completion do not currently exist at the national level. That is to say, the 

accurate measurement of high school on-time graduation rates requires the level of detail that is 

only available with a student record system that includes records on the progression of individual 

students. By the start of the 2005-06 school year some 28 states reported that they had started or 

were in the planning stages for developing student records systems that would provide the data 

needed to produce accurate graduation rates for clearly specified groups of students. However, 4 

years of student record data are required for an accurate measure of an on-time high school 

graduation rate. 

 

The No Child Left Behind Act of 2001 specifically calls for the use of an on-time graduation rate 

as a measure of educational accountability. Prior to the passage of this 2001 legislation, the 

primary emphasis in this arena was on monitoring dropout rates and measuring successful high 

school graduation or completion, independent of time—that is, the emphasis was on measuring 

the percent of students who left school with a high school diploma as compared to an alternative 

certification or no certification at all. That emphasis was the impetus for the development of the 

NCES Graduation Leaver Indicator (GLI) in 1997 using school-based data from the Common 

Core of Data—a universe data collection of data from public schools, districts, and states 

throughout the United States. The GLI provides a measure of the percent of students who left 

high school with a diploma. This measure is based only on those students who have left high 

school, be it through graduation, some alternative form of completion, or dropping out. Students 

who are still in school working towards graduation are not included in the computation of this 

leaver rate. During the same time period, NCES also started using population based data from 

the Current Population Survey (CPS)—a large scale sample survey conducted by the U.S. 

Census Bureau—to provide a high school completion rate that measured the percent of young 

adults in the 18 to 24 year-old age range who were no longer enrolled in high school and who 

had completed a high school diploma or an alternative such as the GED.21 Again, the emphasis in 

the rate computed using CPS data is on determining the educational status of those young adults 

who are no longer in high school.22 

 

21 Prior to 2002, it was possible to report data for these two credentials separately; however a change in data 

collection procedures required the combination of the two credentials with the result being one completion rate. 22 A numerical explanation of the relationship of this measure and the on-time proxy measures is included in volume 

1 of this report. 
 

78 

The 2001 call for an on-time graduation rate shifted the emphasis from graduation, or more 

generally completion, status to timely graduation. The use of an on-time graduation rate as a 

measure of educational accountability in the No Child Left Behind Act attracted the attention of 

a number of researchers. In the absence of the student record data needed to accurately calculate 

on-time graduation rates, researchers promulgated several proxy indicators. Each of the newly 

proposed indicators attempts to use existing cross-sectional data to approximate an on-time 

graduation rate. Typically, each newly proposed indicator has been compared to the existing 

NCES Graduation Leaver Indicator and/or the CPS based graduation or completion rates—

although these are not on-time graduation rates—and sometimes to new proxy indicators 

proposed by other researchers. As the research literature has grown, there has been little 

consensus as to how best to measure on-time graduation rates (Greene 2002; NISS and the 

Education Statistics Services Institute (ESSI) 2004; Swanson 2003). There has also been 

growing confusion over the similarities and distinctions among the various existing and newly 

proposed indicators. These factors led to the Department of Education’s call for the NISS Task 

Force on Graduation, Completion, and Dropout Indicators. That Task Force recommended the 

development and use of student record data to accurately measure on-time high school 

graduation rates (NISS and ESSI 2004). 

While agreeing that the accurate measurement of on-time graduation rates can only come from 

student record data, since four years of student record data are required to compute an on-time 

graduation rate, it will be several years before the necessary student record data could be 

available for the states that are starting to plan and develop student record systems. In the interest 

of determining whether it was feasible to identify an interim measure, the Director of the 

Institute of Education Sciences asked NCES to conduct an analysis of the array of existing and 

proposed rates. This report represents that effort. 

