Mapping State 

Proficiency Standards 

Onto NAEP Scales: 2005-2007 

NCES 2010-456 

U. S. DEPARTMENT OF EDUCATION 

 

Mapping State 

Proficiency Standards U.S. DEPARTMENT OF EDUCATION 

NCES 2010-456 Onto NAEP 

Scales: 2005-2007 

Research and Development 

Report 

October 2009 

Victor Bandeira de Mello 

Charles Blankenship 

American Institutes for Research 

Don McLaughlin 

Statistics and Strategies 

Taslima Rahman 

Project Officer 

National Center for Education Statistics 
 

 

 

 

 

 

 

U.S. Department of Education 

Arne Duncan 

Secretary 

Institute of Education Sciences 

John Q. Easton 

Director 

National Center for Education Statistics 

Stuart Kerachsky 

Acting Commissioner 

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

analyzing, and reporting data related to education in the United States and other nations. It fulfills 

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NCES activities are designed to address high-priority education data needs; provide consistent, 

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October 2009
 

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Suggested Citation 

Bandeira de Mello, V., Blankenship, C., and McLaughlin, D.H. (2009). Mapping State Proficiency 

Standards Onto NAEP Scales: 2005-2007 (NCES 2010-456). National Center for Education Statistics, 

Institute of Education Sciences, U.S. Department of Education. Washington, DC. 

For ordering information on this report, write to 

U.S. Department of Education


 ED 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 

Taslima Rahman 

(202) 502-7316 

taslima.rahman@ed.gov 
 

 

 

 

 

 

 

 

 

FOREWORD
 

The Research and Development (R&D) series of reports at the National Center for Education 

Statistics has been initiated to 

• Share studies and research that are developmental in nature. The results of such studies may 

be revised as the work continues and additional data become available; 

• Share the results of studies that are, to some extent, on the cutting edge of methodological 

developments. Emerging analytical approaches and new computer software development 

often permit new and sometimes controversial analyses to be done. By participating in 

frontier research, we hope to contribute to the resolution of issues and improved analysis; 

and 

• Participate in	 discussions of emerging issues of interest to educational researchers, 

statisticians, and the federal statistical community in general. 

The common theme in all three goals is that these reports present results or discussions that do 

not reach definitive conclusions at this point in time, either because the data are tentative, the 

methodology is new and developing, or the topic is one on which there are divergent views. 

Therefore, the techniques and inferences made from the data are tentative and subject to 

revision. To facilitate the process of closure on the issues, we invite comment, criticism, and 

alternatives to what we have done. 

Such responses should be directed to 

Marilyn Seastrom 

Chief Statistician 

Statistical Standards Program 

National Center for Education Statistics 

1990 K Street NW 

Washington, DC 20006-5651 

iii 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXECUTIVE SUMMARY 

Since 2003, the National Center for Education Statistics (NCES) has sponsored the 

development of a method for mapping each state’s standard for proficient performance onto a 

common scale—the achievement scale of the National Assessment of Educational Progress 

(NAEP). When states’ standards are placed onto the NAEP reading or mathematics scales, the 

level of achievement required for proficient performance in one state can then be compared with 

the level of achievement required in another state. This allows one to compare the standards for 

proficiency across states. 

The mapping procedure offers an approximate way to assess the relative rigor of the states’ 

adequate yearly progress (AYP) standards established under the No Child Left Behind Act of 

2001. Once mapped, the NAEP scale equivalent score representing the state’s proficiency 

standards can be compared to indicate the relative rigor of those standards. The term rigor as 

used here does not imply a judgment about state standards. Rather, it is intended to be 

descriptive of state-to-state variation in the location of the state standards on a common metric. 

This report presents mapping results using the 2005 and 2007 NAEP assessments in mathematics 

and reading for grades 4 and 8. The analyses conducted for this study addressed the following 

questions: 

 How do states’ 2007 standards for proficient performance compare with each other when 

mapped on the NAEP scale? 

 How do the 2007 NAEP scale equivalents for state standards compare with those estimated 

for 2005? 

 Using the 2005 NAEP scale equivalent for state standards to define a state’s proficient level of 

performance on NAEP, do NAEP and that state’s assessment agree on the changes in the 

proportion of students meeting that state’s standard for proficiency from 2005 to 2007? 

To address the first question, the 2007 NAEP scale equivalent of each state reading and 

mathematics proficiency standard for each grade was identified. The mapping procedure was 

applied to the test data of 48 states.1 Key findings of the analysis presented in Section 3 of the 

report are: 

 In 2007, as in 2003 and 2005, state standards for proficient performance in reading and 

mathematics (as measured on the NAEP scale) vary across states in terms of the levels of 

achievement required. For example, the distance separating the five states with the highest 

standards and the five states with the lowest standards in grade 4 reading was comparable to 

the difference between Basic and Proficient performance on NAEP.2

 The distance was as large 

in reading at grade 8 and as large in mathematics in both grades. 

1 Test data for the District of Columbia, Nebraska, and Utah were not available to be included in the analysis. 

California does not test general mathematics in grade 8. 

2 NAEP defines Proficient as competency over challenging subject matter, not grade-level performance. Basic is defined as 

partial mastery of the skills necessary for Proficient performance. 

v 
vi

 In both reading and mathematics, the 29- to 30-point distance separating the five highest 

and the five lowest NAEP scale equivalent of state standards for proficient performance was 

nearly as large as the 35 points that represent approximately one standard deviation in 

student achievement on the NAEP scale. 

 In grade 4 reading, 31 states set grade 4 standards for proficiency (as measured on the NAEP 

scale) that were lower than the cut point for Basic performance on NAEP (208). In grade 8 

reading, 15 states set standards that were lower than the Basic performance on NAEP (243). 

 In grade 4 mathematics, seven states set standards for proficiency (as measured on the NAEP 

scale) that were lower than the Basic performance on NAEP (214). In grade 8 mathematics, 

eight states set standards that were lower than the Basic performance on NAEP (262). 

 Most of the variation (approximately 70 percent) from state to state in the percentage of 

students scoring proficient or above on state tests can be explained by the variation in the 

level of difficulty of state standards for proficient performance. States with higher standards 

(as measured on the NAEP scale) had fewer students scoring proficient on state tests. 

 The rigor of the state standards is not consistently associated with higher performance on 

NAEP. This association is measured by the squared correlation between the NAEP scale 

equivalent of the state standards and the percentages of students who scored at or above the 

NAEP Proficient level. In grade 4 reading and mathematics, the squared correlations are 

around .10 and statistically significant. In grade 8 reading and mathematics, the squared 

correlations are less than .07 and are not statistically significant. 

To address the second question, the analyses focused on the consistency of mapping outcomes 

over time using both 2005 and 2007 assessments. Although NAEP did not change between 2005 

and 2007, some states made changes in their state assessments in the same period, changes 

substantial enough that states indicated that their 2005 scores were not comparable to their 2007 

scores. Other states indicated that their scores for those years are comparable. Comparisons 

between the 2005 and 2007 mappings in reading and mathematics at grades 4 and 8 were made 

separately for states that made changes in their testing systems and for those that made no such 

changes.3

 Key findings of the analysis presented in Section 4 are: 

 In grade 4 reading, 12 of the 34 states with available data in both years indicated substantive 

changes in their assessments. Of those, eight showed significant differences between the 

2005 and 2007 estimates of the NAEP scale equivalent of their state standards, half of which 

showed an increase and half a decrease. 

 In grade 8 reading, 14 of the 38 states with available data in both years indicated substantive 

changes in their assessments. Of those, seven showed significant differences between the 

2005 and 2007 estimates of the NAEP scale equivalent of their state standards, all seven 

showed lower 2007 estimates of the NAEP scale equivalents.

 

3

 The 2005 mappings in this report will not necessarily match previously published results (U.S. Department of 

Education 2007). Methodological differences between the procedures used in both analyses will generally cause 

empirical results to show small differences that are not large enough to change the whole-number scale value 

reported as the NAEP equivalent. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 In grade 4 mathematics, 14 of the 35 states with available data in both years indicated 

substantive changes in their assessments. Of those, 11 showed significant differences 

between the 2005 and 2007 estimates of the NAEP scale equivalent of their state standards: 

6 states showed a decrease and 5 showed an increase. 

 In grade 8 mathematics, 18 of the 39 states with available data in both years indicated 

substantive changes in their assessments. Of those, 12 showed significant differences between 

the 2005 and 2007 estimates of the NAEP scale equivalent of their state standards: 9 showed 

a decrease and 3 showed an increase. 

For the states with no substantive changes in their state assessments in the same period, the 

analyses presented in Section 4 indicate that for the majority of states in the comparison sample 

(14 of 22 in grade 4 reading, 13 of 24 in grade 8 reading, 15 of 21 in grade 4 mathematics and 14 

of 21 in grade 8 mathematics), the differences in the estimates of NAEP scale equivalents of 

their state standards were not statistically significant. 

To address the third question, NAEP and state changes in achievement from 2005 to 2007 were 

compared. The percentage of students reported to be meeting the state standard in 2007 is 

compared with the percentage of the NAEP students in 2007 that is above the NAEP scale 

equivalent of the same state standard in 2005. The analysis was limited to states with (a) 

available data in both years and (b) no substantive changes in their state tests. The number of 

states included in the analyses ranged from 21 to 24, depending on the subject and grade. The 

expectation was that both the state assessments and NAEP would show the same changes in 

achievement between the two years. Statistically significant differences between NAEP and state 

measures of changes in achievement indicate that more progress is made on either the NAEP 

skill domain or the state-specific skill domain between 2005 and 2007. A more positive change 

on the state test indicates students gained more on the state-specific skill domain. For example, a 

focus in instruction on state-specific content might lead a state assessment to show more progress 

in achievement than NAEP. Similarly, a less positive change on the state test indicates students 

gained more on the NAEP skill domain. For example, focus in instruction on NAEP content 

that is not a part of the state assessment might lead the state assessment to show progress in 

achievement that is less than that of NAEP. Key findings from Section 5 are:4 

 In grade 4 reading, 11 of 22 states showed no statistically significant difference between 

NAEP and state assessment measures of changes in achievement; 5 states showed changes 

that are more positive than the changes measured by NAEP, and 6 states showed changes 

that are less positive than those measured by NAEP. 

 In grade 8 reading, 9 of 24 states showed no statistically significant difference between 

NAEP and state assessment measures of achievement changes; 10 states showed changes that 

are more positive than the changes measured by NAEP, and 5 states showed changes that 

are less positive than those measured by NAEP. 

 In grade 4 mathematics, 13 of 21 states showed no statistically significant difference between 

NAEP and state assessment measures of achievement changes; 5 states showed changes that 

Because differences between changes in achievement measured by NAEP and changes measured by the state 

assessment and the NAEP scale equivalents are based on the same data but are analyzed in different ways, 

statistically significant differences can be found in one and not the other because of the nonlinear relationship 

between scale scores and percentiles. 

vii 

4 
 

 

 

 

are more positive than the changes measured by NAEP, and 3 states showed changes that 

are less positive than those measured by NAEP. 

 In grade 8 mathematics, 9 of 21 states showed no statistically significant difference between 

NAEP and state assessment measures of achievement changes, 7 states showed changes that 

are more positive than the changes measured by NAEP, and 5 states showed changes that are 

less positive than those measured by NAEP. 

In considering the results described above, the reader should note that state assessments and 

NAEP are designed for different, though related purposes. State assessments and their associated 

proficiency standards are designed to provide pedagogical information about individual students 

to their parents and teachers, whereas NAEP is designed for summary assessment at an aggregate 

level. NAEP’s achievement levels are used to interpret the meaning of the NAEP scales. NCES 

has determined (as provided by NAEP’s authorizing legislation) that NAEP achievement levels 

should continue to be used on a trial basis and should be interpreted with caution. 

In conclusion, these mapping analyses offer several important contributions. First, they allow 

each state to compare the stringency of its criteria for proficiency with that of other states. 

Second, mapping analyses inform states whether the rigor of their proficiency standards as 

represented by NAEP scale equivalents changed from 2005 to 2007. Significant differences in 

NAEP scale equivalents might reflect changes in state assessments and standards and/or other 

changes such as changes in policies or practices that occurred between the years. Finally, when 

key aspects of a state’s assessment or standards remained the same, these mapping analyses allow 

NAEP to corroborate state-reported changes in student achievement and provide states with an 

indicator of the construct validity and generalizability of their test results. 

viii 
 

 

 

 

 

 

 

 

CONTENTS
 

Page 

Foreword............................................................................................................................................... iii
 

Appendix A
 

Appendix B
 

Appendix C
 

Executive Summary.............................................................................................................................. v
 

List of Tables........................................................................................................................................ xi
 

List of Figures ...................................................................................................................................... xv
 

1 Introduction..................................................................................................................................... 1
 

Using NAEP to compare state performance standards................................................................. 1


 Data sources ..................................................................................................................................... 3
 

Organization of this report.............................................................................................................. 3
 

2 Estimation Methods ........................................................................................................................ 5
 

Estimation of the placement of state performance standards on the NAEP scale ..................... 6


 Relative error ................................................................................................................................... 7
 

Measurement error in comparing NAEP and state measures of change ................................... 10
 

3 Mapping State Performance Standards ....................................................................................... 14


 Reading .......................................................................................................................................... 14


 Mathematics .................................................................................................................................. 18


 Cross-state comparisons ................................................................................................................ 21
 

4 Comparing 2007 With 2005 State Performance Standards....................................................... 26


 Reading .......................................................................................................................................... 27


 Mathematics .................................................................................................................................. 34
 

5 Corroborating State Assessment Measures of Achievement Change With NAEP ................ 41
 

6 Conclusions ................................................................................................................................... 47
 

7 References ...................................................................................................................................... 49
 

Number of Schools in the NAEP Sample and the Percentage of Schools Used in the 2007
 

Mapping .............................................................................................................................................A-1
 

Changes in States’ Assessments Between 2005 and 2007.............................................................. B-1
 

Supplementary Tables.......................................................................................................................C-1
 

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LIST OF TABLES
 

Table	 Page 

1.	 Estimated NAEP scale equivalent scores for the state grades 4 and 8 reading 

proficient standards, their standard error and relative error, by state: 2007........................ 16 

2.	 Estimated NAEP scale equivalents scores for the state grades 4 and 8 mathematics 

proficient standards, their standard error and relative error, by state: 2007........................ 19 

3.	 Frequency of correlations between NAEP and state assessment school-level 

percentages meeting the proficient standards for reading and mathematics, grades 4 

and 8: 2007 ............................................................................................................................... 21 

4.	 Correlations between NAEP and state assessment school-level percentages meeting 

the proficient standard for reading and mathematics grades 4 and 8, by state: 2007 ......... 22 

5.	 Relationship between the percentage of students scoring proficient on the state test 

and the difficulty of grades 4 and 8 state standards as measured by the state’s 

respective NAEP scale equivalent, by subject: 2007............................................................. 23 

6.	 Relationship between the percentage of students scoring proficient on NAEP and the 

difficulty of grades 4 and 8 state standards as measured by the state’s respective NAEP 

scale equivalent t, by subject: 2007......................................................................................... 25 

7.	 State assessment data availability and state reports of whether 2005 and 2007 

assessment results are comparable in grades 4 and 8 reading, by state: 2005 and 2007...... 28 

8.	 States with both 2005 and 2007 data suitable to implement the mapping of grades 4 

and 8 state reading standards, by whether the reported results are directly comparable.... 29 

9.	 Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 4 reading, and percentage of the 

student population represented in these comparison schools, by state: 2005 and 2007..... 30 

10.	 Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 8 reading, and percentage of the 

student population represented in these comparison schools, by state: 2005 and 2007..... 31 

11.	 Difference between the estimated NAEP scale equivalents of state grade 4 reading 

proficient standards and their standard error, by state: 2005 and 2007............................... 32 

12.	 Difference between the estimated NAEP scale equivalents of state grade 8 reading 

proficient standards and their standard error, by state: 2005 and 2007............................... 33 

13.	 State assessment data availability and state reports of whether 2005 and 2007 

assessment results are comparable in grades 4 and 8 mathematics, 

by state: 2005 and 2007 ........................................................................................................... 35 

14.	 States with both 2005 and 2007 data suitable to implement the mapping of grades 4 

and 8 mathematics standards, by whether the reported results are directly comparable.... 36 

15.	 Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 4 mathematics, and percentage of the 

student population in these comparison schools, by state: 2005 and 2007 ......................... 37 

16.	 Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 8 mathematics, and percentage of the 

student population in the comparison schools, by state: 2005 and 2007............................. 38 

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Table	 Page 


17. 	 Difference between the estimated NAEP scale equivalents of state grade 4
 

mathematics proficient standards and their standard error, by state: 2005 and 2007......... 39
 

18.	 Difference between the estimated NAEP scale equivalents of state grade 8
 

mathematics proficient standards and their standard error, by state: 2005 and 2007......... 40
 

19.	 NAEP and state assessment percentages meeting the state grade 4 reading proficient
 

standard in 2007 based on 2005 standards, by state .............................................................. 42
 

20.	 NAEP and state assessment percentages meeting the state grade 8 reading proficient
 

standard in 2007 based on 2005 standards, by state .............................................................. 43
 

21.	 NAEP and state assessment percentages meeting the state grade 4 mathematics
 

proficient standard in 2007 based on 2005 standards, by state............................................. 44
 

22.	 NAEP and state assessment percentages meeting the state grade 8 mathematics
 

proficient standard in 2007 based on 2005 standards, by state............................................. 45
 

23.	 States showing changes in student achievement from 2005 to 2007 in their own tests
 

that are corroborated by NAEP results in the same period, by subject and grade .............. 46
 

24.	 States showing changes in student achievement from 2005 to 2007 in their own tests
 

that are statistically significantly more positive than NAEP’s, by subject and grade ......... 46
 

25.	 States showing changes in student achievement from 2005 to 2007 in their own tests
 

that are statistically significantly less positive than NAEP’s, by subject and grade............ 46
 

A-1	 Number of NAEP schools, percentage of NAEP schools available for comparing 


state assessment results with NAEP results in grades 4 and 8 reading, and the
 

percentage of the student population in these comparison schools, by state: 2007.......... A-2
 

A-2	 Number of NAEP schools, percentage of NAEP schools available for comparing 


state assessment results with NAEP results in grades 4 and 8 mathematics, and
 

percentage of the student population in these comparison schools, by state: 2007.......... A-3
 

B-1	 Selected changes to state reading assessments between the 2004–05 and the
 

2006–07 administrations, by state ........................................................................................ B-2
 

B-2	 Selected changes to state mathematics assessments between the 2004–05 and the 


2006–07 administrations, by state ........................................................................................ B-4
 

B-3 	 Comparability of the 2007 state assessment results in reading and mathematics at
 

grades 4 and 8 with the 2005 reported results, by state....................................................... B-6
 

C-1	 NAEP and state assessment percentages meeting the state grade 4 reading proficient
 

standards in 2007 based on 2005 standards, by state........................................................... C-2
 

C-2	 NAEP and state assessment percentages meeting the state grade 8 reading proficient
 

standards in 2007 based on 2005 standards, by state........................................................... C-3
 

