AERA paper presenting results of analysis of state differences in high school graduation, college going, NAEP scores, ACT-SAT scores. Found state parent education levels most related to differences by state

1. Exploring Demographic and Selected State Policy
Correlates of State Level Educational Attainment
and Achievement Indicators
Paper prepared for:
The American Educational Research Association (AERA)
Annual Meeting
Prepared by:
Margaret Cahalan
Jim Maxwell
Draft
April 10, 2007
Chicago, Ill.
Note: All tabulations and views reported in this paper are the responsibility of the authors and do
not reflect any review, authorization, or clearance by the Department of Education.

2. 1. Introduction
As a nation, we are fascinated by state-by-state comparisons on almost any topic. In
education, increasingly, researchers and policy makers are preparing indicators, often with
rankings and scores assigned to the states. ED Week’s Quality Counts (QC), grades states
and is dedicated to tracking “state efforts to creating a seamless education system from
early childhood through the world of work,” and the National Center for Higher
Education Managers Systems (NCHEMS) provides policy makers with a “State Report
Card” system to help managers make decisions. Similarly, major government surveys and
assessment tools are increasingly designed to provide state- by-state estimates.
In recent years, education policy reform discussion has moved from an emphasis on
understanding the importance of student background characteristics in explaining
differences in outcomes to a focus on the importance of state, district, school and teacher
controlled factors. This has shifted some of the focus from attainment to achievement
test scores, and from compensatory programs to state, district, school, and teacher
accountability. This has been accompanied by an increased emphasis on identifying
practices and policies that all other things being equal, are more effective than others in
providing effective schooling. At the state level, the “state standards movement” and
reform has resulted in state level efforts to promote higher achievement through such
things as increased core curricular requirements, exit exams, higher compulsory school
attendance age, school size reform, requiring teachers to have a major in field taught,
increased technology use, advanced and honors diplomas, and content standards.
In this paper we explore relationship of state aggregated student and family related
background characteristics, and selected state policy variation to aggregated measures of
both student attainment and achievement outcome indicators. We first explore the basic
question of how much of the measured differences in educational outcomes between the
states can be attributed to demographic differences in the composition of the populations
of the states. Second, taking these compositional differences into account, we explore the
extent to which differences in selected state policies are statistically related to differences in
observed outcomes aggregated at the state level. To do this we use aggregated state level
data from the Census Bureau merged with Department of Education data from the
Common Core of Data (CCD), Integrated Postsecondary Data Systems (IPEDS), and the
National Assessment of Education Progress (NAEP), and various other sources to
increase our understanding of what these state-by-state comparisons represent. In
addition we provide some state level descriptive historical data on some of the major
outcomes of interest.
1.1 Research Questions
Specifically we address the following questions.
2

3. 1. How much variation by state is there in state high school and postsecondary
completion rate indicators; and NAEP and SAT/ACT achievement indicators?
2. How much of the variation is associated with variation in state population
demographics? What demographic variables are most related to the outcomes of
interest?
3. Are there states that have higher or lower than expected outcomes based on
demographics?
4. How much of the variation is related to differences in selected state policies?
To a limited extent, we also descriptively address trends over time and the extent of the
gap between race and ethnic minority statistics with regard to high school and
postsecondary completion.
Figure 1 summarizes the state level statistics examined descriptively and in the regression
models. We discuss these measures in more detail as we proceed and appendices provide
additional information on the distribution by state for several of these variables.
Figure 1. Summary of demographic, selected state policy/education statistics, and
student outcomes variables included in models
State Demographics
Education levels, Income/poverty, Employment, Race, Ethnicity/immigration, Mobility, Population
Selected State Policy/Ed System Statistics
Exit exams, Compulsory school age, Course requirements, Technology score, School size,
Teacher salary, Advanced diploma, Algebra 8th grade
Student Outcomes
Attainment
Public school high school cohort survival rate
Postsecondary entrance and completion indicator
Achievement
8th grade NAEP math score
Number per 1000 high school graduates scoring 1200 or 26 an above on SAT/ACT
1. 2 Paper Structure
The remainder of this paper proceeds as follows: 2) Procedure data and methods; 3) Descriptive
data on model outcome variables with some historical perspective 4) Regression models results for
attainment 5) Regression models results for achievement 6) Conclusion/discussion.
3

4. 2. Procedure, Data and Methods
We address the questions posed above by a series of descriptive graphing and building exploratory
regression models. Our first step was to build a state database that consists of state demographic
variables, state education policy variables, and state outcome variables. The primary data source
for most of the data is the Census Bureau (Decennial Census, American Community Survey and
Current Population Reports on Educational Attainment) and the US Department of Education
((Common Core of Data (CCD), and the Integrated Postsecondary Education Data System
(IPEDS)). In addition, data on college entrance scores comes from the College Board and
the ACT. Many of the derived variables/indicators used were directly taken from compilations of
state aggregated data published by the Council of Chief States School Officers (CCSSO) State
Indicator Reports, ED-Week Quality Counts, and NCHEMS web based Information Center. All of the
data used in this paper are aggregated at the State level. Graphs typically include the 50 US states
and the District of Columbia; however DC was removed from regressions due to its unique
demographics. Using these data sources, we first built a database containing about 300 state level
variables. From this database we selected the variables included in Table 1(a-c) to include in our
model building. These are organized conceptually into three groupings (state demographics,
selected state policy and education system statistics, and state level outcomes on attainment and
achievement). Our focus is on educational measures most applicable to the
secondary/postsecondary level.
In the next section, we present descriptive information by state on the outcome variables as a way
of observing the range of differences among the states. We also include some historical
information on the outcomes of interest in the form of graphing historical trends by state. We
then proceed to look at the relationships among the variables and present results of regression
models and examination of the expected vs. the actual rates based on state demographics. Finally
we look at the extent to which the introduction of selected state policy variables changes the
amount of variation explained controlling for the demographic differences. To assist in the
exploratory analysis, we used the SAS proc regression grouped option, which allows for selected
variables to enter into the model together in logical groupings. We used a grouped Forward
selection option, which starts with no variables in the model and adds variable groups one by one
that maximize the fit of the model. We use selection criteria of .15 for entrance into the model.
Predicted and residual values from the estimated regression equation were also tabulated.
Observing partial regression results, we also observe the percent of the variation attributed to each
of the groups in the model. In forming the groups, exploratory factor analysis of the variables was
performed and correlations between the independent variables were observed. These identified
factors contributed to decisions about the groupings used in the models.
4