The first volume of this report took an in-depth look at the various graduation indicators, with a 

description of the computational formulas, the data required for each indicator, the assumptions 

underlying each formula, the strengths and weaknesses of each indicator, and a consideration of 

the conditions under which each indicator does or does not work. This second volume of the 

report starts with the analysis of student record data from two states that have had student record 

systems in place for the number of years required to support the calculation of the true cohort ontime graduation rate and the various proxy graduation indicators over several years, and then 

extends the findings from those two states to an analysis of cross-sectional national and state data 

for all 50 states and DC. 

Chapters 2 and 3 of volume 2 report the data for each of the two states, with a focus on the 

comparison of each of the proxy measures to the true cohort on-time graduation rate for each 

state. Chapter 2 starts with a descriptive analysis of the data for State 1 at the state and school 

district level. A comparison of the average absolute difference between each of the measures 

and the true cohort rate computed over the 3 years of available data showed that at the state level 

the rates for AFGR, FGR, and SCPI are each relatively close to the rates for EACGI (average 

absolute differences of 3.0, 3.5, and 3.2 percentage points, respectively). By comparison, when 

GGI and GLI are compared to EACGI, the averages of the absolute differences are larger (7.4 

and 9.3 percentage points, respectively). A similar analysis, based on the mean of the rates 

computed for individual school districts, showed that over the 3 years of available data, the 
 

79 

average of the absolute differences between the rates for AFGR and SCPI were relatively close 

to the rates for EACGI (1.8 and 2.2 percentage points, respectively). By comparison, the average 

of the absolute differences between the rates for FGR, GGI, and GLI and those for EACGI are 

larger (4.3 for AFGR, 6.5 for GGI, and 10.0 for GLI). 

AFGR, FGR, GGI, and SCPI are the proxy measures that were proposed as estimates of an ontime graduation rate, and they yield estimates closest to EACGI; as a result the analysis is 

narrowed to these four proxy graduation indicators and EACGI. The distributional properties of 

the individual indicators (skewness, kurtosis, and normality) were examined at the school district 

level in preparation for a linear regression of EACGI on each of the proxy graduation indicators, 

and the decision was made to proceed with regression analyses. 

Ordinary least squares regressions were used to examine the association between each proxy 

graduation indicator and the true cohort on-time graduation rate across school districts within the 

state. The correlations between EACGI and AFGR (r = .77 to .87) and FGR (r =.74 to .85) are 

the stronger than the correlations between EACGI and GGI (r =.54 to .67) or SCPI (r =.48 to 

.59). In addition, a 1 percentage point change in AFGR comes the closest of the four indicators to 

a 1 percentage point change in EACGI (slopes of .85 to 1, compared to slopes of .70 to .81 for 

FGR, .46 to .62 for GGI, and .34 to .51 for SCPI). AFGR also explains more of the variance in 

EACGI than the other three proxy indicators (R2

 of .60 to .77 for AFGR compared to R2 of .55 to 

.72 for FGR, .29 to .46 for GGI, and .23 to .35 for SCPI). Finally, the performance of EACGI 

and each of the proxy graduation indicators was examined over time within individual school 

districts by regressing each year’s estimate on the prior year’s estimate. The true cohort rate had 

the highest correlation with itself (r =.82), followed by FGR (r =.76 to .81) and AFGR (r =.72 to 

.78). 

Looking across the analyses for State 1, while SCPI performed well in the descriptive analyses of 

the state and school district rates, it did not perform as well as AFGR in the regression analyses. 

Similarly FGR performed well in the descriptive analysis at the state level, but not as well at the 

district level, and in the regression analysis FGR outperformed SCPI and GGI, but did not 

perform quite as well as AFGR. In summary, the analyses in State 1 showed that while AFGR is 

not an exact approximation of EACGI, it is consistently the most strongly associated with 

EACGI across the measures examined. 

Each of these analyses was replicated using data from State 2. At the descriptive level, a 

comparison of the state rates for the four proxy measures and the true cohort rate showed that the 

rates for AFGR and GGI were closest to EACGI in State 2. The average of the absolute 

differences between AFGR and GGI and EACGI over the 4-years of available data were 2.8 and 

3.5 percentage points, respectively. By comparison, the differences were 4.7 percentage points 

for FGR and 6.0 percentage points for SCPI. When this analysis was repeated using the mean of 

the school district rates computed across each measure, the rates for AFGR and GGI were closest 

to those for EACGI (1.5 percentage points for AFGR and 1.9 for GGI). By comparison, the 

average of the absolute difference between SCPI and EACGI was 2.5 percentage points, and the 

comparable value for FGR was 5.7 percentage points. 