C-3	 NAEP and state assessment percentages meeting the state grade 4 mathematics
 

proficient standards in 2007 based on 2005 standards, by state ......................................... C-4
 

C-4	 NAEP and state assessment percentages meeting the state grade 8 mathematics
 

proficient standards in 2007 based on 2005 standards, by state ......................................... C-5
 

C-5	 Number of states according to the comparability of state-reported results between
 

2005 and 2007, by the statistical significance of the discrepancy between NAEP and
 

state measures of gains in grades 4 and 8 reading ................................................................ C-6
 

xii 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table Page 

C-6 Number of states according to the comparability of state-reported results between 

2005 and 2007, by the statistical significance of the discrepancy between NAEP and 

state measures of gains in grades 4 and 8 mathematics ....................................................... C-6
 

C-7 Selected changes to state reading assessments between 2005 and 2007, by whether 

reports of grade 4 reading achievement changes from 2005 to 2007 in the state test 

and NAEP agree, by state ...................................................................................................... C-7 


C-8 Selected changes to state reading assessments between 2005 and 2007, by whether 

reports of grade 8 reading achievement changes from 2005 to 2007 in the state test 

and NAEP agree, by state ...................................................................................................... C-8 


C-9 Selected changes to state mathematics assessments between 2005 and 2007, by 

whether reports of grade 4 mathematics achievement changes from 2005 to 2007 in 

the state test and NAEP agree, by state ............................................................................... C-9
 

C-10 Selected changes to state mathematics assessments between 2005 and 2007, by 

whether reports of grade 8 mathematics achievement changes from 2005 to 2007 in 

the state test and NAEP agree, by state ............................................................................. C-10
 

xiii 

 

 

 

LIST OF FIGURES 

Figure 	 Page 

1.	 Mapping state proficiency standards onto the NAEP scale ....................................................... 6
 

2.	 NAEP scale equivalent scores for the state grades 4 and 8 reading standards for proficient
 

performance, by state: 2007 ......................................................................................................... 17
 

3.	 NAEP scale equivalent scores for the state grades 4 and 8 mathematics standards for
 

proficient performance, by state: 2007........................................................................................ 20 


4.	 Relationship between the percentage of students scoring proficient on NAEP and the 


difficulty of grades 4 and 8 state standards for reading and mathematics as measured by the
 

state’s respective NAEP scale equivalent: 2007......................................................................... 24
 

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1 INTRODUCTION
 

State-level National Assessment of Educational Progress (NAEP) results are an important 

resource for policymakers and other stakeholders responsible for making sense of—and acting 

on—state assessment results. Since 2003, the National Center for Education Statistics (NCES) 

has been sponsoring research that focuses on comparing the proficiency standards of NAEP and 

states.1

 By mapping each state’s standard for proficient performance onto the NAEP achievement 

scale, state policymakers can make comparisons of standards across states, in terms of the level of 

achievement required for proficient performance. 

Recent studies that map state performance standards onto the NAEP scale have underlined the 

need for ongoing scrutiny of comparisons between NAEP and state assessment results.2

 In this 

report, we examine the consistency of the mapping results by using data from the state 

assessments and NAEP in 2005 and 2007. We investigate the impact and implications of the 

outcomes of the mapping procedure by using multiple years of data. 

At a time when states are working to ensure that all their students reach proficient levels of 

achievement by 2014, as required by the No Child Left Behind Act of 2001 (NCLB), the 

analyses described in this report allow state policymakers to assess how high their state has set 

the bar for proficiency. 

The comparison of achievement presented in this report is not intended to suggest deficiencies 

either in state assessments or in NAEP. The NAEP scales in reading and mathematics are being 

used as a common metric, not as a standard for evaluating state scales. Similarly, the NAEP 

achievement levels are provided simply as a national reference point for comparisons, not as a 

replacement for any given state’s duly adopted state standards. Moreover, as provided by law, 

NCES, upon review of congressionally mandated evaluations of NAEP, has determined that 

NAEP achievement levels are to be used on a trial basis and should be interpreted with caution.3 

State-NAEP comparisons can help in the interpretation of state assessment results by providing a 

benchmark by which to assess changes in achievement that are measured by state assessments. 

Using NAEP to compare state performance standards 

The percentage of students identified as proficient on state assessments varies across states. 

Because each state’s standard for proficient performance is set independently, the standards in 

different states can be quite different, even though they use the same terminology. A student 

who scores proficient in one state can move to another state and find that his or her performance 

is below the proficient range in the new state. NAEP, however, can provide the needed link to 

compare these assessment results across states. This comparison places all states’ reading and 

mathematics standards on a common scale—the NAEP reading or mathematics scale—along 

1 Reports on this research are available at http://nces.ed.gov/nationsreportcard/studies/statemapping.asp. 


2 In early investigations, McLaughlin and Bandeira de Mello (2002, 2003, 2006) and subsequent reports (McLaughlin
 

et al. 2008a, 2008b) mapped state primary performance standards onto the NAEP scale. Braun and Qian (2007) 

used similar methodology and data to conduct similar mappings. The recent mapping report from the National 

Center for Education Statistics is an outgrowth of these studies (U.S. Department of Education 2007). 

3 The status of NAEP achievement levels is available at http://nces.ed.gov/nationsreportcard/achlevdev.asp?. 

1 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

with the NAEP achievement-level cut points. In this way, stakeholders can compare the relative 

stringency of state standards for proficiency in reading and mathematics. 

A number of studies present arguments against the appropriateness of state assessment and 

NAEP comparisons. Criticisms of previous comparisons of state assessments and NAEP are not 

without merit and deserve thoughtful consideration. Prior criticisms of mapping studies have 

focused on three main topics: (1) state assessments and NAEP are developed for different 

purposes and have different goals and, as a result, should not be placed on a common scale; (2) 

state assessments may measure different constructs (e.g., Language Arts vs. Reading vs. Word 

Recognition) and should not be compared with one another; and (3) mapping studies implicitly 

use NAEP as the standard against which state assessments are ultimately determined to be 

deficient (Ho and Haertel 2007). Two National Research Council–sponsored studies have 

concluded that for a variety of reasons, mappings at the student level cannot be constructed 

validly (Feuer et al. 1999; Koretz, Bertenthal, and Green 1999). 

Importantly, these studies do not address the appropriateness of mapping at the school level for 

the purpose of analyzing state-level results, which is the aim of the study described here. In a 

recent critique, Ho and Haertel (2007) posit that “substantial differences between state tests and 

NAEP will render the mapping illogical and subject to drift over time” (p. 1). If the standard 

that students must meet is not the same in 2007 as it was in 2005 (i.e., the standard “drifted”), 

then we cannot know whether achievement was better in one year or the other just because the 

percent achieving the standards was higher or lower in one year than in the other. Therefore, it 

is important to analyze NAEP and state assessment changes in achievement from 2005 to 2007, 

as was done for this report, which can determine whether there was drift. Drift indicates changes 

in either the state test or in NAEP (or in both) between consecutive administrations. 

In an early mapping study, McLaughlin and Bandeira de Mello (2002, 2006) list a number of 

important caveats intended to prevent the misinterpretation of mapping results. They state 

emphatically that their report, among other things, (a) does not address questions about content, 

format, or administration of state assessments, as compared to NAEP, and (b) is not an 

evaluation of state assessments. As pointed out above, state assessments and NAEP are designed 

for different, although overlapping, purposes. For example, in many cases, state assessments are 

designed to provide pedagogical information about individual students to their parents and 

teachers, whereas NAEP is designed for summary assessment at an aggregate level. Findings of 

different standards, different trends, and different gaps should be presented without any 

implication that they be considered deficiencies either in state tests or in NAEP. However, it 

would be premature to conclude that two tests measuring grade 4 reading proficiency would 

assess no overlapping skills. Two tests that look quite different can measure the same variation 

because the various parts of reading (or mathematics) ability are highly correlated with one 

another. The high and consistent school-level correlations between state and NAEP assessment 

results suggests that state assessments and NAEP measure similar or related skills (McLaughlin et 

al. 2008, 2008b). 

Despite the criticisms of NAEP and state assessment comparisons, there is a need for reliable 

information that compares state standards. What does it mean to say that a student is proficient 

in reading in grade 4 in Massachusetts? Would a fourth-grader who is proficient in reading in 

Wyoming be proficient in Oklahoma? However difficult it may be to answer these questions 

2 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

definitively, they are fair questions that deserve consideration. In this study we examine the 

consistency of state standards when mapped onto the NAEP scale from 2005 to 2007. 

Data sources 

The analyses in the report are based on NAEP and state assessment results of public schools that 

participated in NAEP, weighted to represent the states.4

 The analyses use data from these 

sources: (a) NAEP data files for the states participating in the 2005 and 2007 reading and 

mathematics assessments, (b) state assessment school-level files compiled in the National 

Longitudinal School-Level State Assessment Score Database (NLSLSASD), and (c) schoollevel achievement data for the 2006-07 school year from EDFacts.

5 This report also relies on a 

review of state assessment programs conducted to gain contextual information about the general 

characteristics of state assessment programs and to help identify changes in states’ assessments 

between the 2004-05 and 2006-07 school years that could affect the interpretation of the 

mapping results.6 

The analyses presented are based on the standard NAEP estimates, which do not represent the 

achievement of those students with disabilities and/or English language learners who are 

excluded from NAEP testing. 

Organization of this report 

The report presents mapping results using the 2005 and 2007 NAEP assessments in mathematics 

and reading for grades 4 and 8. The analyses conducted for this study addresses the following 

questions: 

 How do states’ 2007 standards for proficient performance compare with each other when 

mapped onto the NAEP scale? 

 How do the cut points on the NAEP scale that are equivalent to the scores required to meet 

a state’s standard in 2007 compare to those estimated for 2005? 

 Using the 2005 NAEP scale equivalent standards to define a state’s proficient level of 

performance on NAEP, do NAEP and that state assessment agree on the changes in the 

proportion of students meeting that state’s standard for proficiency from 2005 to 2007? 

Section 2 of this report provides a description of the estimation methods used in the mapping 

and in the comparisons of results between 2005 and 2007. Section 3 presents the results of the 

analyses that examined the mapping results for 2007 in reading and mathematics at grades 4 and 

8. Addressing the second question, Section 4 focuses on the comparison between the 2005 and 

2007 mappings in reading and mathematics at grades 4 and 8. Addressing the third question, 

4	 The method for sampling private schools in NAEP precludes using private school results in state-related reports. All 

NAEP published statistics at the state level are therefore for public schools only. Also, because private schools are 

not required to participate in a state’s annual academic assessments under NCLB, private school data are not 

generally included in state test score databases. 

5

 EDFacts is a collaborative effort among the U.S. Department of Education, State Education Agencies, and industry 

partners to centralize state–reported data into one federally coordinated, K–12 education data repository, located in 

the U.S. Department of Education. 

6	 State profiles based on the 2007 Survey of State Assessment Program Characteristics are available at 

http://nces.ed.gov/nationsreportcard/studies/statemapping.asp. 

3 
 

Section 5 discusses the NAEP and state assessment changes in achievement from 2005 to 2007, 

including possible explanations for discrepancies in the gains measured by the state tests and 

NAEP so that attention can be turned to identifying the sources of those discrepancies. Tables in 

appendix A show the sample sizes and percentages of the 2007 NAEP samples used in the 

analyses. Tables in appendix B summarize selected changes in states’ assessments between the 

two NAEP administrations of 2005 and 2007 that could affect the interpretation of the mapping 

results. Appendix C includes tables with results complementing those discussed in the body of 

the report. 

4 
 

 

 

 

 

 

 

 

 

 

 

2 ESTIMATION METHODS 

State assessment scores are usually reported as percentages of students in a grade at a school 

whose test scores are sufficiently high to meet a predefined state standard. That standard has 

been shown to vary a great deal from state to state (McLaughlin and Bandeira de Mello 2003). 

As a result, comparisons of percentages of students meeting state standards in different states are 

as much, if not more, a function of the placement of the standards as they are of differences in 

the achievement of the students. 

Of essence in any attempt to compare changes in achievement on two tests is an understanding 

that the increase in the percentage of students meeting the standard depends critically on the 

placement of the standard. Generally, standards placed near the median test score (or more 

specifically, the modal test score) show the most increase in percentages meeting the standard, 

whereas relatively high and low standards lead to smaller changes in percentages meeting the 

standard (McLaughlin and Bandeira de Mello 2003). However, there are exceptions to this 

generality. For example, if instruction focuses on a particular subgroup of students located at one 

end of the distribution, a standard set at that end may show larger changes than a standard set in 

the middle. 

To account for variation in the placement of standards on a scoring scale, the first step in 

comparing NAEP and state assessment measures of change is to measure changes in NAEP 

performance the same way change is measured on state assessments, that is, using the percentage 

of students in the state meeting that state’s standard.7 The process is done by mapping each state’s 

standard onto the NAEP scale; that is, finding the NAEP scale value for the NAEP sample in 

the state for which the estimated percentage of students with higher NAEP scale values matches 

the percentage of students reported by the state as achieving the state’s standard in the same 

schools. Of course, because NAEP is based on a sample of students in each participating school, 

and because both assessments have measurement error, there is some mapping error in 

determining the NAEP equivalent of a state’s standard. It is necessary to consider mapping error 

for valid comparisons between NAEP and state assessment measures of change in achievement. 

This section summarizes the estimation methods used in the mapping procedure to place state 

performance standards onto the NAEP scales and in the comparison analysis between 2005 and 

2007. We develop a framework for evaluating differences between achievement changes 

measured by NAEP and by state tests. Essentially, NAEP and state achievement changes in each 

subject and grade are rendered comparable by summarizing NAEP results in a state as the 

percentage meeting the state’s standard, which requires, as a first step, mapping the state’s 

standard onto the NAEP scale. 

Given that the only test results systematically available for all states are percentages of students in each school with 

scores higher than a cut point (i.e., meeting the standard), finding the NAEP equivalent of that cut point is an 

essential step in comparing achievement gains based on state test data to achievement gains on NAEP. If state test 

means and standard deviations were available for schools in the NAEP sample, mapping of the standards, while 

important in itself, would not be required for comparing state test and NAEP achievement gains. 

5 

7 
 

 

 

 

 

 

 

 

 

 

Estimation of the placement of state performance standards on the NAEP scale 

The method of obtaining equipercentile equivalents involves the following steps: 

1. Obtain for each school in the NAEP sample the proportion of students in that school who 

meet the state performance standard on the state’s test. 

2. Estimate the state proportion of students who meet the standard on the state test, by 

weighting the proportions (from step 1) for the NAEP schools, using NAEP school weights. 

3. Estimate the weighted distribution of scores on the NAEP assessment for the state as a 

whole, based on the NAEP sample of schools and students within schools. 

4. Find the point on the NAEP scale at which the estimated proportion of students in the 

state who score above that point (using the distribution obtained in step 3) equals the 

proportion of students in the state who meet the state’s own performance standard 

(obtained in step 2). 

Using figure 1 to illustrate, we see that 66 percent of the students in State A meet that state’s 

standard (estimated from step 2); based on State A’s NAEP sample, 66 percent of State A’s 

students score above 191 on the NAEP scale (using the distribution obtained in step 3). Suppose 

that in State B, where students perform higher on NAEP than in State A, 66 percent of its 

students also meet its state standard. This translates into a higher NAEP scale equivalent (212 in 

the illustration), because 66 percent of State B’s students score above 212 on the NAEP scale, 

based on State B’s NAEP sample. State A’s standard corresponds to, or maps onto, a lower level 

of NAEP achievement than State B’s standard does, even though each state reports the same 66 

percent meeting its own standard. 

Figure 1. Mapping state proficiency standards onto the NAEP scale 

State A State B

66%

proficient

Performance

on State

Assessment

State Scale

State Scale

NAEP Scale NAEP Scale

State A

Performance

on NAEP

State B

Performance

on NAEP

Performance

on State

Assessment

66%

proficient

66%

66%

500

280

270

260

250

240

230

220

210

200

190

180

170

160

0

500

280

270

260

250

240

230

220

210

200

190

180

170

160

0

212

191

6 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The reported percentage meeting the state’s standard in each NAEP school s, ps (e.g., 66 

percent as in figure 1), is used to compute a state percentage meeting the state’s standards, pS , 

using the NAEP school weights, ws. For each school, ws is the sum of the student weights, wis, for 

the students selected for NAEP in that school.8

 For each of the five sets of NAEP plausible 

values, v = 1 through 5, we solve the following equation for c, the point on the NAEP scale 

corresponding to the percentage meeting the state’s standard:9 

p = p [1] S  wis s  wis is,sS is,sS

=w [2] isisv (c) wis is,sS is,sS

where the sum is over students in schools participating in NAEP, and isv (c) is an indicator 

variable that is 1 if the vth plausible value for student i in school s, y , is greater than or equal isv

to c, and 0 otherwise. The five values of c obtained for the five sets of plausible values are 

averaged to produce the NAEP threshold corresponding to the state standard, that is, the 

reported mapping of the standard onto the NAEP scale.10 Variation in results over the five sets of 

plausible values is a component of the standard error of the estimate, which is computed by 

following standard NAEP procedures.11,12 

Relative error 

When used to place state standards on the NAEP scale, equipercentile mapping will produce an 

answer even if NAEP and state assessment scores are completely unrelated to each other. Some 

additional data, beyond the percentage meeting the standard in the state and the distribution of 

NAEP plausible values—the only data used in the computation—are needed to test the validity 

of the mapping. 

To evaluate the validity of the placement of a state standard on the NAEP scale, we measure 

how well the procedure reproduces the percentages reported by the state as meeting the standard 

in each NAEP-participating school. If the mapping is valid, the procedure should reproduce the 

individual school percentages fairly accurately. However, if the state assessment and NAEP are 

measuring different, uncorrelated characteristics of students, the school-level percentages 

meeting the state standard as measured by NAEP will bear no relationship to the school-level 

percentages meeting the state’s standards as reported by the state. 

8	 To ensure that NAEP and state assessments are equitably matched, NAEP schools that are missing state assessment 

scores (i.e., small schools, typically representing approximately 4 percent of the students in a state) are excluded 

from this process. Even if the small excluded schools perform differently from included schools, no substantial bias 

in the estimation process would be introduced, unless their higher or lower scoring was specific to NAEP or specific 

to the state assessment. 

9	 Estimations of NAEP scale score distributions are based on an estimated distribution of possible scale scores (or 

plausible values), rather than point estimates of a single scale score. More details are available at 

http://nces.ed.gov/nationsreportcard/tdw/analysis/est_pv_individual.asp. 

10 Appendix A of McLaughlin et al. (2008a) describes in more detail the technical aspects of the placement of state 

achievement standards on the NAEP scale. 

11 NAEP computes standard error using a combination of sampling error based on Jackknife resampling and 

measurement error from the variance between plausible values. 

12 This mapping procedure is analogous to the one used in U.S. Department of Education (2007) and produces results 

that are qualitatively similar. The distinctions between the two procedures are discussed in Braun and Qian (2007). 