5. Table 1-a. State aggregated demographic variables included in various models
Standard
Name Label Source Mean Deviation
Income/poverty
pu18po99 Percent under 18 in poverty Census 15.8 4.7
mefain05 Median family income 2005 Census 55834.0 8727.8
Employment Census
Percent of children in
families in which one parent
parempl is working full time for year Census 71.3 4.2
Education
Percent of children in
families in which one parent
has 2 or 4 year
onparpst postsecondary degree Census 43.9 7.1
Percent of population age
25-and older who have high
alhsd20 school diploma or credential Census 82.0 4.4
Race/ethnicity
Percent Black in population
pblk05 2005 Census 10.4 9.7
Ethnicity/Immigratio
n
Percent Hispanic in
phispa05 population 2005 Census 9.0 9.5
Percent foreign born in
pforbo04 2004 Census 7.9 6.0
Percent parents who are
parengsk native English speakers Census 90.1 7.8
Population
repo02 Resident population 2002 Census 5756.0 6386.8
Population density per
posqm05 square mile Census 189.3 257.7
Mobility
Percent of population that
lived in another state one
mobil05 year earlier Census 3.1 1.1
Source: US Census Bureau, Decennial Census and American Community Survey.
<http://www.census.gov/popest/states/asrh/SC-EST2005-04.html
5

6. Table 1-b. Selected State education policy or practice variables included in various models
Standard
Name Content Source Mean Deviation
HSEXIT2 Had exit exam by 2004 CCSSO 0.4 0.5
National
Education
Comsch05 Compulsory school age Association 16.9 .9
QC state indicators
Tecindx5 technology score ED-Week 76.6 6.6
Ratio of teacher salary to per
Ntesal capita income NCES/Census 1.5 0.1
Average school size for
Asssr03 regular secondary schools NCES 772.9 310.8
Number math courses
Mcourreq required for graduation CCSSO 2.8 0.7
Major in field required for
Majsteac teachers ED-Week QC 80.9 .40
Table 1-c. State outcome variables explored
Standard
Name Content Source Mean Deviation
Public 9th grade school CCD/NCEHMS web
PCSR04 cohort survival rate site/Mortenson 71.7 9.15
Percent 9th grade
graduating high
school, entering
postsecondary and
obtaining program
completion in 150 CCD/IPEDS/ACT
PG9DCG04 percent of time NCES/NCHEMS/Mortenson 18.3 14.97
Average 8th grade
Avmatsc5 math score NCES/NAEP 278 7.14
Number per 1000 with
SAT above 1200 or
HISCRT04 ACT above 26 ACT/SAT 173 36.1
Gap between black
and non-hispanic
white high school
completion Census
Source: NCHEMS Higher Information Center http://higheredinfo.org/ and Tom Mortenson—
Postsecondary Education Opportunity http://www.postsecondary.org; SAT. The College Board. "2001 SAT
V+M Score Bands Report," unpublished data; ACT. "Number of 2001 High School Graduates with ACT
Composite Scores of 26 or Higher," unpublished analysis, Iowa City, Iowa
6

7. 3. Descriptive Graphing Information on State Variation on the
Outcomes of Interest
In this section, we present descriptive state data on the outcome variables included in the
models. Appendix A contains additional graphs of some of demographic and state policy/
system variables also included in the model. By way of introduction, we also include some
historical data on decennial census data by state on high school and college educational
attainment.
3.1 Education Attainment Statistics
The publication of reports such as One-Third of A Nation (Barton 2005) and Losing Our
Future (Orfield et al. 2004), reflect the refocusing of attention on high school completion
rates as a national problem. Trend lines and yearly rates differ depending on what
measure of dropping out one chooses. As illustrated in appendix A table 1, recent
estimates nationwide of public school high school completion rates range from 68-70
percent (and around 50 percent for underrepresented minorities) based on ratios of
entering public school cohort size to diplomas awarded four years later --- to 86 percent as
reported by 18-24 year olds in the Current Population Survey and including public and
private school students, alternative completions, and out of grade completions.
3.1.1 Decennial Census Data on Attainment 1940-2000
Figure 2 gives decennial census data on the percent of the total US population 25 years of
age and older that have a high school diploma or equivalent from 1940 to 2000 by
race/ethnicity; and figure 3 gives similar information for those who have a BA degree.
These data document the dramatic increase in the percent of the population with high
school diploma or equivalent, and especially among blacks, narrowing the black-white gap,
over the last 60 years. The figures also document the slowing of gains in the last decade.
Gains for a BA have also occurred over the period with a slowing of rate of increase in
recent years (figure 3).
Figures 4 and 5 plot this same information by state (without state labels) for high school or
higher and BA or higher, respectively. In 1940 the high school completion distribution
ranged from 15 percent in Arkansas to 41 percent in the District of Columbia and 37
percent in California. By 2000, the high school distribution ranged from 73 percent in
Mississippi to 88 percent in 4 states---Utah, Wyoming, Minnesota, and Alaska.1 Figure 4,
shows that the variation among states in rates of high school credential attainment has
narrowed over the period since 1940.
In 1940 the distribution for BA or higher ranged from 2 percent in Arkansas and 3 percent
in Alabama to 11 percent in the District of Columbia and 7 percent in California and
1
This decennial census figure of 88 percent for Alaska is surprising given the relatively lower figure on the
cohort survival rate.
7

8. Nevada. One can see that the range of difference between states for the BA or higher has
appears to have grown over the period since 1940.
Figure 2. Percent of population 25 years of age and older who have a high school
diploma or equivalent by race/ethnicity: Decennial Census Data
1940-2000
100
90 85
79 84
80 80
78
70 75
72
70 69
67
63
60
55 52
50 51 50
52
43 44
40 41
36
34 31
30
26
24 22
20
14
10
8
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
Black Hispanic White White non-hispanic All
Note: Based on Decennial census. White category does not exclude those of Hispanic Origin. Hispanic
Origin can be of any race. White non-Hispanic is available from 1980-2000 only.
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
8