The regression analyses for State 2 showed that although each proxy measure had a stronger 

association with EACGI than AFGR in one of the 4 years, AFGR had the most consistent 
 

80 

pattern. More specifically, AFGR exhibits stronger correlations with EACGI than FGR in 1999-

2000, 2000-01, and 2001-02, and stronger than GGI or SCPI in 2000-01, 2001-02 and 2002-03. 

Thus, although GGI compared favorable to EACGI in the descriptive analysis, albeit not quite as 

favorably as AFGR, the regression analyses show stronger correlation coefficients and larger 

amounts of the variation in EACGI explained for AFGR than for GGI in 3 of the 4 years of 

available data. Furthermore, the examination of the year-to-year correlations within each 

indicator showed strong associations over time for the true cohort on-time graduation rate and for 

AFGR and FGR. 

Although the relationships between the true cohort on-time graduation rate and the proxy 

graduation indicators AFGR and FGR are not as strong in State 2 as those evident in State 1, the 

patterns are the same. The analyses in State 2 showed that while AFGR is not an exact 

approximation of EACGI, it is consistently the most strongly associated with EACGI across the 

measures examined. 

Chapter 4 of this volume draws upon the findings from chapters 2 and 3 to examine the 

performance of the proxy graduation indicators using data from the NCES CCD for individual 

states.23 The relative position of each of the proxy graduation indicators that were observed using 

student record data from States 1 and 2 are evident at the national level in the CCD data—AFGR 

was the highest over the 7-year period, with an average rate of 72 percent, with average rates 

over the 7-year period of 68 percent for GGI and 66 percent for FGR and 67 percent for SCPI. 

At the state level, data for all 50 states and the District of Columbia were analyzed for AFGR, 

FGR, GGI, and SCPI; and GLI was computed for the 30 states that had the required data 

elements. Over the 7-year period the graduation indicators were more variable at the state level 

compared to the national estimates, with annual state rates ranging from the low 50 percent level 

to the low 90 percent level.24

Because AFGR emerged consistently as the best approximation to the true rate using the state 

student record data presented in chapters 2 and 3, AFGR was taken as the standard for the 

analysis of CCD in chapter 4, absent estimates for the true cohort on-time graduation rate for 

each state and the District of Columbia. This analysis was based on the fact that estimates for 

AFGR, FGR, GGI, and SCPI computed from CCD data for States 1 and 2 were strongly 

correlated with the same measures computed using student record data for those states. Also, 

regression analyses for States 1 and 2 of AFGR, FGR, GGI, and SCPI computed using CCD data 

with the student record based EACGI showed that the relationships observed between each 

proxy graduation indicator and EACGI in the student record data are repeated, albeit somewhat 

dampened. Finally, regressions of AFGR on FGR, GGI, and SCPI using both student record and 

CCD data yielded similar results, showing the strongest relationships between AFGR and FGR, 

followed by AFGR and GGI, and then AFGR and SCPI. These analyses provide the basis for 

the analysis of the CCD state data. 

 

23 Missing data at the state level were imputed and students reported in ungraded programs were allocated to specific 

grades. 

24 The one exception was SCPI that had state rates as low as 37 percent. 
 

81 

Thus, the regression analyses conducted using student record data from States 1 and 2 to 

compare EACGI with AFGR, FGR, GGI, and SCPI were repeated using CCD data to compare 

state level rates for AFGR to FGR, GGI, and SCPI. These analyses showed that the relative 

positions of the proxy graduation indicators are consistent with the analyses from States 1 and 2. 