7 
 

 

 

 

 

 

 

 

The correlation coefficient showing the relationship between the percentages reported for 

schools by the state and those estimated from the NAEP scale equivalents provides a 

straightforward measure of the appropriateness of the mapping. However, it does not indicate the 

amount of error that is added to the placement of the standard by the fact that NAEP and the 

state assessment may not measure the same construct. We must determine how high the 

correlation must be to justify inferences that are based on the mapping. Also needed is a measure 

of that error, as a fraction of the total variation of percentages meeting the standard across 

schools. 

The NAEP estimate of the percentage meeting the standard in a school is subject to both 

sampling and measurement error. However, even if the NAEP measure had no sampling or 

measurement error, and even if NAEP measured exactly the same construct as the state 

assessment, NAEP would not reproduce exactly the state assessment percentage for each school. 

The difference occurs because the state assessment scores are based on different administrations, 

at different times of year, with different motivational contexts and different rules for exclusion 

and accommodation. The state assessment scores are also subject to measurement error, although 

for school-level aggregates, the measurement error is smaller than it is for individual student 

estimates. 

Although we recognize that discrepancies between the reported figure from each school and the 

estimate based on the NAEP mapping will occur, it is, nevertheless, important that the 

discrepancies be small relative to the variation in outcomes across schools. If the variance of the 

discrepancies is more than a fraction of the total variance across schools in percentage meeting a 

standard, the validity of the placement of the standard could be considered suspect, even though 

the nominal standard error of the state-level estimate may be small. 

To evaluate the mapping, we therefore compare three variances: 

1. total	 variance of reported percentages meeting the state’s standard across the schools 

participating in NAEP in the state, 2

( ps); 

2. average squared deviation between the reported percentage, ps, and the percentage based 

on the NAEP mapping for each school s, pˆ : averageS ( p  pˆ )

2 ; and s s s

3. average expected sampling and measurement error in the NAEP estimate for each school 

s, averageS ( pˆ s  ( pˆ s))2 

. 

We estimate the sizes of what the (squared) discrepancies would have been if NAEP were not 

subject to sampling and measurement error by subtracting quantity (3) from quantity (2), and we 

compare these adjusted (squared) discrepancies with the overall variation in percentages across 

schools 2

( ps) (quantity (1)). If the adjusted (squared) discrepancies correspond to a large 

component the overall variance of the percentages, the NAEP data do not reproduce the schoollevel percentages with sufficient accuracy to justify inferences based on the placement of the 

standard on the NAEP scale. That is, we want the relative error K < k, 

K = [(averageS ( ps  pˆ s)

2  averageS ( pˆ s  ( pˆ s))2 ) 2

( p )] < k	 [3] s

where 0  k  1. 


8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

We want the discrepancy variance (2) to be less than a threshold k of the variance in the state 

test score school percentages (1), but we do not want to penalize the mapping for the 

measurement and sampling error in pˆ s (quantity 3), which contributes to quantity (2). 

Therefore, we subtract (3) from (2) before dividing by (1). The resulting numerator of the 

relative error K is an estimate of the amount of discrepancy variance that cannot be accounted 

for by NAEP sampling and measurement error. Because both quantities (2) and (3) are sample 

estimates of variances, it is reasonable to expect that they will usually differ from the true 

variances of (2) and (3), and this can lead to (2) – (3) < 0 in some cases. In fact, if there were no 

linking error, we would expect (2) – (3) < 0 in half the cases, because (2) and (3) would be two 

estimates of the same variance. 

Both the discrepancies and the estimation of NAEP random estimation error are more stable in 

schools with larger NAEP samples of students. Therefore, to increase the stability of the estimate 

of K, the average over schools was weighted according to the size of the NAEP sample of 

students in the school; a small number of NAEP schools with fewer than five NAEP participants 

are not included in the computations. 

The NAEP random estimation error variance is the sum of two components, sampling error and 

measurement error. Because at the student level the variable of interest is a simple binomial 

variable (meets or does not meet the standard), to estimate the sampling variance we can use the 

binomial variance of the estimate of a percentage, pˆ (100  pˆ )/ n , where n is the size of the s s s s

NAEP sample in the school and pˆ s is the percentage of NAEP participants in the school with 

plausible values greater than the value estimated to be equivalent to the state standard. The 

binomial variance should be reduced by a finite population correction, fpc = (Ns  ns) /(Ns 1) , 

because the NAEP sample is a sizeable fraction of the number of students in the particular grade, 

Ns, at most schools. If the number of students per grade is not known, the average finite 

population correction for schools with NAEP samples of the same size is used. 

NAEP measurement error is estimated by the variance of the five estimates for each school’s 

percentage meeting the standard, based on the five alternative sets of plausible values v, for the 

participating students, 2

( pˆ ) . Because pˆ is computed as the average of values based on five v s,v s

plausible value sets, the measurement error component is divided by 5. Thus, the quantity in (3) 

above is estimated by 

( pˆ  E( pˆ ))2 = ( p q / n )( fpc)

2 +2

( pˆ )/5. [4] s s s s s v s,v 

In this study, the criterion proposed is to consider relative errors greater than .5 as indicating 

that the mapping error is too large to support any useful inferences from the placement of the 

standard on the NAEP scale. 

Setting the criterion for the validity of this application of the equipercentile mapping method at 

K = .5 is arbitrary but plausible. Clearly, it should not be taken as an absolute inference of 

validity—two assessments, one with a relative error of .6 and the other with .4, have similar 

validity. Setting a criterion serves to call attention to the cases in which we should consider a 

limitation on the validity of the mapping as an explanation for otherwise unexplainable results. 

Although estimates of standards with greater relative error because of differences in measures are 

not thereby invalidated, any inferences based on them require additional evidence. For example, 

a finding of differences in trend measurement between NAEP and a state assessment when the 

9 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

standard mapping has large relative error may be explainable in terms of unspecifiable differences 

between the assessments, ruling out further comparison. Nevertheless, because the relative error 

criterion is arbitrary, results for all states are included in the report and in the discussion of 

findings, irrespective of the relative error of the mapping of the standards. 

Measurement error in comparing NAEP and state measures of change 

Under No Child Left Behind, each state has developed measurements for determining whether 

its schools are making adequate yearly progress (AYP), which refers not to the progress of a child 

from, say, fourth grade to fifth grade but to the progress of a school in increasing the performance 

of its fourth-graders from one year to the next. The basic idea of comparing achievement changes 

from one year’s students in a particular grade with achievement changes from another year’s 

students in the same grade is that a set of skills is to be learned and that these skills might be 

more (or less) thoroughly learned by the students in one year than they were by the students in 

the other year. A test is written that samples the skill domain and is given to each of the two 

cohorts of students, and the scores are compared. Of course, the average scores will not be 

exactly the same in the two years if the test merely samples the skill domain and does so on a 

finite number of students. However, a simple statistical test can be executed to determine 

whether the difference is in the realm of random variation. If the sample of students were 

infinitely large and the test measured all the skills in the domain without error, the standard 

errors would be zero, meaning that any difference between the scores of the two cohorts would be 

statistically significant. Whether a difference is important is another question, but differences that 

are not statistically significant should not be considered further because they may well reflect just 

chance variation. 13 

Letting D be the discrepancy between changes from year 1 to year 2 in percentage meeting the 

state standard identified by the state test and the changes in the same period in the same 

percentages when measured by NAEP, we can test for whether D is statistically significantly 

different from zero by estimating the ratio of D to its standard error. However, to interpret the 

results of such a comparison, we also need to consider the explanations of statistically significant 

values of D. These discrepancies represent an additional source of error that contributes to the 

differences in achievement changes identified by NAEP and by the state assessment program. In 

general, such differences are hypothesized to be the result of some systematic difference between 

what the state assessment measures and what NAEP measures (in test content, student 

populations, or test administration). We call this a true score error to distinguish it from 

discrepancies arising from the finiteness of the samples and the imperfections of measurement.14 

13	 The following discussion is excerpted from a report to NCES on the measurement error in comparing NAEP and 

state test gains (McLaughlin 2008). 

14	 One source of error is due to the systematic differences in the domains of skills assessed by NAEP and the state 

assessment, and not to random measurement error or to sampling error. A second kind of error arises because both 

tests measure the domain with some error and because the mapping is based on a finite sample of students. The 

distribution of NAEP scores in the sample of NAEP students in the specified schools is likely to be slightly different 

from the hypothetical distribution of NAEP achievement of all students tested by the state in those schools, leading 

to small over- or underestimates of the NAEP scale equivalent of the state standard. 

10 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measuring the standard error of D 

Because the data available for mapping states’ standards onto the NAEP scale are limited to 

school-level percentages of students achieving a state’s standard in schools participating in 

NAEP, the critical statistic for comparing NAEP versus state-test score changes is 

D = ( pˆ2S  pˆ2N |map=1) ( pˆ

1S  pˆ1N |map=1) [5] 

where pˆYS is the state percentage meeting the standard in year Y, estimated by the weighted 

average of the percentages in the NAEP schools, and pˆ is the percentage of the YN |map=1

distribution of NAEP plausible values in the state in year Y, estimated by the (same) weighted 

average of the distributions in the NAEP schools, which are above the NAEP scale value that 

was found in year 1 to correspond to the state standard. 

For example, if the state shows a gain from 50 percent to 60 percent meeting the standard and 

NAEP reports a gain from 50 percent to 55 percent meeting the state’s standard, then 

D = (60 – 55) – (50 – 50) = 5. The statistical question to be addressed is whether a value of 5 for 

D is larger than we would expect on the basis of measurement and sampling error. 

The term in the second parenthesis of equation [5] is zero by definition, with no error, because 

the NAEP scale value onto which the state’s standard is mapped (in year 1) is the value that 

forces an exact match of percentages (in year 1). That is not to say that pˆ

1S and pˆ are 1N |map=1

error-free estimates of their respective population statistics, just that the second term in D is 

exactly zero. The errors in pˆ

1S and pˆ contribute to the error in the other term 1N |map=1 

( pˆ2S  ˆ =1 p ) through mapping error. 2N |map

Both NAEP estimates, pˆ and ˆ , are based on percentages of the student score 1N |map=1 p2N |map=1

distribution meeting the same scale value, the one mapped from the year 1 data. To measure 

achievement changes in terms of percentages of students meeting a standard, it is necessary to 

use exactly the same standard for both years.15 In fact, if achievement changes are measured 

purely in terms of percentages meeting a standard, finding an achievement gain in the population is 

equivalent to finding that the test became easier for the population to meet the standard. In other 

words, unless we are assured that the standard has not been lowered, we cannot infer that finding 

that the standard became easier for the population means that the population’s achievement 

increased. We cannot exclude the possibility that the standard was lowered unless we have 

evidence to exclude it. An example of that evidence is finding that in both years, the standard is 

equivalent to the same NAEP score, if we assume that NAEP remained unchanged between the 

years. Thus, the question of whether NAEP and the state assessment agree on the size of 

achievement change is virtually equivalent to the question of whether the mapping of the state’s 

standard onto the NAEP scale was stable over the two years. 

Because the second term in the equation for D is zero, we can redefine D as 

D = ( pˆ2S  pˆ2N|map=1) [6] 

15 If we were to estimate pˆ2N from a mapping based on year 2 data, D would be identically zero, a meaningless result. 

11 
 

 

 

 

 

 

 

 

 

 

 

 

and focus on the estimation of the sources of error; that is, on the expected variation between D 

and the value it would take on if the estimates of the percentages meeting the standard were 

equal to their population values, pˆ2S and ˆ =1 p . 2N |map

Many factors contribute to random variation of D around its true value, which would be zero if 

NAEP and the state assessments show the same gains/losses.16 However, in view of the 

complexity of any psychometric model for D, the most robust procedure for estimating the 

standard error of D is the standard NAEP procedure, combining NAEP measurement error, 

estimated by variation in values of D obtained for each of the five plausible value sets, with 

NAEP sampling error, estimated by the NAEP jackknife technique. 

Measuring the standard error of the mapping 

Estimating the standard error of the mapping is not a necessary step in determining the standard 

error of D because we can apply the NAEP jackknife technique directly to the estimate of D. 

However, an estimate of the standard error of the mapping is necessary to test the question of 

whether the NAEP scale equivalent of the standard is stable across the two years. If we denote 

the NAEP scale equivalent of the standard in year Y by cˆ

Y , then the standard error of the 

difference, 

cˆ = cˆ

1 cˆ2, [7] 

is just the square root of the sum of the squares of the standard errors of the two separate NAEP 

scale equivalents. That is, 

SE(cˆ) = SE(cˆ

1)

2 + SE(cˆ

2 )

2 . [8] 

Each can be estimated by applying the NAEP jackknife technique to the mapping process. 

Summary 

The ultimate purpose for estimating the standard error of D is to decide whether differences 

between changes in achievement showed by NAEP and changes in achievement showed by the 

state are sufficiently large that they are not likely to be due to random factors. If the difference, 

D, is statistically significantly different from zero, students gained more on either the NAEP skill 

domain or on the state-specific skill domain than represented by those domains’ contributions to 

variance in year 1. Focusing on state-specific content during instruction might be expected to 

lead to a positive value for D, whereas focusing entirely on NAEP content might be expected to 

lead to a negative value for D. Other explanations for a larger change on the state test exist. A 

statistically significant value of D may be due to a change in the content, administration, or 

scoring of either the state test or NAEP in the interval. For example, a change in the NAEP 

exclusion rates between years (for whatever reason) can lead to a significant D; a larger apparent 

state gain (i.e., a positive change) could be due to increased familiarity with and focus on the 

state test in the schools, with teaching students how to do particular kinds of items on the state 

test; and decreasing the focus on some aspects of NAEP content in the state curriculum between 

the two assessments could lead to a larger gain on the state test. 

16 These factors are discussed in McLaughlin (2008). 

12 
 

 

 

 

 

 

The key underlying assumption is that NAEP and the state assessment each remain essentially 

the same over the two years. If either test is substantively changed between the two years, then 

comparisons of changes identified on the two tests are not warranted. NAEP did not go through 

any substantive methodological changes between 2005 and 2007. However, in the years from 

2005 to 2007, the focus of this report, many states changed their state assessments to ensure that 

they were complying with the regulations of the NCLB law, and finding values of D significantly 

different from zero in those cases is to be expected.17 

It should be noted that the state assessment data available for this study include only a single 

number (percentages) reported for each school (for each subject and grade). D is based on a 

match of NAEP and a state’s assessment at a single point in the state’s achievement distribution. 

Finally, there is the question of what is meant by stability of the mapping between two years and 

how it can be measured. In practical terms, the value of D is a measure of the instability of the 

mapping. If D = 0, the mappings in the two years yield identical results. If D is positive (the state 

showed a more positive change than the change measured by NAEP), that means that if we were 

to calculate the NAEP scale equivalent of the standard in year 2, the result would be a lower 

value on the NAEP scale than the equivalent obtained from the year 1 mapping. This does not 

necessarily mean that the state’s standard got easier. If both NAEP and the state’s assessment and 

scoring systems remained constant over the 2-year interval, it means that there were more gains 

on state-specific skills than on NAEP skills during the interval. 

17 Tables in appendix B summarize selected changes in states’ assessments between the two NAEP administrations of 

2005 and 2007. 

13 
14

3 MAPPING STATE PERFORMANCE STANDARDS

The results of the mapping procedure are presented below for reading and mathematics. Three 

jurisdictions are not included in the 2007 analyses because data were unavailable: District of 

Columbia, Nebraska, and Utah. In addition, California grade 8 mathematics data were 

unavailable. 

Sample sizes and percentages of the 2007 NAEP samples used in the analyses are shown in 

appendix A. In some states, the student population represented by NAEP is less than 100 

percent of the total population because state assessment scores are missing for some schools. 

Scores may be missing because of either the failure to match schools in the NAEP and state 

databases or the suppression of scores where there are too few students. Overall, with the 

exception of Wisconsin in both subjects and grades, the estimated percentages of the student 

population represented by the schools used in the analyses are at least 90 percent.18

Reading 

Table 1 displays the NAEP scale equivalents of each state’s reading standards for proficient 

performance for grades 4 and 8. Standard errors of the NAEP scale equivalent estimates and the 

relative error criterion, K, a measure of how well the procedure reproduces the percentages 

reported by the state to be meeting the standard in each school in the NAEP sample, are also 

included. As previously discussed, the criterion proposed is to consider relative errors greater 

than .5 as indicating that the mapping error is too large to support useful inferences from the 

placement of the standard on the NAEP scale without any additional evidence. Only one grade 

4 reading standard (Texas) and one grade 8 reading standard (Virginia) have relative errors 

greater than .5. The within-school discrepancies between NAEP and Indiana grade 8 test results 

seem to be smaller than the discrepancies that we would expect owing to NAEP student withinschool sampling error alone.19

In 2007, states’ standards for proficient performance in reading varied greatly in difficulty as 

reflected in their NAEP scale equivalent scores. The NAEP scale equivalents of states’ proficient 

standards ranged from below the NAEP Basic level to the NAEP Proficient level (see figure 2). 

In reading, at grade 4, the average of the estimated standards for proficiency across states was 

equivalent to a score of 199 (data not shown) on the NAEP scale, below the NAEP cut point for 

Basic performance (208). Taking the standard errors into account, the estimated difference 

between the five states with the highest standards and the five states with the lowest standards 

was at least 29 points on the NAEP scale, comparable to the 30-point distance between the 

NAEP Basic standard (208) and the NAEP Proficient standard (238). Another way of looking at 

it is that the distance separating the five most difficult standards to achieve and the five least 

difficult standards to achieve was under one standard deviation in student performance on the 

 

18 For Wisconsin, the grade 4 reading and mathematics analyses are based on 65 percent of the NAEP schools serving 

about 71 percent of the students represented by NAEP. Analyses for grade 8 reading and mathematics are based on 

75 percent of the NAEP schools, serving about 83 percent of the students represented by NAEP. 

19 Because the relative error is actually a sample statistic with its own random variation and because it can take on 

negative values (if the differences between school means on NAEP and the state test are smaller than would be 

expected given within-school sample sizes), those negative values are displayed with the § symbol. 
15 

grade 4 NAEP (36 points). Accounting for the margin of error, 31 of the 48 states set grade 4 

standards for proficiency (as measured on the NAEP scale) that were lower than the Basic

performance on NAEP (208). 

For grade 8 reading, the average NAEP scale equivalent score was 246 (data not shown), above 

the NAEP cut point for Basic performance (243). The variation among states at grade 8 was as 

large as the variation at grade 4. The estimated difference between the five states with the 

highest standards and the five states with the lowest standards was at least 29 points on the 

NAEP scale (also taking the standard error into account), less than the 38-point distance 

between Basic (243) and Proficient performance (281) on NAEP, and below the one standard 

deviation in student performance on the grade 8 NAEP (35 points). Accounting for the margin 

of error, 15 of the 48 states set grade 8 standards for proficiency (as measured on the NAEP 

scale) that were lower than the Basic performance on NAEP. 