9. Figure 3. Percent of population 25 years of age and older who have a BA degree:
Decennial Census Data: 1940-2000
100
90
80
70
60
50
40
30 27
22 26
20 17 22
11 17 11 14
10 7 8 8 10
5 9
4 8
1 2 4
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
Hispanic Black White White non-Hispanic
Note:
Based on Decennial census. White category does not exclude those of Hispanic Origin. Hispanic Origin can
be of any race. White non-Hispanic is available from 1980-2000 only
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
9

10. Figure 4. Percent of total population 25 and older with high school diploma or
equivalent by state: 1940-2000
100
90
80
70
60
50
40
30
20
10
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
NOTE: This distribution ranged from 15 percent in Arkansas to 41 percent in the District of Columbia and
37 percent in California in 1940; and ranged from 73 percent in Mississippi to 88 percent in 4 states, Utah,
Wyoming, Minnesota, and Alaska in the year 2000.
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
10

11. Figure 5. Percent of total population 25 and older with BA degree or higher by
state: 1940-2000
45
40
35
30
25
20
15
10
5
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
NOTE: This distribution ranged from 2 percent in Arkansas to 11 percent in the District of Columbia and 7
percent in California and Nevada in 1940; and ranged from 15 percent in West Virginia to 39 percent in
District of Columbia and 33 percent in Massachusetts in 2000.
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
11

12. Figure 6, also using the decennial-census-data, plots by state the gap between the percent
of white and black persons 25 years of age and older having a high school diploma or
higher from 1940 to 2000; and figure 7 shows similar information for the BA or higher
attainment statistic. Figure 6 shows the increase in the high school gap, up to 1960
followed by a decline in most states. In 2000, there were 4 states where the percent of
blacks having this credential was higher than that of the white population. In 2000, the
high school gap nationwide was 12 percentage points (84 compared to 72) and the BA gap
representing a much higher percentage difference was similar (11/12 percentage points--26
compared to 14). Figure 8 based on figures 2 and 3 plots the national gap at each period
1940-2000 and suggests that in periods of majority population rapid growth in educational
attainment, the black-white gap seems to grow, (such as the period between 1950 and 1970
for high schools and between 1970 and 2000 for BA attainment).
Figure 6. Plot of gap between percent of white and black population over 25 with
high school diploma or equivalent by state: 1940-2000
70
60
50
40
30
20
10
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
-10
-20
-30
-40
NOTE. The gap ranged from 8 in West Virginia in 1940 to 38 percentage points in California in 1940. In
2000 the gap ranged from –8 in North Dakota one of 4 states to have a negative gap to 24 in the District of
Columbia and 19 in Mississippi and 18 in Wisconsin.
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
12

13. Figure 7. Plot of gap between percent of white and black population over 25 with
a BA or higher by state: 1940-2000
70
60
50
40
30
20
10
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
-10
-20
NOTE. The gap ranged from less than 1 in Alaska and Hawaii and 1 in West Virginia in 1940 to –8 in
Montana and –4 in Vermont and –1 in Idaho to 59 percentage point gap in DC and 20 point gap in
Connecticut and 17 percentage gap in Virginia in 2000.
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
13

14. Figure 8. Plot of gap between percent of white and black population over 25 with
high school diploma or equivalent and percent with BA or higher:
1940-2000
25
22.7 23.1
21.5
20
18.5
17.6
15 14.8
11.8
11.3
10 10.1
8.7
6.9
5
4.4 4.6
3.6
0
1930 1940 1950 1960 1970 1980 1990 2000 2010
High school completion gap BA or higher gap
NOTE. This chart based on figures 2 and 3 illustrates that in periods of rapid growth in majority population
educational attainment the gap seems to grow, (such as the period between 1950 and 1970 for high schools
and between 1970 and 2000 for BA attainment).
SOURCE: U.S. Census Population Division Census 2000 PHC-T-41. A Half-Century of Learning: Historical
Statistics on Educational Attainment in the United States, 1940 to 2000
3.1.2 Public School Cohort Survival Rate
The outcome indicator representing high school completion that we used in the
regressions in this paper is the public school cohort survival rate (CSR) for 2004 as
published on the NCHEMS website and developed by Tom Mortenson. This statistic
represents the ratio of the total 9th grade public school enrollment to public school
diplomas awarded 4 years later. It is derived from NCES/CCD data on enrollment and
diplomas awarded and provides a standardized measure across states. It is similar to other
CCD based completion statistics such as those noted in appendix table A-1 and the NCES
averaged freshman cohort completion rate. We used this version due to its’ availability
back to 1990 and ease of merging into our database. The CSR rate by state for 2004 is
graphed below in figure 9. Figure 10 graphs the rate by state for 1990-2004. Apart from
some outliers, there appears to be little change with a slight downward trend. Nationally,
the CSR rate was 71.2 in 1990, 67.1 in 2000, and 69.7 in 2004.
14

15. Figure 9. Public high school cohort survival rate by state: 2004
N ew J ers ey 91. 3
U tah 85. 1
N orth D akota 84. 7
Iowa 84. 5
N eb ras ka 83. 8
M i n n es ota 83. 6
V ermon t 82. 6
S ou th D akota 81. 5
Id ah o 79. 6
M on tan a 78. 6
P en n s yl van i a 78. 4
W i s c on s i n 78
M ai n e 77. 5
M i s s ou ri 77. 2
K an s as 77
O hio 76
C on n ec ti c u t 75. 9
N ew H amp 75. 7
Il l i n oi s 75. 5
A rkan s as 75. 3
W yomi n g 75. 1
M as s ac h u s ett 74. 6
O kl ah oma 74. 1
M aryl an d 73. 7
V i rg i n i a 73. 2
C ol orad o 73. 2
W es t V i rg i n i a 73. 1
O reg on 72. 4
R h od e Is l an d 72. 2
C al i f orn i a 70. 7
W as h i n g ton 70. 2
In d i an a 70. 1
US 69. 7
M i c h i g an 69. 1
L ou i s i an a 68. 6
T exas 67. 7
D el aware 65. 4
H awai i 64. 9
K en tu c ky 64. 8
A ri z on a 64. 3
N orth C arol i n a 64. 2
T en n es s ee 63
N ew Y ork 62. 5
A l as ka 62. 5
N ew M exi c o 61. 8
Mis s is s ip p i 60. 3
A l ab ama 60. 3
F l ori d a 55
G eorg i a 54. 1
S ou th C arol 52. 1
N evad a 50. 7
0 10 20 30 40 50 60 70 80 90 100
NOTE: Calculated based on number of 9th graders/High school graduates four years later (public high
schools). Doesn’t account for students who are still enrolled or transfers to private high schools or out-of-
state
SOURCE National Center for Higher Education Managers Systems (NCHEMS), Higher Education
Information System; Tom Mortenson—Postsecondary Education Opportunity http://www.postsecondary.org
15