Specifically, in the analyses of the CCD data, FGR exhibited performance that was most similar 

to AFGR, GGI outperformed SCPI, and SCPI had the weakest relationship with AFGR. 

 

83 

References 

Greene, J.P. (2002). Public School Graduation Rates in the United States. Civic Report, No. 31. 

New York: The Manhattan Institute for Policy Research. 

Greene, J.P., and Winters, M.A. (2002). Public School Graduation Rates in the United States.

Civic Report No. 31. New York: The Manhattan Institute. 

National Institute of Statistical Sciences and Education Statistics Services Institute. (2004). 

National Institute of Statistical Sciences/Education Statistics Services Institute Task Force on 

Graduation, Completion, and Dropout Indicators (NCES 2005-105). U.S. Department of 

Education. Washington, DC: National Center for Education Statistics. 

No Child Left Behind Act of 2001, P.L. 107-110, 115 Stat. 1425 (2002). 

Swanson, C.B. (2003). Keeping and Losing Count: Calculating Graduation Rates for All 

Students Under NCLB Accountability. Washington, DC: The Urban Institute, Education 

Policy Center. 

U.S. Department of Education, National Center for Education Statistics, Common Core of Data 

(CCD), “Local Education Agency Universe Survey Dropout and Completion Data File,” 

1991-92 through 1997-98, Version 1c; 1998-99 through 2000-01, Version 1b; 2001-02, 

Version 1a. 

 

A-1 

APPENDIX A 

Notes regarding analyses of student-tracking systems in two states 

One point that cannot be stressed enough for states that are developing their own student tracking 

systems, calculations are greatly simplified if students are assigned a unique student 

identification number upon entry into the state system and if that identification number is never 

allowed to change. Though not a significant problem for this study, changing student 

identification numbers over time would lead to obvious problems for determining what happens 

to an individual student over time. 

Two states agreed to share student tracking system data files for this study. Several key 

decisions were necessary in order to conduct tests of the different rates using the tracking system 

data files. These decisions relate to the following points: 

1. Different units of analysis were possible in terms of building student-level, schoollevel, district-level, or state-level cohorts. 

2. Some students apparently entered the system without having a corresponding entry 

code. 

3. Some students were reported as being in multiple grades during a given year. 

4. Some students were never reported as having been enrolled in 9th grade. 

5. Some students had final exit codes that suggested they should have returned the next 

year, and then lacked records the next year. 

6. States differed in terms of who was issued diplomas by their respective school 

systems. 

7. Some students were awarded diplomas during the summer of their graduating year. 

8. Some students were issued multiple credentials. 

9. Some students graduated and then reenrolled. 

10. Some students were enrolled in multiple schools and districts during a given year. 

Extensive analyses were conducted to determine how best to address each of these points. The 

following paragraphs summarize the resulting decisions. 

Data files made available to NCES contained multiple records per student per year. Each time 

the student changed programs in a school, changed schools within a district, changed districts, or 

left the public school system, the student was given a new record in each year’s file. Each record 

contained student identification information, grade level information, school and district 

identifiers, entry dates and entry codes, and exit dates and exit codes. To facilitate analysis of 

such a large amount of data, the data files were sorted by exit dates and one record was 

developed for each student in each year’s file. The yearly files were then merged producing one 

record per student over multiple years. The records contained data for each change in student 

status within and across years. The first year a student ended the year as a 9th grader determined 

the 9th grade cohort of the student. 

 

The approach taken for generating the graduation rate statistics was designed to assure that 

students were counted once. One outcome code was assigned per student within a state. 
 

A-2 

Students were not allowed to shift between cohorts as they moved from school to school or 

district to district. In effect, no graduation rate clocks were allowed to be reset because of 

student moves within a state’s public education system. Lacking information about what 

happened to students before entering into a state’s public school system guarantees that this 

approach was not consistently applied to all students. Some students coming into a state’s 

system, say as 9th graders, had undoubtedly already completed one year of 9th grade at a private 

school or at a school outside of the state. Alternative approaches were considered such as 

building cohorts from the school level up to the state level that allowed students to move into and 

out of a particular school’s first-time 9th-grade population. Because the graduation rates should 

ultimately measure what happens to each individual student and not a given school or school 

district population, such approaches were not pursued. Technically, by counting each student 

once the state level, district level, and school level, student counts summed to the same totals. 