In reading, Missouri, Minnesota, and South Carolina were among the five states with the most 

difficult standards for proficiency at both grade levels. Tennessee appears among the five states 

with the least difficult standards at both grade levels. 
Table 1. Estimated NAEP scale equivalent scores for the state grades 4 and 8 reading 

proficient standards, their standard error and relative error, by state: 2007 

 Grade 4 Grade 8 

NAEP Standard Relative NAEP Standard Relative 

State/jurisdiction scale equivalent error error1 scale equivalent error error1

Alabama 179 1.5 0.4 234 1.5 0.2 

Alaska 183 0.9 0.1 233 1.9 0.2 

Arizona 198 1.4 0.1 245 1.1 #

Arkansas 213 1.4 0.2 249 1.4 0.4 

California 210 0.9 0.1 261 0.6 #

Colorado 187 1.5 0.1 230 1.4 0.1 

Connecticut 213 1.6 0.1 245 1.1 #

Delaware 202 0.9 0.3 240 1.0 0.4 

District of Columbia — † † — † † 

Florida 209 0.8 0.1 262 0.8 #

Georgia 185 1.3 0.5 215 1.7 0.4 

Hawaii 212 1.0 0.2 245 0.7 0.1 

Idaho 197 1.4 0.4 233 1.0 #

Illinois 200 1.4 0.3 236 1.5 0.5 

Indiana 199 1.3 0.1 251 0.7 § 

Iowa 199 1.7 0.4 252 1.1 0.1 

Kansas 192 1.9 0.3 241 1.0 0.3 

Kentucky 205 1.6 0.3 251 1.1 0.3 

Louisiana 193 2.2 0.5 246 1.3 0.2 

Maine 214 1.0 0.2 261 0.9 0.3 

Maryland 186 1.5 0.3 250 1.2 0.1 

Massachusetts 232 1.2 0.2 252 1.1 0.1 

Michigan 178 2.5 0.4 238 1.2 0.1 

Minnesota 215 1.4 0.2 265 0.7 0.3 

Mississippi 163 1.3 0.3 251 0.6 0.1 

Missouri 227 1.1 0.3 272 1.1 #

Montana 203 1.2 0.4 250 1.5 0.3 

Nebraska — † † — † † 

Nevada 207 1.1 0.2 247 1.0 0.3 

New Hampshire 210 0.8 0.4 258 1.5 0.4 

New Jersey 201 2.0 0.2 252 1.1 0.1 

New Mexico 210 0.7 0.3 248 1.0 0.1 

New York 209 1.4 0.1 260 0.9 0.1 

North Carolina 183 1.0 0.3 217 1.2 0.3 

North Dakota 201 1.0 0.4 251 1.4 0.4 

Ohio 198 2.2 0.4 240 1.9 0.2 

Oklahoma 172 3.7 0.4 232 1.6 0.2 

Oregon 186 2.1 0.4 251 1.2 0.3 

Pennsylvania 211 1.2 0.1 245 1.4 0.1 

Rhode Island 210 1.1 0.2 253 1.1 0.1 

South Carolina 223 1.5 0.2 281 1.0 0.2 

South Dakota 185 1.7 0.4 249 0.9 0.3 

Tennessee 175 1.7 0.4 211 2.5 0.3 

Texas 188 1.6 0.6 222 1.1 0.2 

Utah — † † — † † 

Vermont 214 1.0 0.5 263 1.4 0.4 

Virginia 191 1.6 0.5 239 1.2 0.6 

Washington 203 2.1 0.4 253 1.2 0.2 

West Virginia2 182 1.4 0.3 229 1.3 0.4 

Wisconsin2 193 2.0 0.3 231 1.4 0.2 

Wyoming 204 1.2 0.5 247 1.1 0.5 

— State assessment data not available.

† Not applicable.

# Rounds to zero. 


§ The within-school discrepancies between NAEP and state test results are no larger, and possibly smaller, than discrepancies that would be expected 


owing to NAEP student within-school sampling error alone.

1

 Inferences based on estimates with relative error greater than .5 may require additional evidence.

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at least one grade.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of

Educational Progress (NAEP), 2007 Reading Assessments. U.S. Department of Education, Office of Planning, Evaluation and Policy Development, 

EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. 

16
 

Figure 2.	 NAEP scale equivalent scores for the state grades 4 and 8 reading standards for 

proficient performance, by state: 2007 

Grade 4	 Grade 8 

NAEP Basic (208) NAEP Basic (243)

NAEP Proficient (238) NAEP Proficient (281)

Massachusetts 232

227

223

215

214

214

213

213

212

211

210

210

210

210

209

209

207

205

204

203

203

202

201

201

200

199

199

198

198

197

193

193

192

191

188

187

186

186

185

185

183

183

182

179

178

175

172

163

–

–

–

*	 

South Carolina 281

Missouri Missouri 272

South Carolina Minnesota 265

Minnesota Vermont 263

Maine Florida 262

Vermont California 261

Connecticut Maine 261

Arkansas New York 260

Hawaii New Hampshire 258

Pennsylvania Washington 253

California Rhode Island 253

Rhode Island New Jersey 252

New Hampshire Massachusetts 252

New Mexico Iowa 252

New York Kentucky 251

Florida Mississippi 251

Nevada Oregon 251

Kentucky Indiana 251

Wyoming North Dakota 251

Montana Montana 250

Washington Maryland 250

Delaware Arkansas 249

New Jersey South Dakota 249

North Dakota New Mexico 248

Illinois Nevada 247

Indiana Wyoming 247

Iowa Louisiana 246

Ohio Arizona 245

Arizona Pennsylvania 245

Idaho Hawaii 245

Louisiana Connecticut 245

Wisconsin Kansas 241

Kansas Ohio 240

Virginia Delaware 240

Texas Virginia 239 * Colorado Michigan 238

Oregon Illinois 236

Maryland Alabama 234

South Dakota Alaska 233

Georgia Idaho 233

Alaska Oklahoma 232

North Carolina Wisconsin 231

West Virginia Colorado 230

Alabama West Virginia 229

Michigan Texas 222

Tennessee North Carolina 217

Oklahoma Georgia 215

Mississippi Tennessee 211

District of Columbia District of Columbia – Nebraska Nebraska – Utah Utah –

150 200 250

NAEP Scale Equivalents

300 150 200 250

NAEP Scale Equivalents

300

— State assessment data not available. 

* Relative error greater than .5. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading Assessments. U.S. Department of Education, Office of Planning, 

Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State 

Assessment Score Database (NLSLSASD) 2008. 

17 
18

Mathematics 

Table 2 displays the NAEP scale equivalent scores of each state’s mathematics standards for 

proficient performance for grades 4 and 8. Standard errors of the NAEP scale equivalent 

estimates and the relative error criterion, K, are also included. Seven of the 48 grade 4 

mathematics standards (Alabama, Georgia, Indiana, Michigan, New Hampshire, Oklahoma, and 

Virginia) have relative errors greater than .5 indicating that the variation in results for 

individual schools are large enough to call into question the use of these equivalents without 

additional supporting evidence. In grade 8, only Virginia has a mapping with relative error above 

.5. For two states, Connecticut and South Carolina, the within-school discrepancies between 

NAEP and state grade 8 test results are smaller than the discrepancies that we would expect 

owing to NAEP student within-school sampling error alone. 

In mathematics at grade 4, the average NAEP scale equivalent across states was 223 (data not 

shown), about one-third of the way between the NAEP cut points for Basic (214) and Proficient

(249) performance, as shown in figure 3. Taking the standard errors into account, the difference 

between the five states with the highest standards and the five states with the lowest standards 

was estimated to be 29 points on the NAEP scale, close to the distance between the NAEP Basic

standard and the NAEP Proficient standard (35 points) and about a full standard deviation in 

grade 4 NAEP mathematics achievement (29 points). Accounting for the margin of error, 7 of 

the 48 states set grade 4 standards for proficiency (as measured on the NAEP scale) that were 

lower than the Basic performance level on NAEP, and 1 state set standards above the 249 NAEP 

Proficient cut point. 

In mathematics at grade 8, the mean NAEP scale equivalent was 271 (data not shown) on the 

NAEP scale, above the NAEP cut point for Basic performance (262). The difference between the 

five states with the highest standards and the five states with the lowest standards was at least 29 

points on the NAEP scale, less than the distance between the NAEP Basic standard and the 

NAEP Proficient standard (37 points) and close to one standard deviation in grade 8 NAEP 

mathematics achievement (36 points). Accounting for the margin of error, we see that 8 of the 

47 states set grade 8 standards for proficiency (as measured on the NAEP scale) that were lower 

than the Basic performance on NAEP, and 2 states set standards above the 299 NAEP Proficient

cut point. 

In mathematics, Massachusetts, Missouri, South Carolina, and Washington were among the 

states with the most difficult standards at both grade levels in 2007. At both grade levels, 

Tennessee was the state with the least difficult standards.
Table 2. Estimated NAEP scale equivalent scores for the state grades 4 and 8 mathematics 

proficient standards, their standard error and relative error, by state: 2007 

 Grade 4 Grade 8 

NAEP Standard Relative NAEP Standard Relative 

State/jurisdiction scale equivalent error error1 scale equivalent error error1

Alabama 205 1.5 0.8 253 1.9 0.4 

Alaska 216 1.3 0.3 265 1.2 0.3 

Arizona 213 1.4 0.1 268 1.1 0.1 

Arkansas 229 0.6 0.2 277 1.3 0.1 

California 226 0.7 0.4 — † † 

Colorado 201 1.6 0.2 259 1.3 0.1 

Connecticut 220 0.7 0.1 252 2.0 § 

Delaware 225 0.7 0.2 272 0.9 # 

District of Columbia — † † — † † 

Florida 230 0.8 0.2 266 0.9 # 

Georgia 213 0.8 0.9 243 1.7 0.3 

Hawaii 238 0.5 0.2 294 0.8 0.2 

Idaho 217 0.9 0.5 265 1.6 # 

Illinois 208 0.9 0.3 251 0.8 0.1 

Indiana 228 0.9 0.6 266 1.6 0.1 

Iowa 220 1.1 0.3 264 1.5 0.1 

Kansas 219 1.3 0.5 270 1.6 0.4 

Kentucky 229 1.0 0.4 279 0.7 0.2 

Louisiana 223 1.3 0.3 267 1.2 0.1 

Maine 236 0.8 0.2 286 0.9 0.1 

Maryland 206 1.3 0.5 278 1.5 # 

Massachusetts 254 1.0 0.3 302 1.1 0.1 

Michigan 204 1.6 0.6 260 1.5 0.1 

Minnesota 237 0.9 0.2 286 0.9 0.2 

Mississippi 204 0.8 0.5 262 0.9 # 

Missouri 245 0.8 0.4 289 1.2 0.1 

Montana 234 1.0 0.3 281 1.7 0.1 

Nebraska — † † — † † 

Nevada 224 1.1 0.3 267 1.2 0.1 

New Hampshire 239 1.1 0.6 282 0.8 0.3 

New Jersey 220 1.1 0.4 272 0.8 0.1 

New Mexico 233 0.8 0.3 285 0.9 0.1 

New York 219 0.8 0.2 273 1.1 0.1 

North Carolina 231 0.6 0.3 270 1.3 0.1 

North Dakota2 226 1.0 0.4 279 0.8 0.3 

Ohio 225 1.3 0.5 265 1.2 0.2 

Oklahoma 213 1.5 0.8 249 1.1 0.3 

Oregon 220 0.8 0.4 262 1.2 0.2 

Pennsylvania 223 0.9 0.2 271 1.0 0.1 

Rhode Island 236 0.7 0.1 279 0.6 # 

South Carolina 245 0.9 0.2 312 1.4 § 

South Dakota 224 1.0 0.2 271 0.7 0.1 

Tennessee 198 1.3 0.4 234 2.2 0.4 

Texas 217 0.9 0.5 268 1.0 0.2 

Utah — † † — † † 

Vermont2 239 1.0 0.3 284 0.9 0.1 

Virginia 219 0.9 0.6 259 1.6 0.6 

Washington 240 0.8 0.2 286 1.1 # 

West Virginia2 217 1.3 0.4 253 1.0 0.1 

Wisconsin2 222 2.3 0.2 262 1.7 0.1 

Wyoming 216 0.6 0.5 279 0.8 0.4 

— State assessment data not available.

† Not applicable.

# Rounds to zero. 


§ The within-school discrepancies between NAEP and state test results are no larger, and possibly smaller, than discrepancies that would be expected 


owing to NAEP student within-school sampling error alone.

1

 Inferences based on estimates with relative error greater than .5 may require additional evidence.

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at least one grade.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of

Educational Progress (NAEP), 2007 Mathematics Assessments. U.S. Department of Education, Office of Planning, Evaluation and Policy Development,

EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. 

19 
 

Figure 3.	 NAEP scale equivalent scores for the state grades 4 and 8 mathematics standards for 

proficient performance, by state: 2007 

Grade 4	 Grade 8 

NAEP Basic (214) NAEP Basic (262)

NAEP Proficient (249)

Massachusetts 254 South Carolina
 

Missouri
 245 Massachusetts
 

South Carolina
 245 Hawaii
 

Washington
 240 Missouri
 

Vermont
 239 Washington
 

New Hampshire
 239	 Minnesota * Hawaii 238 Maine
 

Minnesota
 237 New Mexico
 

Rhode Island
 236 Vermont
 

Maine
 236 New Hampshire
 

Montana
 234 Montana
 

New Mexico
 233 Wyoming
 

North Carolina
 231 Rhode Island
 

Florida
 230 Kentucky
 

Kentucky
 229 North Dakota
 

Arkansas
 229 Maryland
 

Indiana
 228 Arkansas * North Dakota 226 New York
 

California
 226 New Jersey
 

Delaware
 225 Delaware
 

Ohio
 225 Pennsylvania
 

South Dakota
 224 South Dakota
 

Nevada
 224 Kansas
 

Pennsylvania
 223 North Carolina
 

Louisiana
 223 Texas
 

Wisconsin
 222 Arizona
 

Connecticut
 220 Louisiana
 

Oregon
 220 Nevada
 

New Jersey
 220 Indiana
 

Iowa
 220 Florida
 

Virginia
 219 Alaska * New York 219 Ohio
 

Kansas
 219 Idaho
 

Idaho
 217 Iowa
 

Texas
 217 Oregon
 

West Virginia
 217 Mississippi
 

Wyoming
 216 Wisconsin
 

Alaska
 216 Michigan
 

Arizona
 213 Colorado
 

Georgia
 213 Virginia * Oklahoma 213 West Virginia * Illinois 208 Alabama
 

Maryland
 206 Connecticut
 

Alabama
 205 Illinois * Mississippi 204 Oklahoma
 

Michigan
 204 Georgia
 

Colorado
 * 201 Tennessee
 

Tennessee
 198 California

District of Columbia District of Columbia
 

Nebraska
 

– Nebraska
 

Utah
 

–

– Utah

312

302

294

289

286

286

286

285

284

282

281

279

279

279

279

278

277

273

272

272

271

271

270

270

268

268

267

267

266

266

265

265

265

264

262

262

262

260

259

259

253

253

252

251

249

243

234

NAEP Proficient (299)

–

–

–

–

*

180 230 280

NAEP Scale Equivalents

330 180 230 280

NAEP Scale Equivalents

330

— State assessment data not available. 

* Relative error greater than .5. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Mathematics Assessments. U.S. Department of Education, Office of Planning, 

Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State 

Assessment Score Database (NLSLSASD) 2008. 

20 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cross-state comparisons 

The majority of the states included in the analyses had state assessment results that were 

correlated with NAEP, with correlations of .7 or more: that is, both assessments identified similar 

patterns of achievement across schools within the state.20 The school-level correlations between 

the percentage of schools’ students meeting the NAEP and the state assessment standards for 

proficiency are summarized in table 3 and listed by state in table 4. 

Table 3.	 Frequency of correlations between NAEP and state assessment school-level 

percentages meeting the proficient standards for reading and mathematics, grades 4 

and 8: 2007

 Reading Mathematics

 Correlation Grade 4 Grade 8 Grade 4 Grade 8

 .3  r < .4 0 1 0 0 

.4  r < .5 0 1 2 0 

.5  r < .6 7 9 3 3 

.6  r < .7 14 13 12 6 

.7  r < .8 13 11 18 22 

.8  r < .9 14 12 13 14 

.9  r 0 1 0 2 

 Number of states1 48 48 48 47 

1

 Test data for the District of Columbia, Nebraska, and Utah were not available to be included in the analysis. California does not 

test grade 8 mathematics. 

NOTE: Frequency counts are based on unrounded correlation coefficients as opposed to the rounded coefficients shown in table 4. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading and Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

In reading, at both grade levels, at least half the states had correlations of .7 or more. 

Correlations were higher in mathematics than in reading. In mathematics, 31 of the 48 states 

included in grade 4 and 38 of the 47 states in grade 8 had correlations of .7 or higher. 

Although the majority of states reported assessment results that identified the same patterns of 

achievement across schools as did NAEP, a small number of states (ranging from 3 to 11 

depending on subject and grade) had test results that did not correlate as well with NAEP 

results, with correlations of less than .6, as shown in tables 3. For example, from table 4, North 

Dakota, Oklahoma, West Virginia, and Wyoming had correlations below .6 on at least three of 

the four assessments. This could be the result of small enrollments in schools in these states 

which affect the reliability of the percentages of students meeting a standard. Another possible 

explanation is that the tests measure different things. It is possible that assessments that sample 

and measure different parts of the reading and mathematics domain might still be highly 

correlated; that is, they might still identify the same schools as high achieving and low 

achieving.21,22 Nevertheless, the relatively low correlations in a few states need to be considered 

when we interpret the results of comparisons of NAEP and state assessment results. 

20 A correlation of .7 implies that 50% of the variance of one variable can be predicted from the other variable. 

21 A variety of factors can lead to low correlations between tests covering the same content: size of the school sample 

of students on which the percentage is based, conditions of testing, time of testing, motivation to perform, similarity 

of accommodations provided, match of the student populations included in the statistics, etc. 

22 Indiana, Iowa, Michigan, New Hampshire, North Dakota, Rhode Island, Vermont, and Wisconsin are states with 

testing in the fall and they may be measuring previous grade skills. 