16. Figure 10. Public School Cohort Survival Rate by State 1990-2004
100
90
80
70
60
50
40
30
20
10
0
1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
NOTE: Calculated based on number of 9th graders/High school graduates four years later (public high
schools)
SOURCE National Center for Higher Education Managers Systems (NCHEMS), Higher Education
Information System; Tom Mortenson—Postsecondary Education Opportunity http://www.postsecondary.org
16

17. 3.1.2 Postsecondary Pipeline/Completion Indicator
Figure 11 graphs state differences in the postsecondary pipeline/completion indicator
statistic used as the outcome variable in the regression models. This statistics is also Tom
Mortenson’s calculation as included on the NCHEMS web site. It is based on CCD
enrollment figures for 9th graders, estimating the number who graduate from high school
within 4 years (based on the public HS graduation rates), the number who go directly to
college (based on the college going rates of recent HS graduates), the number who return
for their second year of college (based on the first-year retention rates), and the number
who graduate from postsecondary program within 150% of program time (based on the
IPEDS graduation rates). The calculation for high school graduation doesn’t account for
transfers to private high schools and out-of-state. The calculation for college graduation
doesn’t account for transfers across institutions. By state, rates range from 5.8 in Alaska
to 27.9 in South Dakota.
Figure 11. Postsecondary pipeline/completion indicator, percent of 9th grade high
school cohort estimated to graduate high school, enter postsecondary
directly and obtain postsecondary degree within 150 percent of program
time by state: 2004
S out h Da kot a 27. 9
Iowa 27. 4
Ne w J e rs e y 27. 3
Minne s ot a 27. 3
P e nns ylva nia 27. 1
Ma s s a c hus e t t s 26. 1
Nort h Da kot a 25. 1
Wyoming 24. 9
Ne bra s ka 24. 7
Ne w Ha mp 24. 5
C onne c t ic ut 24. 0
Wis c ons in 23. 7
V irg inia 22. 4
Ka ns a s 22. 2
V e rmont 22. 1
India na 21. 7
De la wa re 20. 4
C olora do 20. 4
R hode Is la nd 20. 3
Ne w York 20. 2
Ma ine 20. 2
Illinois 19. 9
Mis s ouri 19. 8
O hio 19. 5
Ma ryla nd 19. 4
Mont a na 18. 8
Nort h C a rolina 18. 7
US 18. 4
Mic hig a n 17. 9
C a lifornia 16. 9
Ut a h 16. 8
Te nne s s e e 16. 7
Wa s hing t on 16. 3
We s t V irg inia 15. 7
Ida ho 15. 7
O kla homa 15. 3
A rka ns a s 15. 3
A rizona 15. 3
S out h C a rolina 15. 0
O re g on 15. 0
F lorida 14. 5
L ouis ia na 14. 3
G e org ia 14. 1
A la ba ma 13. 8
Te xa s 13. 3
Ha wa ii 12. 8
Ke nt uc ky 12. 3
Ne w Me xic o 11. 9
Mis s is s ippi 11. 0
Ne va da 9. 9
A la s ka 5. 8
0 5 10 15 20 25 30
NOTE: This statistics is calculated based on CCD enrollment figures for 9th graders, estimating the number
who graduate from high school within 4 years (based on the public HS graduation rates), the number who go
directly to college (based on the college going rates of recent HS graduates), the number who return for their
second year of college (based on the first-year retention rates), and the number who graduate from
postsecondary program within 150% of program time (based on the IPEDS graduation rates).
The calculation for high school graduation doesn’t account for transfers to private high schools and out-of-
state. The calculation for college graduation doesn’t account for transfers across institutions.
SOURCE: NCHEMS Information System web site; Tom Mortenson—Public high school graduation rates,
Tom Mortenson—College-going rates of students directly from HS, ACT Institutional Survey—Freshmen to
sophomore retention rates, NCES-IPEDS Graduation Rate Survey—Graduation Rates
17

18. 3.2 Selected Achievement Outcome Variables
Figures 12a to 15 present statistics on the achievement variables included in the regression
models. Our historical information is much more limited than with attainment.
3.2.1 NAEP 8th Grade Math Scores
We used state 8th grade NAEP math scores for our achievement indicator outcome
variable. Unfortunately, 12th grade NAEP is not state representative. By state, NAEP 8th
grade math average scores range from 262 in Alabama and Mississippi to 292 in
Massachusetts and 290 in Minnesota (figure 12a).
Figure 12b shows another NAEP statistic, the percent categorized as at or above
proficient in 8th grade math by state. We use this variable in the regression models
discussed in section 5. Figure 12b shows much the same state line up as in figure 12a, with
a few differences.
Looking at Figure 13, which graphs the state average score for 1990, 2000, and 2005, we
see the trend upward in the period graphed, continuing a trend that was also apparent
nationally between 1980 and 1990.
Figure 12a. NAEP average 8th grade math score by state: 2005
Ma s s a c h u s e tts 292
Min n e s o ta 290
V e rmo n t 287
S o u th D a ko ta 287
No rth D a ko ta 287
Mo n ta n a 286
Wis c o n s in 285
Wa s h in g to n 285
Ne w Ha mp s h ire 285
V irg in ia 284
Ne w J e rs e y 284
Ne b ra s ka 284
Ka ns a s 284
Io wa 284
O h io 283
Wyo min g 282
O re g o n 282
No rth C a ro lin a 282
In d ia n a 282
Te xa s 281
S o u th C a ro lin a 281
P e n n s ylva n ia 281
Ma in e 281
Id a h o 281
D e la wa re 281
C o n n e c tic u t 281
C o lo ra d o 281
Ne w Y o rk 280
U ta h 279
A la s ka 279
US 278
Ma ryla n d 278
Illin o is 278
Mic h ig a n 277
Mis s o u ri 276
K e n tu c ky 274
F lo rid a 274
A riz o n a 274
R h o d e Is la n d 272
G e o rg ia 272
A rka n s a s 272
Te n n e s s e e 271
O kla h o ma 271
Ne va d a 270
We s t V irg in ia 269
C a lifo rn ia 269
L o u is ia n a 268
Ha wa ii 266
Ne w Me xic o 263
Mis s is s ip p i 262
A la b a ma 262
245 250 255 260 265 270 275 280 285 290 295
18

19. SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment
of Educational Progress (NAEP) 2005 data
Figure 12b.NAEP percent at or above proficient in 8th grade math by state: 2005
Min n e s o ta 43
Ma s s a c h u s e tts 43
V e rmo n t 38
Wis c o n s in 36
Wa s h in g to n 36
S o u th D a ko ta 36
Ne w J e rs e y 36
Mo n ta n a 36
No rth D a ko ta 35
Ne w Ha mp s h ire 35
Ne b ra s ka 35
C o n n e c tic u t 35
O h io 34
Ka ns a s 34
Io wa 34
V irg in ia 33
O re g o n 33
No rth C a ro lin a 32
C o lo ra d o 32
Te xa s 31
P e n n s ylva n ia 31
Ne w Y o rk 31
U ta h 30
S o u th C a ro lin a 30
Mic h ig a n 30
Ma ryla n d 30
Ma in e 30
In d ia n a 30
Id a h o 30
D e la wa re 30
Wyo min g 29
A la s ka 29
Illin o is 28
Mis s o u ri 26
F lo rid a 26
A riz o n a 26
R h o d e Is la n d 23
G e o rg ia 23
K e n tu c ky 22
C a lifo rn ia 22
A rka n s a s 22
Te n n e s s e e 21
Ne va d a 21
O kla h o ma 20
Ha wa ii 18
We s t V irg in ia 17
L o u is ia n a 16
A la b a ma 15
Ne w Me xic o 14
Mis s is s ip p i 13
0 5 10 15 20 25 30 35 40 45 50
SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment
of Educational Progress (NAEP) 2005 data
19

20. Figure 13. NAEP average 8th grade math score by state: 1990, 2000, 2005
300
290
280
270
260
250
240
1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
NOTE: Nationwide NAEP 8th grade math scores were 262 in 1990; 270 in 2000; and 274 in 2005. Among
states included in 1990, the highest score was North Dakota and the lowest was Louisiana with 246. By 2005
the highest score was obtained by Massachusetts 292 and the lowest by Alabama, 262 and Mississippi. In
1990 state estimates were available only for 32 states and did not include Massachusetts.
SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment
of Educational Progress (NAEP) 1990, 2000, 2005 data
20

21. 3.2.2 Rate per 1000 High School Graduates who Score above 1200 on SAT or 26 on ACT
The other achievement outcome indicator we included in our regressions is another
statistic from the NCHEMS web site—the rate per 1000 high school graduates who score
above 1200 on the SAT or above 26 on the ACT (figure 14). This statistic is limited in
that it does not take into account those who might have taken both tests—and differences
in states in the percent taking two of the tests may affect these tabulations. It should also
be noted that this is the rate per 1000 high school graduates and differential rates of high
school graduation would also affect comparisons by state. Rates range from 98 in
Mississippi to 259 in Colorado. Figure 15, graphing results between 1999 and 2004 show
the increase in this rate for most states, and also a little more spread among the states in
2004 than in 1999.
Figure 14. Rate per 1000 high school graduates who scored 1200 or above on
combined SAT or 26 or above on ACT: 2004
C o lo ra d o 259
Ma s s a c h u s e tts 253
Illin o is 237
C o n n e c tic u t 234
Ne w Y o rk 228
Min n e s o ta 2 18
Ne w Ha mp s h ire 2 17
O h io 2 13
Mo n ta n a 207
Ne w J e rs e y 206
Te n n e s s e e 205
Ka ns a s 201
Ne b ra s ka 19 8
Wis c o n s in 19 5
Ma ryla n d 19 4
V e rmo n t 18 9
V irg in ia 18 5
Wa s h in g to n 18 5
US 18 4
Mic h ig a n 18 4
Mis s o u ri 18 2
A la s ka 17 8
O re g o n 17 1
No rth D a ko ta 17 0
Io wa 16 9
F lo rid a 16 7
Id a h o 16 7
G e o rg ia 16 6
S o u th D a ko ta 16 5
U ta h 16 2
Ma in e 16 1
No rth C a ro lin a 16 1
R h o d e Is la n d 15 7
P e n n s ylva n ia 15 7
In d ia n a 15 6
K e n tu c ky 15 6
Wyo min g 15 3
Ha wa ii 15 3
D e la wa re 15 0
C a lifo rn ia 14 6
A la b a ma 14 4
S o u th C a ro lin a 14 0
Te xa s 13 8
A rka n s a s 13 3
O kla h o ma 13 2
L o u is ia n a 13 2
We s t V irg in ia 12 8
Ne w Me xic o 12 7
Ne va d a 12 2
A riz o n a 116
Mis s is s ip p i 98
0 50 10 0 15 0 200 250 300
NOTE: The number of SAT Math and Verbal Scores 1200 and above + ACT Composite Scores 26 and
above) per 1,000 high school graduates
SOURCE: SAT. The College Board. "2001 SAT V+M Score Bands Report," unpublished data ACT.
"Number of 2001 High School Graduates with ACT Composite Scores of 26 or Higher," unpublished
analysis, Iowa City, Iowa. High School Graduates. Western Interstate Commission for Higher Education.
Knocking at the College Door: Projections of High School Graduates by State and Race/Ethnicity 1996-2012. Boulder, C0
21