Students who entered into the system lacking corresponding entry codes were assigned to a given 

cohort based on the grade level at which they entered the system. For example, students whose 

first entry indicated that they were in 10th grade in 1999-2000 were assigned to the cohort of 

first-time freshmen who were to graduate at the end of the 2001-2002 school year (i.e., they were 

assumed to have started 9th grade in 1998-99). In most cases, these students were students 

transferring into the state’s public education system from out-of-state, private school, or a home 

schooling program. If the entry code for the student stated that they were transferring into the 

system, enrolled at grade 9 or higher, and had not been previously enrolled in the state’s public 

education system, then the student was coded as a transfer student. 

Students who were enrolled in multiple grades in a given year were assigned to the last grade 

level that they were enrolled in during a given year. The student was assigned to a 9th-grade 

cohort if this grade was 9 and the student was not already assigned to a cohort. That is, if the 

student had not already attended 9th grade or higher in previous years. More involved were 

decisions about cohort assignments for students who apparently skipped 9th grade altogether by 

skipping 9th grade within a given year or skipping 9th grade between school years. Such students 

tended to graduate early suggesting that they could be treated as members of prior cohorts. For 

example, students who skipped from 8th grade in 1997 to 10th grade in 1998 were treated as firsttime 9th-graders in 1997. In a few cases, students skipped multiple grades. Such cases were 

assigned to cohorts as though they had entered 9th grade on schedule. For example, if a student 

skipped from grade 8 in 1997 to grade 11 in 1998, the student was treated as though they had 

started 9th grade in 1996. 

Related cohort assignment decisions had to be made for students who did not reenter the school 

system though they had exit codes from the previous year indicating that reenrollment was 

expected. Such students were considered to be part of the cohort to which they were originally 

assigned. They were considered dropouts from this cohort. 

Apart from cohort assignment and adjustment decisions, decisions about how to account for 

graduates were necessary because states treated different kinds of completers differently. For the 

most part, if the state considered a student to be a regular high school graduate, we counted the 

student as a graduate. One key exception was how those who earned diplomas through adult 
 

A-3 

education programs were treated. In both states, students who earned such diplomas were not 

counted as graduates. 

A second key decision about how to adjust graduate counts involved how to account for students 

who graduated the summer after their expected senior year. Such students were treated as ontime graduates. 

Less straightforward was how to assign students who earned multiple credentials, sometimes 

from multiple schools. For these rare students, if any of the credentials were a high school 

diploma, he or she was counted as a graduate. If the student earned more than one diploma and 

earned them from different schools, the student was assigned to one school and counted as one 

graduate for purposes of graduate counts. This was done in order to avoid counting individual 

students as multiple graduates. 

Similarly, some students graduated, reenrolled in another school, and then did not graduate from 

this second school. Such students were considered to be graduates for the school from which 

they earned their credential. They were treated as though they had not reenrolled and were not 

counted in graduation rate calculations for the second school. 

Finally, many students moved from school-to-school in a given year or across years. Such 

students were assigned to the final school and district attended for purposes of calculating 

graduation rates. As noted above, exceptions were made for students who graduated multiple 

times or who graduated then reenrolled and then did not graduate again. 

 

B-1 

APPENDIX B 

Analysis of Change Component of Greene Graduation Indicator 

The Greene Graduation indicator uses the ratio of the difference between the number of students 

enrolled in grades 9 through12 in the graduating year and the number of students enrolled in 

grades 9 through 12 in the freshman year to the number of students enrolled in grades 9-12 in the 

freshman year as a measure of the rate of change in the population to capture the amount of 

student migration that should be incorporated into the denominator for his graduation indicator. 