21 
Table 4. Correlations between NAEP and state assessment school-level percentages meeting 

the proficient standard for reading and mathematics grades 4 and 8, by state: 2007 

 Reading Mathematics 

State/jurisdiction Grade 4 Grade 8 Grade 4 Grade 8 

Alabama 0.67 0.72 0.67 0.74

Alaska 0.81 0.81 0.75 0.78

Arizona 0.86 0.84 0.86 0.80

Arkansas 0.76 0.69 0.82 0.73

California 0.88 0.84 0.76 — 

Colorado 0.84 0.75 0.80 0.80

Connecticut 0.90 0.90 0.90 0.90

Delaware 0.68 0.71 0.79 0.92

District of Columbia — — — — 

Florida 0.80 0.81 0.81 0.82

Georgia 0.70 0.58 0.76 0.75

Hawaii 0.73 0.78 0.74 0.77

Idaho 0.59 0.68 0.61 0.74

Illinois 0.80 0.60 0.83 0.79

Indiana1 0.75 0.80 0.65 0.78

Iowa1 0.53 0.66 0.65 0.75

Kansas 0.60 0.65 0.60 0.61

Kentucky 0.67 0.63 0.65 0.72

Louisiana 0.71 0.71 0.79 0.83

Maine 0.64 0.54 0.75 0.72

Maryland 0.71 0.82 0.70 0.89

Massachusetts 0.80 0.82 0.75 0.86

Michigan1 0.71 0.79 0.78 0.88

Minnesota 0.73 0.65 0.78 0.72

Mississippi 0.65 0.80 0.67 0.81

Missouri 0.72 0.77 0.72 0.81

Montana 0.63 0.68 0.68 0.71

Nebraska — — — — 

Nevada 0.82 0.70 0.82 0.78

New Hampshire1 0.61 0.60 0.63 0.69

New Jersey 0.82 0.84 0.77 0.87

New Mexico 0.74 0.71 0.75 0.79

New York 0.85 0.81 0.83 0.83

North Carolina 0.66 0.67 0.81 0.82

North Dakota1 0.63 0.50 0.59 0.58

Ohio 0.76 0.74 0.72 0.82

Oklahoma 0.59 0.56 0.43 0.53

Oregon 0.71 0.69 0.69 0.69

Pennsylvania 0.87 0.84 0.84 0.86

Rhode Island1 0.80 0.90 0.86 0.93

South Carolina 0.79 0.69 0.81 0.78

South Dakota 0.65 0.58 0.73 0.75

Tennessee 0.73 0.67 0.75 0.70

Texas 0.64 0.68 0.66 0.73

Utah — — — — 

Vermont1 0.54 0.49 0.67 0.68

Virginia 0.56 0.55 0.60 0.63

Washington 0.68 0.68 0.85 0.79

West Virginia 0.56 0.38 0.59 0.55

Wisconsin1 0.82 0.81 0.87 0.85

Wyoming 0.56 0.53 0.45 0.65

— State assessment data not available. 

1

 State with fall testing. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading and Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

22
 

 

 

 

 

 

 

 

 

 

 

0 0 8 0

0 0

0 0 0 0 0

0 0

 

 

 

 

 

 

In 2007, as was the case for the 2003 and 2005 mapping results, most of the variation between 

states in the proportion of proficient students on state assessments can be explained by the rigor 

of a state’s standard for proficient performance. Table 5 shows the estimated linear relationships 

between the difficulty of each state’s standard for proficiency, as measured by its NAEP scale 

equivalent and the percentage of students scoring proficient on the state test: states with a more 

difficult standard for proficiency (as measured on the NAEP scale) tend to have fewer students 

scoring proficient, whereas states with less difficult standards tend to have more students scoring 

proficient. The negative slopes of the lines fitted to the data points (states) show that each 1­

point increase in the difficulty of a state’s standard for proficiency in reading as measured by the 

NAEP scale is associated with .7 to .8 percentage point fewer students meeting the standards in 

grades 4 and 8, respectively. In mathematics, the relationship is similar. 

Table 5. Relationship between the percentage of students scoring proficient on the state test 

and the difficulty of grades 4 and 8 state standards as measured by the state’s 

respective NAEP scale equivalent, by subject: 2007 

Percent proficient on state test = f(state standards as measured by the state’s NAEP scale equivalent) 

 Grade 4 Grade 8 

R2 R2 Subject Intercept Slope Intercept Slope 

Estimate 214.1 -.7 * .70 272.7 -.8 * .69 Reading Standard error 13.49 .07 † 19.96 .08 † 

Estimate 268.5 -.9 * .70 288.7 -.8 * .71 Mathematics Standard error 19.10 .09 † 21.68 .08 † 

† Not applicable. 

* Statistically significant at p < .05. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading and Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

Whereas table 5 addresses the question of how the variability of performance standards relates to 

the percentages of students meeting the standards, figure 4 and table 6 address the question of 

how the variation among performance standards relates to the performance of students on 

NAEP. Figure 4 displays, for each subject and grade, the percentage of each state’s students 

meeting the NAEP Proficient standard as a function of the placement of their own standard for 

proficient performance. Table 6 summarizes the linear relationships. Although three of the 

functions slope upward, this is mainly caused by a single state that set a high standard and had 

high scores. If that state is removed (the circled dot on figure 4), the squared correlations are .10 

(from .16) for grade 4 reading, .04 (unchanged) for grade 8 reading, .09 (from .15) for grade 4 

mathematics, and .06 (from .12) from grade 8 mathematics. The two squared correlations for 

grade 4 are statistically significant, but the two grade 8 relationships are not. 

In general, from figure 4, we see that setting a higher state standard is not necessarily associated 

with higher performance on NAEP. In grade 8 at least, students in states with high standards for 

proficient performance score just about the same on NAEP as students in states with low 

standards for proficiency. 

23 
 

 

 

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Figure 4.	 Relationship between the percentage of students scoring proficient on NAEP and 

the difficulty of grades 4 and 8 state standards for reading and mathematics as 

measured by the state’s respective NAEP scale equivalent: 2007 

Percent proficient Percent proficient on NAEP on NAEP
 

80
 80 reading grade 4 reading grade 8

60 60

• • 40 • 40 •

• •

• • 20 • • 20 ••

0 0

0 175 200 225 250 500 0 175 200 225 250 275 500

NAEP scale equivalent of state proficiency standard NAEP scale equivalent of state proficiency standard

Percent proficient Percent proficient

on NAEP on NAEP

80 80

mathematics grade 4 mathematics grade 8

60 60

•

•

•• • • • 40 • • ••••	 40 ••• • • •

• • • • •

20 • 20 • •

0 0

0 175 200 225 250 275 300 0 175 200 225 250 275 300 500 500

NAEP scale equivalent of state proficiency standard NAEP scale equivalent of state proficiency standard

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading and Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

24 
 

 

 

 

 

0 0 0 0

0 0 0 0 0

 

 

Table 6.	 Relationship between the percentage of students scoring proficient on NAEP and 

the difficulty of grades 4 and 8 state standards as measured by the state’s respective 

NAEP scale equivalent, by subject: 2007 

Percent proficient on NAEP = f(state standards as measured by the state’s NAEP scale equivalent) 

 Grade 4	 Grade 8 

R2 	 R2 Subject	 Intercept Slope Intercept Slope 

Estimate	 -1.3 .2 * .16 6.8 .1 .04 Reading Standard error 11.36 .06 † 16.12 .07 † 

Estimate -17.3 .3 * .15 -18.9 .2 * .12 Mathematics Standard error 19.92 .09 † 20.26 .07 † 

† Not applicable. 

* Statistically significant at p < .05. 

NOTE: Removing one state that set a high standard and had high scores, the R2

 are .10 (from .16) for grade 4 reading, .04 

(unchanged) for grade 8 reading, .09 (from .15) for mathematics grade 4, and .06 (from .12) from mathematics grade 8. The two R2 

for grade 4 are statistically significant, but the two grade 8 relationships are not. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading and Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

25 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 COMPARING 2007 WITH 2005 STATE PERFORMANCE STANDARDS 

Although the NAEP assessment in reading and mathematics did not change between 2005 and 

2007, some states made changes in their state assessments in these subjects during the same 

period, changes substantial enough that these states indicated that their 2005 scores were not 

comparable to their 2007 scores.23 Nevertheless, both 2005 and 2007 scores could be mapped 

onto the NAEP scale as a means for comparison. For these states, the analyses compared the 

NAEP equivalent scores estimated for 2007 with those for 2005. Significant differences in NAEP 

scale equivalents might reflect changes in policies and/or practices that occurred between the 

years in addition to the changes in state assessments and standards. 

Other states reported no changes in their state assessments in the same period and indicated that 

their 2005 scores were comparable to their 2007 scores. For these states, the analyses compared 

the NAEP equivalent scores estimated for 2007 to those for 2005 to evaluate the stability of the 

mapping of each state’s standard for proficient performance onto the NAEP scale. 

When the 2005 and 2007 NAEP equivalents of the state standards are not stable, that is, the 

NAEP equivalent score for 2007 is statistically significantly different from that of the 2005, 

further investigation is warranted. Several factors could lead to such instability. For example, 

changes in classroom instructional practices or curricula might have placed more emphasis on 

subject matter covered more on the state test than on NAEP from one assessment year to the 

next, or changes in state exclusion policies might have changed the rates of participation of 

students with disabilities and/or English language learners in the NAEP or state assessments.24 

Regardless of whether states reported that 2005 scores are comparable to 2007 or not, when 

NAEP scale equivalents are significantly different, further investigations can help ascertain the 

factors that may have contributed to the differences in the NAEP scale equivalents of state 

standards seen in this study. When the 2005 NAEP equivalents of the state standards are not 

different from those for 2007, that is, when standards are considered stable, NAEP can be used to 

corroborate the state reported progress (or lack of progress) through further analysis, an issue 

discussed in Section 5. 

This section makes comparisons between the 2005 and 2007 mappings in reading and 

mathematics for grades 4 and 8. The 2005 mappings in this report will not necessarily match 

previously published results (U.S. Department of Education 2007). Methodological differences 

between the procedures used in the two analyses may result in small differences.25 Moreover, 

since the release of the 2005 mapping study, some states have revised their 2005 assessment data 

files and other states have made public previously unavailable results. 

23	 This was reported in a survey conducted for this study to gain contextual information about the general 

characteristics of state assessment programs and, specifically, to help identify changes in states’ assessments between 

the 2004-05 and 2006-07 school years that could affect the interpretation of the mapping results. See appendix B 

for more information on the survey. 

24 These issues were not covered by the survey of state assessment programs referenced above.
 

25 The small differences are not large enough to change the whole number scale value reported as the NAEP
 

equivalent. 

26 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reading 

Table 7 displays the availability of state assessment data in 2005 and 2007 suitable for 

implementing the mapping of the states’ grades 4 and 8 reading standards onto the NAEP scale. 

Table 7 also shows, for each grade, whether changes in the states’ assessments between 2005 and 

2007 were deemed by state representatives to affect the comparability of the 2005 with the 2007 

reported results.26 States with both years of data are listed in table 8 by grade and by whether 

those data are comparable. In grade 4 reading, of the 34 states with valid test data in both years, 

22 states indicated that no significant changes in their tests were made that would affect the 

comparability of test results across the two years. For grade 8 reading, of the 38 states with valid 

test data in both years, 14 indicated that their scores were not comparable and 24 indicated 

comparability of results. 

For states with both years of data, tables 9 and 10 display, for each year, the number of public 

schools selected for NAEP in each state, the percentage of these schools included in the 

analyses, and the percentage of the student population represented by the schools. 

Tables 11 and 12 compare the NAEP scale equivalents between the two years for grades 4 and 8, 

respectively, according to whether states reported comparable assessment results. Table 11 shows 

that, for the 12 states indicating substantive changes in their grade 4 reading assessments, 8 

showed significant differences between the 2005 and 2007 estimates of the NAEP equivalents of 

their state standards. Half of these showed an increase of up to 12 points (Idaho), and half 

showed a decrease of up to 24 points (Wyoming). Table 11 also shows that, among the 22 states 

indicating no substantive changes in grade 4 state tests, 14 states did not show statistically 

significant differences between their NAEP scale equivalents in 2005 and 2007; 8 states showed 

statistically significant differences in the estimated NAEP scale equivalent, with 5 showing 

standards that are as much as 11 points higher (New Jersey) and 3 showing a decrease of up to 6 

points (South Carolina). 

Table 12 shows that among those states indicating substantive changes in their grade 8 reading 

assessments, seven showed significant differences between the 2005 and 2007 estimates of the 

NAEP equivalents of their state standards; all seven showed lower 2007 NAEP scale equivalent 

of their standards, by up to 31 points (Wyoming). 

Table 12 also shows that, among the 24 states indicating no changes in their state tests, the 

NAEP equivalent standards of 13 states in 2007 were not statistically different from their 

standards in 2005. The 11 remaining states showed statistically significant differences in the 

estimates of the NAEP scale equivalent, 8 of which showed decreases in NAEP scale equivalent 

of state standards of up to 12 points (Pennsylvania) and 3 showed increases in NAEP equivalent 

of state standards of up to 5 points (Maryland). 

26	 Tables B-1 to B-3 of appendix B summarize for each state selected changes to the main state assessment in reading 

and mathematics between 2005 and 2007 and information about the comparability of the reported results between 

2005 and 2007. 

27 
Table 7. State assessment data availability and state reports of whether 2005 and 2007 

assessment results are comparable in grades 4 and 8 reading, by state: 2005 and 2007 

 Grade 4 Grade 8 

State/jurisdiction 2005 data 2007 data Comparable results 2005 data 2007 data Comparable results 

Alabama   Yes   Yes 

Alaska   Yes   Yes 

Arizona —  Yes   Yes 

Arkansas   Yes   Yes 

California   Yes   Yes 

Colorado   Yes   Yes 

Connecticut   No   No 

Delaware —  No   No 

District of Columbia — — No — — No 

Florida   Yes   Yes 

Georgia   No   No 

Hawaii   No   No 

Idaho   No   No 

Illinois —  No   Yes 

Indiana   Yes   Yes 

Iowa   Yes   Yes 

Kansas —  No   No 

Kentucky   No —  No 

Louisiana   Yes   Yes 

Maine   No   No 

Maryland   Yes   Yes 

Massachusetts   Yes —  No 

Michigan   No —  No 

Minnesota —  No —  No 

Mississippi   Yes   Yes 

Missouri —  No —  No 

Montana   No   No 

Nebraska — — No — — No 

Nevada —  No   Yes 

New Hampshire —  No —  No 

New Jersey   Yes   Yes 

New Mexico   Yes   Yes 

New York   No   No 

North Carolina   Yes   Yes 

North Dakota   Yes   Yes 

Ohio   Yes   Yes 

Oklahoma   No   No 

Oregon —  No   No 

Pennsylvania —  No   Yes 

Rhode Island —  Yes —  Yes 

South Carolina   Yes   Yes 

South Dakota —  Yes —  Yes 

Tennessee   Yes   Yes 

Texas   Yes   Yes 

Utah — — Yes — — No 

Vermont —  Yes —  Yes 

Virginia —  No   No 

Washington   Yes —  No 

West Virginia   No   No 

Wisconsin   Yes   Yes 

Wyoming   No   No 

 State assessment data available. 

— State assessment data not available. 

SOURCE: U.S. Department of Education, Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, 

Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. U.S. 

Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of 

Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

28
Table 8. States with both 2005 and 2007 data suitable to implement the mapping of grades 4

and 8 state reading standards, by whether the reported results are directly 


comparable 

2005 and 2007 state assessment reported grade 4 results 2005 and 2007 state assessment reported grade 8 results 

 directly comparable directly comparable 

Alabama Alabama 

Alaska Alaska 

Arkansas Arizona 

California Arkansas 

Colorado California 

Florida Colorado 

Indiana Florida 

Iowa Illinois 

Louisiana Indiana 

Maryland Iowa 

Massachusetts Louisiana 

Mississippi Maryland 

New Jersey Mississippi 

New Mexico Nevada 

North Carolina New Jersey 

North Dakota New Mexico 

Ohio North Carolina 

South Carolina North Dakota 

Tennessee Ohio 

Texas Pennsylvania 

Washington South Carolina 

Wisconsin Tennessee 

 Texas 

Wisconsin 

2005 and 2007 state assessment reported grade 4 results 

not comparable 

2005 and 2007 state assessment reported grade 8 results 

not comparable 

Connecticut Connecticut 

Georgia Delaware 

Hawaii Georgia 

Idaho Hawaii 

Kentucky Idaho 

Maine Kansas 

Michigan Maine 

Montana Montana 

New York New York 

Oklahoma Oklahoma 

West Virginia Oregon 

Wyoming Virginia 

 West Virginia 

 Wyoming 

SOURCE: U.S. Department of Education, Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, 

Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. U.S. 

Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of 

Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

29 
Table 9. Number of NAEP schools, percentage of NAEP schools available for comparing 

state assessment results with NAEP results in grade 4 reading, and percentage of the 

student population represented in these comparison schools, by state: 2005 and 2007 

 2005 2007 

Percent of Percent of Percent of Percent of 

State/jurisdiction 

NAEP 

schools1

NAEP schools 

matched 

population 

represented 

 NAEP 

schools1

NAEP schools 

matched 

population 

represented 

Alabama 130 98.5 97.6 110 99.1 99.1

Alaska2 160 61.8 83.7 180 99.4 99.9

Arkansas 150 84.8 91.5 120 96.6 97.6

California 450 94.6 96.3 320 97.8 99.0

Colorado 150 91.8 97.1 120 95.8 99.0

Connecticut 130 100.0 100.0 110 100.0 100.0

Florida 170 94.1 96.3 160 97.6 97.2

Georgia 180 92.6 91.7 160 98.7 96.4

Hawaii 130 100.0 100.0 120 99.1 99.1

Idaho 160 95.5 94.9 130 95.5 91.2

Indiana 140 100.0 100.0 110 100.0 100.0

Iowa 130 96.2 97.0 140 97.8 96.7

Kentucky 150 99.3 99.1 120 97.4 98.1

Louisiana 140 99.3 98.5 110 97.2 98.4

Maine2 190 74.1 81.3 150 93.4 95.4

Maryland 130 98.4 99.2 110 98.2 98.4

Massachusetts 200 98.5 99.7 170 100.0 100.0

Michigan 140 92.3 95.3 120 99.2 98.7

Mississippi 130 99.2 99.8 120 97.4 97.1

Montana 240 80.5 94.3 190 98.9 99.1

New Jersey 140 99.3 98.9 110 98.2 95.1

New Mexico2 160 83.9 83.9 130 95.3 97.9

New York 190 97.9 98.8 150 99.3 99.8

North Carolina 180 96.0 97.4 170 97.6 96.5

North Dakota 260 74.3 93.0 210 80.5 93.3

Ohio 200 98.5 99.3 160 98.1 99.3

Oklahoma 180 99.4 99.8 140 98.5 98.8

South Carolina 120 99.2 99.3 110 97.2 98.7

Tennessee 140 98.6 97.8 120 100.0 100.0

Texas 380 98.2 97.6 300 98.6 97.9

Washington 140 97.8 99.0 130 99.2 100.0

West Virginia2 200 97.4 97.9 150 92.5 89.7

Wisconsin2 170 58.6 65.3 130 65.4 71.0

Wyoming 170 85.9 96.6 170 96.5 97.2

1

 Rounded to the nearest 10 for confidentiality. 

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at 

least one of the years. 