22. Figure 15. Rate per 1000 high school graduates who scored 1200 or above on
combined SAT or 26 or above on ACT: 1999, 2001, 2004
300
250
200
15 0
10 0
50
0
19 9 8 19 9 9 2000 2001 2002 2003 2004 2005
NOTE: The number of SAT Math and Verbal Scores 1200 and above + ACT Composite Scores 26 and
above per 1,000 high school graduates
SOURCE: SAT. The College Board. " SAT V+M Score Bands Report," unpublished data ACT. "Number
of High School Graduates with ACT Composite Scores of 26 or Higher," unpublished analysis, Iowa City,
Iowa. High School Graduates. Western Interstate Commission for Higher Education. Knocking at the College
Door: Projections of High School Graduates by State and Race/Ethnicity 1996-2012. Boulder, C0
4. Results of the Regression Runs on Attainment
4.1 High School Cohort Survival Rate
4.1.1 Demographic Predictors of High School Cohort Survival Rate
Table 1 and figures 16 and 17 summarize results from a forward selection regression
model for the outcome variable public high school cohort survival rate (CSR) in 2004.
The demographic model “explains” 72 percent of the variation, with the group’s entitled
“parent education”, “ parent employment”, and “population density” having a positive
sign and “mobility”, “race” and “ethnicity/immigration” having a negative sign. In this
model, the “race” group only includes percent black. Based on a factor analysis, we
included the Hispanic percentage variable with the “ethnicity/immigration” group that
also includes percent foreign born and percent speaking English as first language. The
group “population density” is the number per square mile and “mobility” is the percent of
state population that lived in a different state 1 year earlier. The group “parent education”
accounts for 40 percent of the variation, with “mobility” adding another 9 percent. The
22

23. model groups “race” and “ethnicity/immigration” each contribute 7 percent and the
“parent employment” variable adds another 3 percent and “population density” 2 percent
(figure 15). Differences by state between actual and predicted rates, (figure 17) range
from +14 in New Jersey and +11 in Arkansas to –8 in Indiana, South Carolina, and
Nevada. We note here that the models we ran initially included variables representing
poverty and also income directly; however, the income variables were highly related to
education levels and so did not enter the models. The poverty variable did enter the
model at the last step, and controlling for the other SES variables already in the model its
sign was positive and it explained an additional 3 percent of the variation. We did not
include it in the model presented here.
Table 1. Summary of forward selection regression model using grouped option
explaining variation in state differences in public school high school
cohort survival rate: demographic variables only
Step Group Direction Number Partial Model F Pr> F
entered of R- R- Value
variables Square Square
Parent +
1 Education+ 2 0.4022 0.4022 15.81 <.0001
2 Mobility- - 3 0.0916 0.4938 8.32 0.0059
3 Race- - 4 0.0732 0.567 7.61 0.0084
4 Ethnicity/imm- - 6 0.0735 0.6405 4.39 0.0184
Parent +
5 Employment+ 7 0.0276 0.6681 3.49 0.0689
Population +
6 density+ 8 0.024 0.6921 3.2 0.081
NOTE: Calculated based on number of 9th graders/High school graduates four years later (public high
schools). Doesn’t account for students who are still enrolled or transfers to private high schools or out-of-
state
SOURCE National Center for Higher Education Managers Systems (NCHEMS), Higher Education
Information System; Tom Mortenson—Postsecondary Education Opportunity http://www.postsecondary.org
Represents residuals tabulated based on SAS PROC REG SIMPLE;
PROC REG SIMPLE;
ID State1;
MODEL PCSR04 =
{alhsd20 onparpst}
{pblk05} {phispa05 pforbo04}{parempl} {posqm05} {mobil05}
/ p r cli clm sle = .15 SELECTION = Forward
GROUPNAMES = 'education' 'race' 'ethnicity/immigration'
'employment' 'pop density' 'mobility' ;
23

24. Figure 16. Distribution of variance among “groups” in the demographic model
examining state variation in public school high school cohort survival:
2004
Unexplained
31%
Education+
41%
Pop density+
2%
Employment+
3%
Ethnicityimmigration-
7% Mobility-
Race-
9%
7%
NOTE: Model R-square =.69 Allocation of variance based on Partial R-Squares. PCSR04 =
Dependent variable public high school cohort survival rate: 2004
SOURCE: See table 1 above
24

25. Figure 17. Difference between actual and predicted (residuals) high school cohort
survival rate (CSR) from model with demographic variables only: 2004
Ne w J e rs e y 14
A rka ns a s 11
Ida ho 9
Ut a h 9
L ouis ia na 8
C a lifornia 6
V irg inia 6
Mis s is s ippi 5
V e rmont 5
Ma ryla nd 5
O re g on 4
Illinois 4
Mont a na 3
We s t V irg inia 3
Mis s ouri 3
O kla homa 2
Iowa 2
Te xa s 2
Nort h Da kot a 2
Ne bra s ka 2
A rizona 2
S out h Da kot a 1
Minne s ot a 0
C olora do 0
P e nns ylva nia 0
Nort h C a rolina
-1
-1 ine
Ma
-2 Ha wa ii
-2 Wyoming
-3 A la s ka
-3 Ka ns a s
-3 De la wa re
-3 Te nne s s e e
-3 O hio
-4 Ne w York
-4 A la ba ma
-4 Wis c ons in
-4 Wa s hing t on
-4 C onne c t ic ut
-5 R hode Is la nd
-5 Ne w Me xic o
-5 Ne w Ha mps hire
-5 Ma s s a c hus e t t s
-6 Ke nt uc ky
-6 G e org ia
-7 Mic hig a n
-7 F lorida
-8 Ne va da
-8 S out h C a rolina
-8 India na
-10 -5 0 5 10 15 20
NOTE: Model R-square = .69. Allocation of variance based on Partial R-Squares. PCSR04 = Dependent
variable public high school cohort survival rate: 2004
SOURCE: see table 1 above
25

26. 4.1.2 Adding Selected State Policy and Education Related Statistics to the
Demographic Model of High School Cohort Survival Rate
Table 2 and figure 18 summarize the change in the model when selected state policy and
system statistics are entered into the model using the same forward selection procedure.
The total R-squared is not much increased from the demographic model; however, several
of the state policy variables enter into the model—demonstrating what simple correlations
revealed that some of the policies are highly related to the demographic differences. The
“Parent education” group remains the major explanatory variable with a Partial R-squared
of .36 “School size” is negative and adds 16 percent explanation. “Mobility” adds 9
percent and exit exams 5 percent—both with a negative sign. “Parent employment”
contributes an additional 2 percent and “technology” marginally significant in the model
also contributes 2 percent. Note that “race” and “ethnicity/immigration” did not enter
the model with this configuration. “Exit exams” is highly correlated (.40) with
race/ethnicity variables, so it is not clear if the apparent negative effect is related to the exit
exams themselves or to other variables with which it is correlated. The findings for
school size are consistent with other research that has found a relationship to high school
completion to this variable (Garrett Z, Newman, Elbourne, Bradley, Noden, Taylor, West 2004).
The variables representing “course requirements”, “teacher salaries”, and “teaching requirements”
did not reach the significance levels needed to enter the model and were not included. As these
variables were missing for 9 states, after testing the model with these variables and without, we
removed them from the model.
26