Simply put, if there are more students enrolled in high school the year students graduate than 

there were the year in which students enrolled, the estimate of first-time freshman is increased to 

yield a larger denominator of seniors eligible to graduate. Conversely, if there is fewer students 

enrolled in high school the year students graduate than there were the year in which students 

enrolled, the estimate of first-time freshman is decreased to yield a smaller denominator of 

seniors eligible to graduate. 

This approach attributes all of the change in the size of the high school population to migration 

and fails to take into account underlying changes in the size of the entering population of 

freshmen. In any year, the number of students enrolled in grades 9 through 12 is in part a 

function of the number of students enrolling as freshmen in each of four consecutive years. 

Thus, if the number of freshmen increases due to an underlying change in the population 

structure (e.g., the baby boom-let moving through school), the number of students enrolled in 

grades 9 through 12 will also increase. 

An examination of freshmen enrollment data shows that the number of freshmen has increased 

over each of the years that are used to compute the Greene graduation indicators for school years 

1995-96 through 2001-02 (table B-1). If the freshman class is not growing (or shrinking) over 

time, the number of students expected in grades 9 through 12, absent migration is simply four 

times the number of freshmen. The impact of the growth in freshman class can be computed by 

comparing the sum of four consecutive freshmen classes with the number of freshmen in year 

one multiplied by four and computing the percentage difference. This percentage then is 

compared to the overall percent change to determine how much of the change is due to migration 

that should be accounted for in the denominator of eligible seniors versus the amount that is due 

to a growth in the number of students entering high school as freshmen. Table B-2 shows the 

overall rate of change between the freshman and senior years for the senior years from 1995-96 

through 2001-02. The rates ranged from 3.5 percent to 7.4. Table B-2 also shows that the rates 

of changes attributable to population change for the same time period ranged from 1.4 to 5.3 

percent and the rates of change due to migration ranged from 1.3 to 3.6 percent. In the 

individual years the percentage of the overall change that was associated with increases in the 

size of consecutive freshmen classes ranges from 34 to 81 percent. When the overall rate of 

change is used in the Greene graduation indicator, the graduation rates range from 66.4 to 70.1 

percent (i.e., population change as a percent of the overall rate of change). However, when the 

lower rates of change associated with migration (i.e., controlling for growth in the entering 

population) are used in the Greene graduation indicator, the adjusted rates range from 68.7 to 

71.9 percent. 
 

B-2 

Table B-1. Number of freshmen students in 

Table E-1. the public schools in the United 

Table E-1. States: 1990-91 through 2001-02 

School year Freshmen

1990-91 3,233,541

1991-92 3,379,488

1992-93 3,416,533

1993-94 3,549,274

1994-95 3,664,898

1995-96 3,766,542

1996-97 3,852,120

1997-98 3,873,128

1998-99 3,911,292

1999-2000 3,986,992

2000-01 4,005,781

2001-02 4,050,398

SOURCE: U.S. Department of Education, 

National Center for Education Statistics, 

Common Core of Data (CCD), "State 

Nonfiscal Survey of Public 

Elementary/Secondary Education," school 

years 1991-92 through 2001-02. 

Table B-2. Rate of change components of Greene graduation indicator and resulting estimates: 

Table F.2. 1995-96 through 2001-02 

School year 

Overall rate 

of change 

Migration 

change

Population 

change

Greene 

indicator

Adjusted 

Greene 

indicator

1995-96 6.6 1.3 5.3 68.3 71.9

1996-97 7.4 3.0 4.5 66.4 69.2

1997-98 7.0 3.6 3.4 66.7 68.9

1998-99 5.6 3.4 2.2 67.3 68.7

1999-2000 4.1 2.7 1.4 68.8 69.8

2000-01 3.5 1.7 1.8 69.2 70.5

2001-02 4.1 2.1 2.0 70.1 71.4

SOURCE: U.S. Department of Education, National Center for Education Statistics, Common 

Core of Data (CCD), "State Nonfiscal Survey of Public Elementary/Secondary Education," 

school years 1991-92 through 2001-02.