NOTE: In the comparison schools, the population represented by NAEP is less than 100 percent of the total population where state 

assessment scores are missing for some schools. Scores may be missing either because of the failure to match schools in the two

surveys or the suppression of scores where there are too few students. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

30
Table 10. Number of NAEP schools, percentage of NAEP schools available for comparing 

state assessment results with NAEP results in grade 8 reading, and percentage of the 

student population represented in these comparison schools, by state: 2005 and 2007 

 2005 2007 

Percent of Percent of Percent of Percent of 

State/jurisdiction 

NAEP 

schools1

NAEP schools 

matched 

population 

represented 

 NAEP 

schools1

NAEP schools 

matched 

population 

represented 

Alabama 110 98.2 98.1 120 100.0 100.0

Alaska2 100 52.9 89.1 110 98.2 99.3

Arizona 130 96.2 99.1 130 97.7 99.2

Arkansas2 130 84.0 89.0 120 91.1 94.5

California 370 95.2 97.2 310 97.1 99.0

Colorado 120 90.0 98.2 120 93.1 98.5

Connecticut 110 96.2 97.0 100 100.0 100.0

Delaware 40 86.0 92.9 50 97.8 100.0

Florida 160 96.3 95.2 160 98.7 98.6

Georgia 120 92.7 91.9 120 97.5 95.6

Hawaii 70 98.5 99.9 70 100.0 100.0

Idaho 100 94.1 97.1 110 97.2 99.0

Illinois 190 98.4 98.2 200 98.0 99.3

Indiana 110 98.1 97.9 110 100.0 100.0

Iowa 110 98.2 97.0 130 97.0 96.8

Kansas 120 97.4 99.1 150 97.3 98.0

Louisiana 110 98.2 98.5 110 96.4 97.7

Maine2 130 67.7 80.2 130 94.7 97.4

Maryland 110 98.1 99.2 110 99.1 97.3

Mississippi 120 96.5 97.0 110 97.4 97.9

Montana 160 81.8 96.3 170 98.2 99.4

Nevada 80 87.2 92.9 70 93.2 93.3

New Jersey 110 99.1 96.9 110 100.0 100.0

New Mexico2 110 81.1 84.7 110 97.3 99.4

New York 180 95.1 95.3 160 98.1 98.5

North Carolina 140 95.0 97.5 150 99.3 99.8

North Dakota 180 73.6 92.9 190 70.3 90.0

Ohio 140 95.1 96.9 190 98.4 99.1

Oklahoma 150 96.6 97.1 150 96.6 96.8

Oregon 120 99.2 99.8 110 96.5 99.0

Pennsylvania 110 94.5 96.0 110 98.2 97.6

South Carolina 110 96.3 95.6 110 97.2 98.5

Tennessee 110 99.1 99.5 120 99.2 99.1

Texas 280 97.1 98.1 220 96.4 97.4

Virginia 110 100.0 100.0 110 99.1 98.9

West Virginia 110 97.3 98.8 120 91.5 91.1

Wisconsin2 120 79.7 86.1 130 74.6 82.1

Wyoming 80 98.7 96.8 80 95.1 96.1

1

 Rounded to the nearest 10 for confidentiality. 

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at 

least one of the years. 

NOTE: In the comparison schools, the population represented by NAEP is less than 100 percent of the total population where state 

assessment scores are missing for some schools. Scores may be missing either because of the failure to match schools in the two

surveys or the suppression of scores where there are too few students. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

31 
Table 11. Difference between the estimated NAEP scale equivalents of state grade 4 reading 


proficient standards and their standard error, by state: 2005 and 2007

2005 2007 

NAEP NAEP 

scale Standard scale Standard Difference Standard 

State/jurisdiction equivalent error equivalent error 2007-2005 error 

2005 and 2007 state assessment reported results are comparable

Alabama 172 2.1 179 1.5 6.8 * 2.63 

Alaska 182 2.8 183 0.9 1.1 2.93 

Arkansas 217 1.4 213 1.4 -4.1 * 1.96 

California 210 0.7 210 0.9 0.3 1.10 

Colorado 186 1.5 187 1.5 0.5 2.08 

Florida 202 0.9 209 0.8 6.8 * 1.22 

Indiana 199 1.2 199 1.3 0.4 1.74 

Iowa 197 1.4 199 1.7 1.8 2.21 

Louisiana 198 1.4 193 2.2 -4.5 2.57 

Maryland 187 1.5 186 1.5 -1.0 2.15 

Massachusetts 234 0.9 232 1.2 -2.3 1.54 

Mississippi 161 2.1 163 1.3 2.5 2.48 

New Jersey 191 1.7 201 2.0 10.6 * 2.61 

New Mexico 208 1.0 210 0.7 1.6 1.23 

North Carolina 183 1.3 183 1.0 -0.8 1.64 

North Dakota 204 0.7 201 1.0 -2.5 * 1.21 

Ohio 199 1.8 198 2.2 -0.5 2.88 

South Carolina 228 1.1 223 1.5 -5.9 * 1.86 

Tennessee 170 1.5 175 1.7 4.9 * 2.31 

Texas 190 1.0 188 1.6 -2.8 1.85 

Washington 197 1.9 203 2.1 5.9 * 2.80 

Wisconsin 189 1.7 193 2.0 4.1 2.60 

2005 and 2007 state assessment reported results are not comparable 

Connecticut 212 1.1 213 1.6 0.8 1.95 

Georgia 174 1.6 185 1.3 11.0 * 2.06 

Hawaii 205 0.8 212 1.0 7.2 * 1.28 

Idaho 185 3.2 197 1.4 11.9 * 3.43 

Kentucky 206 1.6 205 1.6 -1.6 2.24 

Maine 224 1.1 214 1.0 -10.1 * 1.55 

Michigan 182 3.8 178 2.5 -4.1 4.57 

Montana 197 1.5 203 1.2 5.6 * 1.93 

New York 207 1.2 209 1.4 2.6 1.83 

Oklahoma 182 2.3 172 3.7 -10.3 * 4.38 

West Virginia 186 1.3 182 1.4 -4.1 * 1.92 

Wyoming 228 0.6 204 1.2 -23.8 * 1.30 

* Difference is statistically significant at p < .05. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

32
Table 12. Difference between the estimated NAEP scale equivalents of state grade 8 reading 


proficient standards and their standard error, by state: 2005 and 2007

2005 2007 

NAEP NAEP 

scale Standard scale Standard Difference Standard 

State/jurisdiction equivalent error equivalent error 2007-2005 error 

2005 and 2007 state assessment reported results are comparable

Alabama 236 1.1 234 1.5 -2.7 1.92 

Alaska 230 1.3 233 1.9 2.7 2.25 

Arizona 244 1.1 245 1.1 1.0 1.58 

Arkansas 254 1.0 249 1.4 -5.2 * 1.67 

California 262 0.7 261 0.6 -0.7 0.93 

Colorado 229 1.9 230 1.4 1.9 2.33 

Florida 265 1.2 262 0.8 -3.0 * 1.45 

Illinois 245 1.1 236 1.5 -9.6 * 1.89 

Indiana 249 1.9 251 0.7 1.3 2.04 

Iowa 250 1.0 252 1.1 1.4 1.45 

Louisiana 251 1.2 246 1.3 -4.7 * 1.81 

Maryland 245 1.7 250 1.2 5.0 * 2.09 

Mississippi 246 1.4 251 0.6 4.5 * 1.52 

Nevada 253 0.9 247 1.0 -5.2 * 1.38 

New Jersey 250 1.2 252 1.1 1.8 1.67 

New Mexico 251 1.4 248 1.0 -2.1 1.74 

North Carolina 217 1.4 217 1.2 0.4 1.82 

North Dakota 255 0.8 251 1.4 -4.0 * 1.62 

Ohio 241 1.6 240 1.9 -1.0 2.52 

Pennsylvania 258 1.7 245 1.4 -12.3 * 2.25 

South Carolina 276 1.2 281 1.0 4.8 * 1.55 

Tennessee 221 1.8 211 2.5 -10.6 * 3.09 

Texas 225 0.9 222 1.1 -2.6 1.41 

Wisconsin 229 1.5 231 1.4 1.5 2.06 

2005 and 2007 state assessment reported results are not comparable 

Connecticut 242 1.4 245 1.1 2.6 1.79 

Delaware 242 1.1 240 1.0 -2.3 1.50 

Georgia 224 1.3 215 1.7 -8.4 * 2.17 

Hawaii 261 1.2 245 0.7 -16.7 * 1.37 

Idaho 235 1.9 233 1.0 -2.5 2.18 

Kansas 242 1.4 241 1.0 -1.3 1.68 

Maine 275 1.3 261 0.9 -14.4 * 1.62 

Montana 253 0.9 250 1.5 -2.7 1.79 

New York 268 1.3 260 0.9 -7.9 * 1.58 

Oklahoma 244 1.3 232 1.6 -11.7 * 2.08 

Oregon 254 1.3 251 1.2 -3.1 1.76 

Virginia 243 1.3 239 1.2 -4.3 * 1.83 

West Virginia 228 1.8 229 1.3 0.2 2.22 

Wyoming 278 1.4 247 1.1 -31.2 * 1.77 

* Difference is statistically significant at p < .05. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

33 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mathematics 

Table 13 displays the availability of state assessment data in 2005 and 2007 suitable for 

implementing the mapping of grades 4 and 8 mathematics standards. It also displays, for each 

grade, whether changes in the states’ assessments between 2005 and 2007 were deemed to affect 

the direct comparability of the 2005 and 2007 reported results. States with both years of data are 

listed in table 14 by grade and by whether those data are comparable according to state 

assessment staff. In grade 4 mathematics, of the 35 states with valid test data in both years, 14 

indicated that their 2005 scores were not comparable to their 2007 scores and 21 states indicated 

that no significant changes in their tests were made. For grade 8 mathematics, of the 39 states 

with valid test data in both years, 18 indicated that their scores were not comparable and 21 

indicated comparability of results. 

For states with both years of data, tables 15 and 16 display, for each year, the number of public 

schools selected for NAEP in each state, the percentage of these schools included in the 

analyses, and the percentage of the student population represented by the schools. 

Tables 17 and 18 compare the NAEP scale equivalent between the two years for grades 4 and 8, 

respectively, according to whether states reported comparable assessment results. Table 17 shows 

that for the 14 states indicating substantive changes in their grade 4 assessments, 11 showed 

significant differences between the 2005 and 2007 NAEP equivalents of their state standards. Six 

of them had lower 2007 NAEP equivalent of state standards with decreases of up to 34 points 

(Wyoming), and five had higher 2007 NAEP equivalent standards, with increases of up to 28 

points (North Carolina). 

Table 17 also shows that among the 21 states indicating no substantive changes in grade 4 state 

tests, 15 did not have statistically significant differences between their NAEP scale equivalents 

in 2005 and 2007. Six states had statistically significant differences in the NAEP scale 

equivalent, with two showing increases of up to 4 points (Washington), and four showing 

decreases of up to 8 points (Maryland). 

Table 18 shows that among those 18 states indicating substantive changes in their grade 8 

mathematics assessments, 12 showed significant differences between the 2005 and 2007 

estimates of the NAEP equivalents of their state standards: 9 states showed lower 2007 NAEP 

equivalent standards, by up to 25 points (Illinois), and 3 showed increases of up to 23 points 

(North Carolina). Table 18 also shows that, among the 21 states indicating no changes in their 

state tests, the NAEP scale equivalent of state standards of 14 states in 2007 were not statistically 

different from the standards in 2005. The remaining seven states had statistically significant 

differences in their NAEP equivalent standards; six showed decreases by up to 12 points 

(Georgia), and South Carolina increased its NAEP equivalent standard by 7 points. 

Such discrepancies illustrate that the method used for mapping state standards onto the NAEP 

scales may produce an apparent change in the state’s standard, causing it to appear somewhat 

easier or more stringent. For this reason, the results of studies like this one need to be reestimated with each NAEP state assessment to ensure that the NAEP-equivalent mapping is upto-date. This method relies on NAEP and state tests to track the same progress over time. 

Section 5 explores this issue in more detail. 

34 
Table 13. State assessment data availability and state reports of whether 2005 and 2007 

assessment results are comparable in grades 4 and 8 mathematics, 

by state: 2005 and 2007 

 Grade 4 Grade 8 

State/jurisdiction 2005 data 2007 data Comparable results 2005 data 2007 data Comparable results 

Alabama   Yes —  Yes 

Alaska   Yes   Yes 

Arizona —  Yes   Yes 

Arkansas   Yes   Yes 

California   Yes — — Yes 

Colorado   Yes   Yes 

Connecticut   No   No 

Delaware —  No   No 

District of Columbia — — No — — No 

Florida   Yes   Yes 

Georgia   Yes   Yes 

Hawaii   No   No 

Idaho   No   No 

Illinois —  No   No 

Indiana   Yes   Yes 

Iowa   Yes   Yes 

Kansas   No —  No 

Kentucky —  No   No 

Louisiana   Yes   Yes 

Maine   No   No 

Maryland   Yes   Yes 

Massachusetts   Yes   No 

Michigan   No   No 

Minnesota —  No —  No 

Mississippi   Yes   Yes 

Missouri   No   No 

Montana   No   No 

Nebraska — — No — — No 

Nevada —  No   Yes 

New Hampshire —  No —  No 

New Jersey   Yes   Yes 

New Mexico   Yes   Yes 

New York   No   No 

North Carolina   No   No 

North Dakota   Yes   Yes 

Ohio   No   Yes 

Oklahoma   No   No 

Oregon —  No   No 

Pennsylvania —  No   Yes 

Rhode Island —  Yes —  Yes 

South Carolina   Yes   Yes 

South Dakota —  Yes —  Yes 

Tennessee   Yes   Yes 

Texas   Yes   Yes 

Utah — — Yes — — Yes 

Vermont —  Yes —  Yes 

Virginia —  No   No 

Washington   Yes —  No 

West Virginia   No   No 

Wisconsin   Yes   Yes 

Wyoming   No   No 

 State assessment data available. 

— State assessment data not available. 

SOURCE: U.S. Department of Education, Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, 

Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. U.S. 

Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of 

Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

35 
Table 14. States with both 2005 and 2007 data suitable to implement the mapping of grades 4

and 8 mathematics standards, by whether the reported results are directly 


comparable 

2005 and 2007 state assessment reported grade 4 results 2005 and 2007 state assessment reported grade 8 results 

 directly comparable directly comparable 

Alabama Alaska

Alaska Arizona

Arkansas Arkansas

California Colorado

Colorado Florida

Florida Georgia

Georgia Indiana

Indiana Iowa

Iowa Louisiana

Louisiana Maryland

Maryland Mississippi

Massachusetts Nevada

Mississippi New Jersey

New Jersey New Mexico

New Mexico North Dakota

North Dakota Ohio

South Carolina Pennsylvania

Tennessee South Carolina

Texas Tennessee

Washington Texas

Wisconsin Wisconsin

2005 and 2007 state assessment reported grade 4 results 

not comparable 

2005 and 2007 state assessment reported grade 8 results 

not comparable 

Connecticut Connecticut

Hawaii Delaware

Idaho Hawaii

Kansas Idaho

Maine Illinois

Michigan Kentucky

Missouri Maine

Montana Massachusetts

New York Michigan

North Carolina Missouri

Ohio Montana

Oklahoma New York

West Virginia North Carolina

Wyoming Oklahoma

 Oregon

Virginia

West Virginia

Wyoming

SOURCE: U.S. Department of Education, Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, 

Washington, DC, 2008. The National Longitudinal School-Level State Assessment Score Database (NLSLSASD) 2008. U.S. 

Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of 

Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

36
Table 15. Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 4 mathematics, and percentage of the 

student population in these comparison schools, by state: 2005 and 2007

 2005 2007 

Percent of Percent of Percent of Percent of 

NAEP NAEP schools population NAEP NAEP schools population 

State/jurisdiction schools1 matched represented schools1 matched represented 

Alabama 130 98.5 97.9 110 99.1 99.1 

Alaska 150 70.6 91.2 180 100.0 100.0 

Arkansas 150 84.8 91.9 120 96.6 97.5 

California 450 94.4 96.4 330 97.5 98.9 

Colorado 150 92.5 96.9 120 95.8 99.1 

Connecticut 130 100.0 100.0 110 100.0 100.0 

Florida 170 94.1 96.6 160 97.6 97.2 

Georgia 180 92.6 92.1 160 98.7 96.4 

Hawaii 130 100.0 100.0 120 99.1 99.0 

Idaho 160 95.6 95.1 130 95.5 91.8 

Indiana 140 100.0 100.0 110 100.0 100.0 

Iowa 130 95.4 96.2 140 97.8 96.9 

Kansas 140 96.4 98.0 140 98.6 99.0 

Louisiana 140 99.3 98.3 110 97.2 98.4 

Maine2 190 74.2 82.2 150 93.4 95.6 

Maryland 130 99.2 99.7 110 98.2 98.5 

Massachusetts 200 99.0 99.8 170 100.0 100.0 

Michigan 140 92.9 95.5 120 99.2 98.8 

Mississippi 130 100.0 100.0 120 97.4 97.2 

Missouri 160 97.5 98.7 130 98.4 99.6 

Montana 250 77.9 93.3 190 98.9 99.3 

New Jersey 140 99.3 98.6 110 98.2 95.0 

New Mexico2 160 83.3 84.7 130 93.8 97.5 

New York 190 97.9 98.9 150 99.3 99.8 

North Carolina 180 96.0 97.5 170 97.6 96.4 

North Dakota 260 74.3 93.3 210 81.3 93.1 

Ohio 200 99.0 99.4 160 98.1 99.4 

Oklahoma 180 98.9 99.6 140 98.6 98.7 

South Carolina 120 99.2 99.2 110 97.2 98.3 

Tennessee 140 98.6 98.2 120 100.0 100.0 

Texas 380 98.4 97.7 300 98.6 98.0 

Washington 140 97.8 99.0 130 99.2 100.0 

West Virginia 200 97.4 98.0 150 92.5 89.5 

Wisconsin2 170 58.6 65.5 130 65.4 70.7 

Wyoming 160 89.0 97.2 170 97.6 97.2 

1

 Rounded to the nearest 10 for confidentiality. 

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at 

least one of the years. 