27. Table 2. Summary of forward selection regression model using grouped option
explaining variation in state differences in public school high school
cohort survival rate: state policy and system statistics added to
demographic model
Step Group Direction Number Partial Model F Pr> F
entered of R- R- Value
variables Square Square
Parent +
1 education 2 0.3639 0.3639 11.16 0.0001
2 school size - 3 0.1629 0.5268 13.08 0.0009
3 mobility - 4 0.09 0.6168 8.69 0.0055
4 exit exam - 5 0.0478 0.6646 5.13 0.0296
5 pop density + 6 0.032 0.6966 3.7 0.0627
Parent +
6 employment 7 0.0244 0.721 2.98 0.0936
7 technology + 8 0.0207 0.7417 2.64 0.1138
NOTE: Calculated based on number of 9th graders/High school graduates four years later (public high
schools). Doesn’t account for students who are still enrolled or transfers to private high schools or out-of-
state
SOURCE National Center for Higher Education Managers Systems (NCHEMS), Higher Education
Information System; Tom Mortenson—Postsecondary Education Opportunity http://www.postsecondary.org
SOURCE: Represents residuals tabulated based on SAS PROC REG SIMPLE;
ID State1;
MODEL PCSR04 =
{pu18po99}{alhsd20 onparpst}{pblk05}
{phispa05 pforbo04 parengsk} {parempl} {posqm05} {mobil05}
{Tecindx5} {HSEXIT2} {comsch05} {ASSSr03} {ntesal}
{Majsteac} {Mcourreq}
/ p r cli clm sle = .15 SELECTION = Forward
GROUPNAMES = 'Poverty'
'Education' 'Race' 'Ethnicity' 'Employment'
'Popdens' 'Mobility' 'technology' 'Exit exam'
'Comp age' 'Schoolsize' 'teachsal' 'majteach' 'math course';
27

28. Figure 18. Distribution of variance among “groups” in the model examining state
variation in public school high school cohort survival: demographic
and state policy/system variables 2004
U n exp l ai n ed
26%
E d u c ati on +
37%
T ec h n ol og y+
2%
E mp l oymen t+
2%
P op d en s i ty+
3%
E xi t exam-
5%
S c h ool s i z e-
16%
M ob i l i ty-
9%
NOTE: Model R-square = .74. Allocation of variance based on Partial R-Squares. PCSR04 =
Dependent variable public high school cohort survival rate: 2004
SOURCE: See table 1 above
28

29. 4.2 A Postsecondary Pipeline/Completion Indicator—(Rate of Graduation from
High School, Entering Postsecondary the Next Year and Completing a
Postsecondary Program in 150 percent of Program Time)
4.2.1 Demographic Predictors of Postsecondary Pipeline/Completion Indicator
Table 3 and figures 19 and 20 summarize results from a forward selection regression
model for the outcome variable representing the postsecondary pipeline/completion
indicator. Results show that the demographic variables account for .78 percent of the
variation. “Parent education” has a partial r square of .53, followed by “parent
employment” and “mobility.” Comparing the postsecondary pipeline/completion results
with those from the high school cohort survival model, we see that “parent education” and
“parent employment” both explain a relatively higher proportion of the variation; and
ethnicity/immigration explains less. The “race” variable does not meet the .15 threshold
for entrance into this model. Wyoming, Pennsylvania and South Dakota have the largest
positive difference between actual and predicated results and Utah, Alaska, and Maryland
the largest negative differences. As this measure may be subject to bias related to
differences in in-state and out of state postsecondary attendance rates it is difficult to
interpret these results for individual states.
Table 3. Postsecondary pipeline/completion indicator, summary of forward
selection regression model: demographic variables only
Step Group Direction Number Partial Model F Pr> F
entered of R- R- Value
variables Square Square
1 Parent Education+ + 2 0.5384 0.5384 27.41 <.0001
2 Parent Employment+ + 3 0.0783 0.6167 9.4 0.0036
3 Mobility- - 4 0.0888 0.7055 13.57 0.0006
4 Ethnicity/immigration- - 6 0.0418 0.7473 3.56 0.0371
5 Pop density+ + 7 0.0285 0.7759 5.34 0.0258
29

30. NOTE: This statistic is calculated based on CCD enrollment figures for 9th graders, estimating the number
who graduate from high school within 4 years (based on the public HS graduation rates), the number who go
directly to college (based on the college going rates of recent HS graduates), the number who return for their
second year of college (based on the first-year retention rates), and the number who graduate from
postsecondary program within 150% of program time (based on the IPEDS graduation rates).
SOURCE: NCHEMS Information System web site; Tom Mortenson—Public high school graduation rates,
Tom Mortenson—College-going rates of students directly from HS, ACT Institutional Survey—Freshmen to
sophomore retention rates, NCES-IPEDS Graduation Rate Survey—Graduation Rates
SOURCE: Represents residuals tabulated based on SAS PROC REG SIMPLE;
ID State1;
MODEL PG9DCG04 =
{pu18po99}{alhsd20 onparpst}
{pblk05} {phispa05 pforbo04}{parempl}{posqm05}{mobil05}
/ p r cli clm sle = .15 SELECTION = Forward
GROUPNAMES = 'education' 'race' 'ethnicity/immigration'
'employment' 'pop density' 'mobility' ;
30

31. Figure 19. Distribution of variance among “groups” in the demographic model
examining state variation in postsecondary pipeline/completion
indicator): 2004
Unexplained
22%
E duc ation+
54%
P op dens ity-
3%
E thnic ity/immi-
4%
Mobility-
9%
E mployment+
8%
NOTE: Model R-square =. 78 Allocation of variance based on Partial R-Squares. Postsecondary
pipeline/completion indicator is calculated based on chance of graduation from high
school, enter postsecondary and complete a postsecondary program in 150 percent of
program time
SOURCE: See table 3 above.
31