NOTE: In the comparison schools, the population represented by NAEP is less than 100 percent of the total population where state 

assessment scores are missing for some schools. Scores may be missing either because of the failure to match schools in the two

surveys or the suppression of scores where there are too few students. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

37 
Table 16. Number of NAEP schools, percentage of NAEP schools available for comparing state 

assessment results with NAEP results in grade 8 mathematics, and percentage of the 

student population in the comparison schools, by state: 2005 and 2007 

 2005 2007 

Percent of Percent of Percent of Percent of 

NAEP NAEP schools population NAEP NAEP schools population 

State/jurisdiction schools1 matched represented schools1 matched represented 

Alaska 100 58.4 90.7 110 98.2 99.3 

Arizona 130 96.2 98.7 130 97.7 99.1 

Arkansas2 130 84.0 88.8 130 90.4 94.5 

Colorado 120 89.3 97.7 120 93.1 98.6 

Connecticut 110 96.2 96.7 100 100.0 100.0 

Delaware 40 86.0 93.4 50 100.0 100.0 

Florida 160 95.7 95.7 160 98.7 98.6 

Georgia 120 92.7 92.0 120 97.5 95.4 

Hawaii 70 98.5 99.8 70 95.7 99.8 

Idaho 100 93.2 97.3 100 98.1 99.1 

Illinois 190 98.4 98.6 200 98.0 99.4 

Indiana 110 98.1 98.1 110 100.0 100.0 

Iowa 110 98.2 96.6 140 96.3 96.9 

Kentucky 120 99.1 99.2 110 98.2 98.7 

Louisiana 110 98.2 98.5 110 96.4 97.7 

Maine2 130 67.2 80.5 130 94.7 97.6 

Maryland 110 98.1 99.2 110 99.1 97.2 

Massachusetts 130 97.7 99.4 130 99.3 99.2 

Michigan 120 95.7 97.6 120 96.7 97.9 

Mississippi 120 96.5 97.6 110 97.4 97.7 

Missouri 130 96.2 97.7 130 94.7 96.2 

Montana 160 79.9 96.0 170 98.2 99.4 

Nevada 80 88.3 92.5 80 93.3 93.6 

New Jersey 110 99.1 96.9 110 100.0 100.0 

New Mexico2 110 81.1 84.2 110 97.3 99.6 

New York 180 95.1 95.7 160 98.1 98.5 

North Carolina 140 95.0 97.7 150 99.3 99.7 

North Dakota2 180 73.4 92.5 180 70.3 89.6 

Ohio 140 95.1 97.0 190 98.9 98.8 

Oklahoma 150 95.9 97.2 150 96.6 96.8 

Oregon 120 99.2 99.8 110 96.5 99.2 

Pennsylvania 110 94.5 96.1 110 98.2 97.5 

South Carolina 110 97.2 95.8 110 97.2 98.8 

Tennessee 110 99.1 99.4 120 99.2 99.2 

Texas 280 97.1 98.0 220 96.4 97.6 

Virginia 110 100.0 100.0 110 100.0 100.0 

West Virginia 110 97.3 99.0 120 91.5 91.0 

Wisconsin2 120 79.7 86.5 130 74.6 82.6 

Wyoming 80 96.3 96.5 80 96.3 97.1 

1

 Rounded to the nearest 10 for confidentiality. 

2

 The percentage of the student population represented by the NAEP schools used in the estimations was less than 90 percent in at 

least one of the years. 

NOTE: In the comparison schools, the population represented by NAEP is less than 100 percent of the total population where state 

assessment scores are missing for some schools. Scores may be missing either because of the failure to match schools in the two

surveys or the suppression of scores where there are too few students. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

38
Table 17. Difference between the estimated NAEP scale equivalents of state grade 4 

mathematics proficient standards and their standard error, by state: 2005 and 2007 

2005 2007 

NAEP NAEP 

scale Standard scale Standard Difference Standard 

State/jurisdiction equivalent error equivalent error 2007-2005 error 

2005 and 2007 state assessment reported results are comparable

Alabama 207 0.9 205 1.5 -1.6 1.72 

Alaska 222 1.1 216 1.3 -5.8 * 1.74 

Arkansas 236 1.1 229 0.6 -6.7 * 1.26 

California 231 0.6 226 0.7 -5.1 * 0.92 

Colorado 201 1.2 201 1.6 -0.1 2.04 

Florida 230 0.8 230 0.8 -0.7 1.19 

Georgia 215 1.0 213 0.8 -1.4 1.28 

Indiana 225 228 0.9 2.5 * 1.14 0.7 

Iowa 219 0.8 220 1.1 0.4 1.38 

Louisiana 223 0.9 223 1.3 0.2 1.61 

Maryland 215 1.1 206 1.3 -8.3 * 1.65 

Massachusetts 255 0.8 254 1.0 -0.9 1.24 

Mississippi 206 1.1 204 0.8 -1.6 1.38 

New Jersey 221 220 1.1 1.4 -0.9 1.77 

New Mexico 232 1.3 233 0.8 0.4 1.50 

North Dakota 224 0.8 226 1.0 1.8 1.29 

South Carolina 246 245 0.9 1.0 -1.4 1.33 

Tennessee 200 1.2 198 1.3 -1.4 1.75 

Texas 219 1.0 217 0.9 -2.5 1.36 

Washington 236 240 0.8 4.3 * 1.12 0.8 

Wisconsin 224 1.4 222 2.3 -2.1 2.73 

2005 and 2007 state assessment reported results are not comparable 

Connecticut 221 0.8 220 0.7 -0.8 1.12 

Hawaii 247 1.0 238 0.5 -8.9 * 1.13 

Idaho 207 2.2 217 0.9 10.2 * 2.34 

Kansas 218 1.6 219 1.3 0.8 2.02 

Maine 249 0.8 236 0.8 -12.8 * 1.13 

Michigan 222 1.6 204 1.6 -18.3 * 2.23 

Missouri 242 245 0.8 2.8 * 1.28 1.0 

Montana 220 0.6 234 1.0 13.4 * 1.16 

New York 207 219 0.8 1.4 12.0 * 1.60 

North Carolina 203 231 0.6 0.9 28.4 * 1.12 

Ohio 233 0.9 225 1.3 -8.1 * 1.57 

Oklahoma 218 0.8 213 1.5 -5.1 * 1.68 

West Virginia 215 1.1 217 1.3 2.2 1.66 

Wyoming 251 0.8 216 0.6 -34.7 * 0.98 

* Difference is statistically significant at p < .05. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

39 
Table 18. Difference between the estimated NAEP scale equivalents of state grade 8 

mathematics proficient standards and their standard error, by state: 2005 and 2007 

2005 2007 

NAEP NAEP 

scale Standard scale Standard Difference Standard 

State/jurisdiction equivalent error equivalent error 2007-2005 error 

2005 and 2007 state assessment reported results are comparable

Alaska 268 1.2 265 1.2 -3.0 1.70 

Arizona 265 1.0 268 1.1 2.7 1.46 

Arkansas 288 0.7 277 1.3 -11.0 * 1.54 

Colorado 258 1.7 259 1.3 1.2 2.19 

Florida 269 1.1 266 0.9 -3.0 * 1.37 

Georgia 255 0.9 243 1.7 -11.7 * 1.89 

Indiana 266 0.9 266 1.6 0.7 1.80 

Iowa 262 1.3 264 1.5 2.0 2.00 

Louisiana 264 0.8 267 1.2 2.7 1.50 

Maryland 276 1.2 278 1.5 1.9 1.94 

Mississippi 262 1.4 262 0.9 0.5 1.62 

Nevada 271 1.5 267 1.2 -3.8 * 1.90 

New Jersey 273 1.1 272 0.8 -0.9 1.37 

New Mexico 287 1.6 285 0.9 -1.3 1.79 

North Dakota 277 0.9 279 0.8 2.1 1.22 

Ohio 274 1.2 265 1.2 -9.2 * 1.64 

Pennsylvania 272 0.6 271 1.0 -0.7 1.20 

South Carolina 305 0.9 312 1.4 6.8 * 1.63 

Tennessee 230 1.3 234 2.2 4.3 2.51 

Texas 272 0.6 268 1.0 -4.2 * 1.21 

Wisconsin 263 1.1 262 1.7 -1.5 2.00 

2005 and 2007 state assessment reported results are not comparable 

Connecticut 257 1.6 252 2.0 -4.6 2.56 

Delaware 275 0.9 272 0.9 -3.2 * 1.30 

Hawaii 296 1.2 294 0.8 -2.1 1.39 

Idaho 266 1.8 265 1.6 -0.8 2.43 

Illinois 276 0.9 251 0.8 -25.1 * 1.25 

Kentucky 285 1.1 279 0.7 -6.2 * 1.34 

Maine 300 1.2 286 0.9 -13.9 * 1.47 

Massachusetts 301 1.1 302 1.1 1.6 1.52 

Michigan 269 1.3 260 1.5 -8.4 * 1.98 

Missouri 311 1.3 289 1.2 -22.2 * 1.77 

Montana 271 1.1 281 1.7 10.4 * 2.02 

New York 275 0.8 273 1.1 -2.5 1.40 

North Carolina 247 1.5 270 1.3 22.7 * 1.92 

Oklahoma 258 0.7 249 1.1 -8.9 * 1.33 

Oregon 269 1.2 262 1.2 -6.9 * 1.64 

Virginia 253 1.0 259 1.6 6.1 * 1.84 

West Virginia 253 0.9 253 1.0 0.4 1.36 

Wyoming 293 1.0 279 0.8 -13.4 * 1.30 

* Difference is statistically significant at p < .05. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

40
41 

5 CORROBORATING STATE ASSESSMENT MEASURES OF ACHIEVEMENT 

CHANGE WITH NAEP 

In this section, we compare the change from 2005 to 2007 in the percentage of students meeting 

the state’s standard and the change from 2005 to 2007 in the percentage of students meeting the 

NAEP scale equivalent of the same state’s standard. For the year for which the NAEP scale 

equivalent is computed, the percentage meeting the state’s standard and the percentage meeting 

the NAEP scale equivalent are, by definition, the same. Therefore, to compare NAEP and state 

changes in achievement from 2005 to 2007, the percentage of students reported to be meeting 

the state standard in 2007 is compared with the percentage of the NAEP students in 2007 that 

are above the NAEP scale equivalent of the state standard in 2005. 

Described in Section 2, the statistic D is defined as the discrepancy between the change from 

2005 to 2007 in the percentage meeting the state standard on the state test and the change in 

the same percentage when measured by NAEP.27 If the statistical test indicates that D is different 

from zero, students gained more between 2005 and 2007 on either the NAEP skill domain or on 

the state-specific skill domain, depending on whether D is positive or negative. When D is 

greater than zero, the change from 2005 to 2007 on the state assessment is more positive (or less 

negative) than the change from 2005 to 2007 on NAEP. This could happen in two ways. If the 

percentage of students meeting the standard on the state test increased, the comparison with 

NAEP would show a smaller increase in NAEP’s percentage (or even a decrease). If a smaller 

percentage of students met the standard on the state test, the comparison with NAEP would 

show a larger loss on NAEP. 

When D is less than zero, the change on the state assessment is less positive (or more negative) 

than the change on NAEP. This could also happen in two ways. If more students met the 

standard on the state test over these 2 years, the comparison with NAEP would show that even 

more students gained on NAEP than on the state test. If fewer students met the standard on the 

state test over this period, the comparison with NAEP would show either a smaller loss or a gain 

in student achievement. A focus on state-specific content during instruction might lead to a 

positive value for D, whereas a focus on NAEP content might lead to a negative value for D. 

 

27 In Section 2, equation 5 defined D. Rearranging the terms in the equation, D can be rewritten as (DS – DN ), where 

DS is the change from 2005 to 2007 in achievement measured by the state test, and DN is the change from 2005 to 

2007 in achievement measured by the mapping. When D > 0, i.e., DS > DN, the change from 2005 to 2007 on the 

state assessment is more positive (or less negative) than the change from 2005 to 2007 on NAEP. For D < 0, that is 

DS < DN, the change on the state assessment is less positive (or more negative) than the change on NAEP. 

To use Wisconsin reading grade 4 as an example from table 19, 

DS = 79.5 – 82.8 = -3.3 

DN = 83.3 – 82.8 = -3.5 

D = DS – DN = -3.8 

For Wisconsin reading grade 8, 

DS = 82.7 – 85.8 = -3.1 

DN = 84.8 – 85.8 = -1.0 

D = DS – DN = -2.1 

In both situations, the changes on the state assessment are less positive (or more negative) than the changes on 

NAEP. 
If either NAEP or a state test has substantively changed between the two years, then 

comparisons of achievement changes identified by the two tests are not warranted. In the years 

from 2005 to 2007, many states changed their state assessments as shown in the tables in 

appendix B, and finding values of D significantly different from zero in those cases is to be 

expected. 

Tables 19 through 22 display comparisons limited to the states that reported no significant 

changes in their own assessments between 2005 and 2007 that are large enough to affect the 

direct comparability of the 2005 and the 2007 reported results.28

Table 19 shows that of the 22 states with comparable test results in grade 4 reading, 11 showed 

no statistically significant difference between NAEP and state assessment changes in 

achievement between 2005 and 2007 (Alaska, California, Colorado, Indiana, Iowa, Maryland, 

Massachusetts, Mississippi, New Mexico, North Carolina, and Ohio), 5 showed changes that are 

more positive than the changes measured by NAEP (Arkansas, Louisiana, North Dakota, South 

Carolina, and Texas), and 6 states showed changes that are less positive than those measured by 

NAEP (Alabama, Florida, New Jersey, Tennessee, Washington, and Wisconsin). 

Table 19. NAEP and state assessment percentages meeting the state grade 4 reading proficient 

standard in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at Standard 

the standard the 2005 standard the standard Difference error of 

State/jurisdiction in 20051 in 2007 in 2007 D D 

Alabama 82.4 88.8 85.3 -3.5 * 0.86 

Alaska 79.2 81.0 80.4 -0.6 0.77 

Arkansas 53.5 53.2 57.9 4.6 * 1.05 

California 47.8 51.0 50.7 -0.3 0.73 

Colorado 86.0 86.0 85.7 -0.3 0.78 

Florida 70.8 76.2 69.5 -6.7 * 0.75 

Indiana 72.3 76.6 76.1 -0.4 0.97 

Iowa 77.3 82.9 81.5 -1.3 1.29 

Louisiana 65.4 62.7 67.1 4.4 * 1.63 

Maryland 82.0 86.4 86.9 0.5 1.00 

Massachusetts 48.3 53.4 56.3 2.8 1.46 

Mississippi 88.1 91.2 90.1 -1.2 0.65 

New Jersey 81.0 88.2 81.7 -6.5 * 0.92 

New Mexico 50.3 57.6 55.7 -1.9 1.31 

North Carolina 82.4 84.5 85.0 0.5 0.74 

North Dakota 76.5 79.6 81.8 2.2 * 1.12 

Ohio 76.6 81.4 81.6 0.2 1.13 

South Carolina 34.7 36.2 42.4 6.2 * 1.21 

Tennessee 87.9 89.8 87.6 -2.2 * 0.79 

Texas 80.6 81.6 83.5 1.9 * 0.81 

Washington 79.6 79.4 75.1 -4.3 * 1.11 

Wisconsin 82.8 83.3 79.5 -3.8 * 0.95 

* Difference is statistically significant at p < .05. 

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

28 Appendix C presents the results for all states with available data. 

42
Table 20. NAEP and state assessment percentages meeting the state grade 8 reading proficient

standard in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

Alabama 69.3 69.1 71.4 2.3 * 1.07 

Alaska 81.8 81.3 79.3 -2.0 * 0.93 

Arizona 63.2 63.6 62.8 -0.9 1.06 

Arkansas 57.6 58.0 63.8 5.8 * 1.22 

California 39.2 41.1 41.9 0.8 0.82 

Colorado 85.9 87.9 87.0 -0.9 0.87 

Florida 43.5 46.9 50.7 3.7 * 0.78 

Illinois 72.5 73.0 80.8 7.8 * 1.22 

Indiana 66.3 70.0 68.5 -1.5 0.96 

Iowa 72.3 74.1 72.8 -1.3 1.17 

Louisiana 54.0 55.0 60.5 5.5 * 1.40 

Maryland 67.7 74.4 69.3 -5.1 * 1.17 

Mississippi 57.3 56.2 50.5 -5.7 * 1.14 

Nevada 52.7 52.1 57.6 5.5 * 0.98 

New Jersey 73.8 75.7 74.0 -1.7 1.13 

New Mexico 51.9 53.6 56.0 2.4 * 1.17 

North Carolina 87.6 88.1 87.9 -0.2 0.76 

North Dakota 72.2 71.4 76.5 5.2 * 1.46 

Ohio 80.1 81.4 82.2 0.8 0.89 

Pennsylvania 64.3 65.5 77.2 11.7 * 1.31 

South Carolina 30.3 30.0 24.7 -5.3 * 1.19 

Tennessee 87.4 88.0 92.5 4.4 * 0.81 

Texas 83.4 86.5 87.8 1.3 0.68 

Wisconsin 85.8 84.8 82.7 -2.1 * 0.90 

* Difference is statistically significant at p < .05.

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 


Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-


Level State Assessment Score Database (NLSLSASD) 2008.

For grade 8 reading, table 20 shows that 9 of the 24 states with comparable assessments did not 

show statistically significant differences between NAEP and state assessment changes in 

achievement between 2005 and 2007 (Arizona, California, Colorado, Indiana, Iowa, New Jersey, 

North Carolina, Ohio, and Texas), 10 states showed changes that are more positive than the 

changes measured by NAEP (Alabama, Arkansas, Florida, Illinois, Louisiana, Nevada, New 

Mexico, North Dakota, Pennsylvania, and Tennessee), and 5 showed changes that are less 

positive than those measured by NAEP (Alaska, Maryland, Mississippi, South Carolina, and 

Wisconsin). 

43 
Table 21. NAEP and state assessment percentages meeting the state grade 4 mathematics 

proficient standard in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

Alabama 74.0 77.3 78.7 1.4 1.29 

Alaska 70.7 71.3 76.7 5.3 * 1.20 

Arkansas 52.9 55.3 64.8 9.5 * 1.09 

California 51.4 51.2 57.3 6.1 * 0.76 

Colorado 89.7 90.1 90.1 0.0 0.67 

Florida 63.1 68.9 69.7 0.8 1.09 

Georgia 74.5 77.4 78.9 1.5 0.95 

Indiana 72.3 79.9 77.0 -2.9 * 1.13 

Iowa 79.5 82.6 82.2 -0.4 1.04 

Louisiana 62.6 61.7 61.3 -0.4 1.48 

Maryland 78.1 79.5 86.3 6.9 * 1.28 

Massachusetts 38.5 47.0 48.6 1.5 1.78 

Mississippi 78.8 79.3 81.0 1.8 1.06 

New Jersey 80.7 84.5 85.3 0.8 0.98 

New Mexico 38.6 46.7 46.1 -0.5 1.07 

North Dakota 80.1 82.3 80.4 -1.9 * 0.85 

South Carolina 38.9 39.8 41.7 1.9 1.07 

Tennessee 86.8 88.3 89.2 0.9 0.82 

Texas 81.7 82.5 84.9 2.3 * 0.88 

Washington 60.5 62.9 56.9 -5.9 * 1.14 

Wisconsin 74.1 75.6 76.1 0.5 1.33 

* Difference is statistically significant at p < .05.

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-


Level State Assessment Score Database (NLSLSASD) 2008.

Table 21 shows that of the 21 states with comparable test results in grade 4 mathematics, 13 

showed no statistically significant difference between NAEP and state assessment changes in 

achievement between 2005 and 2007 (Alabama, Colorado, Florida, Georgia, Iowa, Louisiana, 

Massachusetts, Mississippi, New Jersey, New Mexico, South Carolina, Tennessee, and 

Wisconsin), 5 states showed changes that are more positive than the changes measured by 

NAEP (Alaska, Arkansas, California, Maryland, and Texas), and 3 showed changes that are less 

positive than those measured by NAEP (Indiana, North Dakota, and Washington). 