32. Figure 20. Difference between actual and predicted (residuals) for postsecondary
pipeline/completion indicator from model with demographic variables
only: 2004
Wyo min g 6. 6
P e n n s ylva n ia 4. 4
S o u th D a ko ta 4. 4
C a lifo rn ia 3. 1
Io wa 2. 9
A riz o n a 2. 8
Ne w Y o rk 2. 7
We s t V irg in ia 2. 5
Ma s s a c h u s e tts 2. 2
Ne w J e rs e y 2. 0
Mo n ta n a 1. 8
No rth C a ro lin a 1. 8
A rka n s a s 1. 6
Min n e s o ta 1. 4
O re g o n 1. 3
Te n n e s s e e 1. 1
V irg in ia 1. 1
C o lo ra d o 0. 9
L o u is ia n a 0. 8
Wa s h in g to n 0. 6
Ma in e 0. 5
Ne w Ha mp s h ire 0. 3
Wis c o n s in 0. 2
Mis s o u ri 0. 1
- 0. 1 Id a h o
- 0 . 2 Mis s is s ip p i
- 0 . 2 In d ia n a
- 0 . 3 Ne b ra s ka
- 0 . 3 - 0 . 3D e la wa re
- 0 . 4 S o u th C a ro linis
Illin o
a
- 0. 7
- 0. 8 V e rmo n t
Ne w Me xic o
- 0. 9 R h o d e Is la n d
- 1. 1 rth D a ko ta
No
- 1. 3 F lo rid a
- 1. 7 Ne va d a
- 1. 8 Ka ns a s
- 1. 8 O kla h o ma
- 1. 8 Ha wa ii
- 2. 0 G e o rg ia
- 2. 3 C o n n e c tic u t
- 2. 4 A la b a ma
- 2. 4 Te xa s
- 2. 5 Mic h ig a n
- 2. 6 O h io
- 3. 1 K e n tu c ky
- 4. 3 Ma ryla n d
- 4. 6 A la s ka
- 7. 1 U ta h
- 8. 0 - 6. 0 - 4. 0 - 2. 0 0. 0 2. 0 4. 0 6. 0 8. 0
NOTE: Model R-square = .77. Allocation of variance based on Partial R-Squares. =
SOURCE: See table 3 above.
32

33. 4.2.2 Adding Selected State Policy and Education Related Statistics to the
Demographic Model of the Postsecondary Pipeline/Completion
Indicator
Table 4 and figure 21 summarize the change in the model when selected state policy and
system statistics are entered into the model using the same forward selection procedure.
The total R-squared is increased to .83. “Parent education” is highly related to the
postsecondary pipeline/completion statistic accounting for 57 percent of the variation.
Mobility (percent of population who lived out of the state one year earlier) is persistently
negative. Of the state education system variables (advanced diploma, teacher salary, math
course requirements, technology score, compulsory school age, and exit exam) only school
size entered this model.
Table 4. Summary of forward selection regression model using grouped option
explaining variation in state differences in postsecondary
pipeline/completion indicator: state policy and system statistics added
to demographic model
Step Group Direction Number Partial Model F Pr> F
entered of R- R- Value
variables Square Square
Parent +
1 Education+ 2 0.5734 0.5734 30.91 <.0001
Parent -
2 Mobility- 3 0.0777 0.6511 10.02 0.0028
Parent +
3 Employment+ 4 0.1041 0.7552 18.72 <.0001
4 School size - 5 0.0499 0.8051 11.01 0.0019
5 Pop Density + 6 0.0224 0.8275 5.45 0.0244
SOURCE: see table 3 above
Represents residuals tabulated based on SAS PROC REG SIMPLE;
PROC REG SIMPLE;
ID State1;
MODEL PG9DCG04 =
{alhsd20 onparpst} {pblk05}
{phispa05 pforbo04 parengsk} {parempl} {posqm05} {mobil05}
{Tecindx5} {HSEXIT2} {comsch05} {ASSSr03} {advdiplo}
/ p r cli clm sle = .15 SELECTION = Forward
GROUPNAMES =
'Education' 'Race' 'Ethnicity' 'Employment'
'Popdens' 'Mobility' 'technology' 'Exit exam'
'Comp age' 'Schoolsize' 'advdiploma' /*'teachsal' 'majteach' 'math
course'*/;
33

34. Figure 21. Distribution of variance among “groups” in model examining state
variation in postsecondary pipeline/completion indicator: demographic
and state policy and system variables: 2004
Unexplained
17%
Popdens
2%
Schoolsize
5%
Education
58%
Employment
10%
Mobility
8%
NOTE: Model R-square = .85 Allocation of variance based on Partial R-Squares.
SOURCE: See table 3 above
34

35. 5. Exploring Selected Achievement Measures
Standardized achievement measures aggregated at the state level for secondary school and
above are much harder to obtain. In this section we follow the same regression
procedures as with the attainment indicators using the two measures of achievement:
NAEP 8th grade math scores (using the percent proficient or above measure for 2005) and
rate per 1000 high school graduates scoring at 1200 on SAT combined or 26 on ACT or
above for 2004.
5.1 NAEP 8th Grade Math Scores
5.1.1 Demographic Predictors of NAEP 8th Grade Math Scores
Table 5 and figures 22 and 23 summarize results from running forward regression models.
Results indicate that fewer of the demographic variables were significant and entered the
model. Parent education accounts for 67 percent of the variation and mobility barely
enters the model with 2 percent of the variation. “Ethnicity” and “race” variables do not
enter the model once parent education is taken into account. As shown in figure 23, the
states with the greatest positive and negative differences between actual and predicted
based on the model taking into account education levels within the state are quite different
than the ones identified looking at the attainment variables. Texas, South Carolina, North
Carolina and Ohio had the largest positive differences and Hawaii, New Mexico, Rhode
Island, and Alabama the largest negative differences.
Table 5. Percent at or above proficient on 8th grade NAEP math, summary of
forward selection regression model: demographic variables only
Step Group Direction Number Partial Model F Pr> F
entered of R- R- Value
variables Square Square
1 Parent education+ + 2 0.6689 0.6689 47.48 <.0001
2 Mobility- - 3 0.0178 0.6867 2.61 0.113
SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment
of Educational Progress (NAEP) 2005 data
Results of SAS tabulation as specified below.
PROC REG SIMPLE;
ID State1;
MODEL promat5 = {pu18po99} {mefain05}
{alhsd20 onparpst}
{pblk05} {phispa05 pforbo04} {parempl} {posqm05} {mobil05}
/ p r cli clm sle = .15 SELECTION = Forward
GROUPNAMES = 'poverty' 'median income'
'education' 'race' 'ethnicity/immigration'
'employment' 'pop density' 'mobility';
35