44
Table 22. NAEP and state assessment percentages meeting the state grade 8 mathematics 

proficient standard in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

Alaska 65.1 67.2 70.0 2.9 * 1.12 

Arizona 60.5 63.1 60.2 -2.9 * 1.12 

Arkansas 33.7 36.3 48.4 12.1 * 1.34 

Colorado 74.1 78.7 77.6 -1.0 0.94 

Florida 58.2 60.8 64.1 3.4 * 0.92 

Georgia 68.7 71.9 82.5 10.6 * 1.35 

Indiana 70.2 72.2 71.5 -0.7 1.23 

Iowa 75.6 77.6 75.6 -2.0 1.09 

Louisiana 56.3 62.3 58.7 -3.6 * 1.37 

Maryland 53.0 60.4 58.4 -2.0 1.22 

Mississippi 52.5 54.4 53.6 -0.8 1.13 

Nevada 51.1 49.6 53.8 4.1 * 0.89 

New Jersey 63.9 67.8 68.5 0.7 1.10 

New Mexico 23.6 28.5 29.7 1.2 0.92 

North Dakota 65.5 70.6 68.0 -2.6 * 1.28 

Ohio 62.7 65.0 74.0 9.0 * 1.22 

Pennsylvania 62.4 68.9 69.7 0.8 1.16 

South Carolina 23.8 25.7 19.9 -5.7 * 1.18 

Tennessee 87.8 90.8 88.5 -2.3 * 0.91 

Texas 60.9 67.4 71.9 4.5 * 0.99 

Wisconsin 74.9 75.4 74.4 -1.0 1.16 

* Difference is statistically significant at p < .05.

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-


Level State Assessment Score Database (NLSLSASD) 2008.

For grade 8 mathematics, table 22 shows that 9 out of 21 states with comparable assessments 

showed no statistically significant difference between NAEP and state assessment measures of 

changes in achievement between 2005 and 2007 (Colorado, Indiana, Iowa, Maryland, 

Mississippi, New Jersey, New Mexico, Pennsylvania, and Wisconsin), 7 states with changes that 

are more positive than the changes measured by NAEP (Alaska, Arkansas, Florida, Georgia, 

Nevada, Ohio, Texas), and 5 states with changes that are less positive than those measured by 

NAEP (Arizona, Louisiana, North Dakota, South Carolina, and Tennessee). 

Tables 23 through 25 summarize the results by listing where NAEP and state assessment do and 

do not agree. Table 23 lists the states that show changes in achievement in their own test that 

are corroborated by NAEP results, in the sense that state assessment and NAEP measures of 

changes in percentages of students meeting the state standards are not statistically significantly 

different from each other. Table 24 lists the states showing more positive changes in student 

achievement from 2005 to 2007 than NAEP, and table 25 lists the states with less positive 

changes than NAEP from 2005 to 2007. 

It is important to understand the reasons for the discrepancies. Because of the complexity of 

testing, in most cases, the source of the discrepancy (or drift) is likely to be some change in 

testing, such as in accommodation, exclusions, time of testing, or scaling methods. Even when 

these sources are ruled out, differences in the domains covered by the two tests can lead to 

discrepancies in achievement changes. While it is beyond the scope of this report to 

undertake such analyses, it may be valuable for the states where such differences exist to do so. 

45 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 23. States showing changes in student achievement from 2005 to 2007 in their own tests 

that are corroborated by NAEP results in the same period, by subject and grade 

Reading 	 Mathematics 

Grade 4 Grade 8	 Grade 4 Grade 8 

Alaska Arizona Alabama Colorado 

California California Colorado Indiana 

Colorado Colorado Florida Iowa 

Indiana Indiana Georgia Maryland 

Iowa Iowa Iowa Mississippi 

Maryland New Jersey Louisiana New Jersey 

Massachusetts North Carolina Massachusetts New Mexico 

Mississippi Ohio Mississippi Pennsylvania 

New Mexico Texas New Jersey Wisconsin 

North Carolina New Mexico 

Ohio South Carolina 

Tennessee 

Wisconsin 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading and Mathematics Assessments. U.S. Department of Education, 

Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal 

School-Level State Assessment Score Database (NLSLSASD) 2008. 

Table 24.	 States showing changes in student achievement from 2005 to 2007 in their own tests 

that are statistically significantly more positive than NAEP’s, by subject and grade 

Reading Mathematics 

Grade 4 Grade 8 Grade 4 Grade 8 

Arkansas

Louisiana

North Dakota 

South Carolina 

Texas

 Alabama 

 Arkansas 

Florida 

Illinois 

 Louisiana 

Nevada 

 New Mexico 

 North Dakota

 Pennsylvania

 Tennessee 

Alaska 

Arkansas 

California 

Maryland 

Texas 

Alaska 

Arkansas 

Florida 

Georgia 

Nevada

Ohio

Texas 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading and Mathematics Assessments. U.S. Department of Education, 

Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal 

School-Level State Assessment Score Database (NLSLSASD) 2008. 

Table 25.	 States showing changes in student achievement from 2005 to 2007 in their own tests 

that are statistically significantly less positive than NAEP’s, by subject and grade 

Reading Mathematics 

Grade 4 Grade 8 Grade 4 Grade 8 

Alabama 

Florida

New Jersey 

Tennessee 

Washington

Wisconsin 

Alaska 

 Maryland 

Mississippi 

South Carolina 

 Wisconsin 

Indiana 

North Dakota 

Washington 

Arizona 

Louisiana 

North Dakota 

South Carolina 

Tennessee 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading and Mathematics Assessments. U.S. Department of Education, 

Office of Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal 

School-Level State Assessment Score Database (NLSLSASD) 2008. 

46 
 

 

 

 

 

 

 

 

 

6 CONCLUSIONS
 

The mapping results described in this study have made it possible to compare state reading and 

mathematics proficiency standards across states, using grade 4 and 8 NAEP reading and 

mathematics scales as common yardsticks. The findings have also made it possible to evaluate 

consistency in the state standards over time and use NAEP to corroborate progress (or lack 

thereof) in the achievement assessed by states. Identifying a NAEP scale equivalent score for the 

state’s standard was an essential step for the analyses conducted in this study. These analyses 

were based on school-level percentages of students meeting a state’s standard on a state’s own 

tests, which are systematically available for almost every state and could be compared with 

student performance on NAEP in the same schools. 

The purpose of state-to-NAEP comparisons is to aid in the interpretation of state assessment 

results by providing a benchmark. Despite the limitations of state-to-NAEP comparisons, there is 

a need for reliable information that compares state standards to one another. What does it mean 

to say that a student is proficient in reading in grade 4 in Massachusetts? Would a fourth-grader 

who is proficient in reading in Wyoming also be proficient in Massachusetts? The analyses 

presented in this study provide a basis for answering such questions. 

Mapping state standards for proficient performance on the NAEP scales showed wide variation 

among states in the rigor of their standards. The implication is that students of similar academic 

skills, but residing in different states, are being evaluated against different standards for 

proficiency in reading and mathematics. All NAEP scale equivalents of states’ reading standards 

were below NAEP’s Proficient range; and in mathematics, only two states’ NAEP scale equivalent 

were in the NAEP Proficient range (Massachusetts in grades 4 and 8, and South Carolina in grade 

8). In many cases, the NAEP scale equivalent for a state's standard, especially in grade 4 reading, 

mapped below the NAEP achievement level for Basic performance. There may well be valid 

reasons for state standards to fall below NAEP’s Proficient range. The comparisons simply provide 

a context for describing the rigor of performance standards that states across the country have 

adopted. 

Almost one-half of the states changed aspects of their assessment policies or the assessment itself 

between 2005 and 2007 in ways that prevented their reading or mathematics test results from 

being comparable across these two years. Either explicitly or implicitly, such states have adopted 

new performance standards. By mapping the state standards in both years to the same NAEP 

scale, the changes in rigor of the standards can be measured. For states with both years of data, 

the mapping results showed that the NAEP equivalents representing state standards for 

proficiency were lower in 2007 in one-third to one-half of the states that made such changes 

(depending on subject and grade). A decrease in the stringency of the NAEP equivalent of state 

standards was more likely to occur for grade 8 than for grade 4. 

In the remaining states in which no changes were made or the changes in assessment policies 

were minor enough that their test results remained comparable, it was possible to check the 

extent to which NAEP corroborates the changes in achievement measured in the states’ 

assessments. In two-fifths to three-fifths of the states (depending on subject and grade), NAEP’s 

measurements of student progress agreed with the progress measured by state assessments. In 

cases in which NAEP and the state disagreed on their measurement of student progress, the 

47 
 

 

findings could both be accurate, as the underlying domains of the two tests may not involve the 

same skills or the same skills in equal weights. Similarly, there may have been a methodological 

change between 2005 and 2007 in the state tests, in such areas as exclusions, time of 

administrations, or scaling. 

In all three sets of analyses, assessing the relative rigor of state standards, describing changes in 

relative rigor of standards when states establish new policies or testing systems, and corroborating 

state progress in student performance, the results of this study show that NAEP, as a common 

yardstick, is an essential benchmark for states in evaluating their standards. 

48 
 

 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES
 

Braun, H.I., and Qian, J. (2007). Mapping State Performance Standards Onto the NAEP Scale. 

Princeton, NJ: Educational Testing Service. 

Feuer, M.J., Holland, P.W., Green, B.F., Bertenthal, M.W., and Hemphill, F.C. (Eds). (1999). 

Uncommon Measures: Equivalency and Linkage of Educational Tests (Committee on Equivalency 

and Linkage of Educational Tests, National Research Council). Washington, DC: The National 

Academies Press. 

Ho, A., and Haertel, E. (2007). Apples to Apples: The Underlying Assumptions of State-NAEP 

Comparisons (Research brief). Retrieved July 14, 2007, from 

http://www.ccsso.org/content/PDFs/Ho Haertel CCSSO Brief2 Final.pdf. 

Koretz, D.M., Bertenthal, M.W., and Green, B.F. (Eds). (1999). Embedding Questions: The 

Pursuit of a Common Measure in Uncommon Tests, (Committee on Embedding Common Test 

Items in State and District Assessments, National Research Council). Washington, DC: The 

National Academies Press. 

McLaughlin, D.H. (2008). Measurement Error in Comparing NAEP and State Test Gains. Palo 

Alto, CA: American Institutes for Research. 

McLaughlin, D., and Bandeira de Mello, V. (2002). Comparison of State Elementary School 

Mathematics Achievement Standards, Using NAEP 2000. Paper presented at the annual meeting of 

the American Educational Research Association, New Orleans. 

McLaughlin, D., and Bandeira de Mello, V. (2003). Comparing State Reading and Math 

Performance Standards Using NAEP. Paper presented at the annual National Conference on 

Large-Scale Assessment, San Antonio. 

McLaughlin, D., and Bandeira de Mello, V. (2006). How to Compare NAEP and State Assessment 

Results. Paper presented at the annual National Conference on Large-Scale Assessment. 

Retrieved December 2007, from http://www.naepreports.org/task 1.1/LSAC_20050618.ppt. 

McLaughlin, D.H., Bandeira de Mello, V., Blankenship, C., Chaney, K., Esra, P., Hikawa, H., 

Rojas, D., William, P., and Wolman, M. (2008a). Comparison Between NAEP and State Reading 

Assessment Results: 2003 (NCES 2008-474). National Center for Education Statistics, Institute 

of Education Sciences, U.S Department of Education. Washington, DC. 

McLaughlin, D.H., Bandeira de Mello, V., Blankenship, C., Chaney, K., Esra, P., Hikawa, H., 

Rojas, D., William, P., and Wolman, M. (2008b). Comparison Between NAEP and State 

Mathematics Assessment Results: 2003 (NCES 2008-475). National Center for Education 

Statistics, Institute of Education Sciences, U.S Department of Education. Washington, DC. 

U.S. Department of Education, National Center for Education Statistics (2007). Mapping 2005 

State Proficiency Standards Onto the NAEP Scales (NCES 2007-482). Washington, DC: Author. 

Retrieved July 14, 2007, from http://nces.ed.gov/nationsreportcard/pdf/studies/2007482.pdf. 

49 

 

APPENDIX A 

NUMBER OF SCHOOLS IN THE NAEP SAMPLE AND THE PERCENTAGE OF 

SCHOOLS USED IN THE 2007 MAPPING 

Sample sizes and percentages of the 2007 NAEP samples used in comparisons are shown in tables 

A-1 and A-2 for reading and mathematics, respectively. For each grade, the tables display the 

number of public schools selected for NAEP in each state, the percentage of these schools 

included in the analyses in this report, and the percentage of the student population represented 

by the comparison schools. The percentage of the population represented by NAEP can be less 

than 100 percent either because of failure to match schools in the two databases or because 

scores for the school are suppressed on the data source. In general, because the schools missing 

state assessment scores are generally small schools, the percentages of student populations 

represented by the school used in the comparisons are generally higher than the percentages of 

schools. 

A-1 
Table A-1. Number of NAEP schools, percentage of NAEP schools available for comparing 

state assessment results with NAEP results in grades 4 and 8 reading, and the 

percentage of the student population in these comparison schools, by state: 2007 

 Grade 4 Grade 8 

Percent of Percent of Percent of Percent of 

NAEP NAEP schools population NAEP NAEP schools population 

State/jurisdiction schools1 matched represented schools1 matched represented 

Alabama 110 99.1 99.1 120 100.0 100.0 

Alaska 180 99.4 99.9 110 98.2 99.3 

Arizona 120 100.0 100.0 130 97.7 99.2 

Arkansas 120 96.6 97.6 120 91.1 94.5 

California 320 97.8 99.0 310 97.1 99.0 

Colorado 120 95.8 99.0 120 93.1 98.5 

Connecticut 110 100.0 100.0 100 100.0 100.0 

Delaware 100 100.0 100.0 50 97.8 100.0 

District of Columbia † — † † — †

Florida 160 97.6 97.2 160 98.7 98.6 

Georgia 160 98.7 96.4 120 97.5 95.6 

Hawaii 120 99.1 99.1 70 100.0 100.0 

Idaho 130 95.5 91.2 110 97.2 99.0 

Illinois 180 98.9 99.6 200 98.0 99.3 

Indiana 110 100.0 100.0 110 100.0 100.0 

Iowa 140 97.8 96.7 130 97.0 96.8 

Kansas 140 98.6 99.0 150 97.3 98.0 

Kentucky 120 97.4 98.1 110 98.2 98.3 

Louisiana 110 97.2 98.4 110 96.4 97.7 

Maine 150 93.4 95.4 130 94.7 97.4 

Maryland 110 98.2 98.4 110 99.1 97.3 

Massachusetts 170 100.0 100.0 140 99.3 99.4 

Michigan 120 99.2 98.7 120 96.7 98.3 

Minnesota 130 100.0 100.0 140 97.9 98.4 

Mississippi 120 97.4 97.1 110 97.4 97.9 

Missouri 130 98.4 99.4 130 94.7 95.8 

Montana 190 98.9 99.1 170 98.2 99.4 

Nebraska † — † † — †

Nevada 110 94.5 94.0 70 93.2 93.3 

New Hampshire 130 89.9 92.2 90 96.7 99.2 

New Jersey 110 98.2 95.1 110 100.0 100.0 

New Mexico 130 95.3 97.9 110 97.3 99.4 

New York 150 99.3 99.8 160 98.1 98.5 

North Carolina 170 97.6 96.5 150 99.3 99.8 

North Dakota 210 80.5 93.3 190 70.3 90.0 

Ohio 160 98.1 99.3 190 98.4 99.1 

Oklahoma 140 98.5 98.8 150 96.6 96.8 

Oregon 140 97.0 98.9 110 96.5 99.0 

Pennsylvania 110 99.1 98.5 110 98.2 97.6 

Rhode Island 110 100.0 100.0 60 100.0 100.0 

South Carolina 110 97.2 98.7 110 97.2 98.5 

South Dakota 190 98.4 98.0 140 99.3 99.7 

Tennessee 120 100.0 100.0 120 99.2 99.1 

Texas 300 98.6 97.9 220 96.4 97.4 

Utah † — † † — †

Vermont 190 85.4 93.9 120 86.8 97.5 

Virginia 110 97.4 97.1 110 99.1 98.9 

Washington 130 99.2 100.0 130 100.0 100.0 

West Virginia 150 92.5 89.7 120 91.5 91.1 

Wisconsin 130 65.4 71.0 130 74.6 82.1 

Wyoming 170 96.5 97.2 80 95.1 96.1 

— State assessment data not available.

† Not applicable.

1

 Rounded to the nearest 10 for confidentiality. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Reading Assessments. U.S. Department of Education, Office of Planning, 

Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State 

Assessment Score Database (NLSLSASD) 2008. 

A-2
Table A-2. Number of NAEP schools, percentage of NAEP schools available for comparing 

state assessment results with NAEP results in grades 4 and 8 mathematics, and 

percentage of the student population in these comparison schools, by state: 2007 

 Grade 4 Grade 8 

Percent of Percent of Percent of Percent of 

NAEP NAEP schools population NAEP NAEP schools population 

State/jurisdiction schools1 matched represented schools1 matched represented 

Alabama 110 99.1 99.1 120 100.0 100.0 

Alaska 180 100.0 100.0 110 98.2 99.3 

Arizona 120 100.0 100.0 130 97.7 99.1 

Arkansas 120 96.6 97.5 130 90.4 94.5 

California 330 97.5 98.9 310 95.5 97.8 

Colorado 120 95.8 99.1 120 93.1 98.6 

Connecticut 110 100.0 100.0 100 100.0 100.0 

Delaware 100 100.0 100.0 50 100.0 100.0 

District of Columbia † — † † — †

Florida 160 97.6 97.2 160 98.7 98.6 

Georgia 160 98.7 96.4 120 97.5 95.4 

Hawaii 120 99.1 99.0 70 95.7 99.8 

Idaho 130 95.5 91.8 100 98.1 99.1 

Illinois 180 98.9 99.5 200 98.0 99.4 

Indiana 110 100.0 100.0 110 100.0 100.0 

Iowa 140 97.8 96.9 140 96.3 96.9 

Kansas 140 98.6 99.0 150 97.3 98.0 

Kentucky 120 97.4 98.2 110 98.2 98.7 

Louisiana 110 97.2 98.4 110 96.4 97.7 

Maine 150 93.4 95.6 130 94.7 97.6 

Maryland 110 98.2 98.5 110 99.1 97.2 

Massachusetts 170 100.0 100.0 130 99.3 99.2 

Michigan 120 99.2 98.8 120 96.7 97.9 

Minnesota 130 100.0 100.0 140 98.5 98.2 

Mississippi 120 97.4 97.2 110 97.4 97.7 

Missouri 130 98.4 99.6 130 94.7 96.2 

Montana 190 98.9 99.3 170 98.2 99.4 

Nebraska † — † † — †

Nevada 110 94.6 93.6 80 93.3 93.6 

New Hampshire 130 89.9 92.1 90 97.8 99.2 

New Jersey 110 98.2 95.0 110 100.0 100.0 

New Mexico 130 93.8 97.5 110 97.3 99.6 

New York 150 99.3 99.8 160 98.1 98.5 

North Carolina 170 97.6 96.4 150 99.3 99.7 

North Dakota 210 81.3 93.1 180 70.3 89.6 

Ohio 160 98.1 99.4 190 98.9 98.8 

Oklahoma 140 98.6 98.7 150 96.6 96.8 

Oregon 140 97.0 98.9 110 96.5 99.2 

Pennsylvania 110 99.1 98.6 110 98.2 97.5 

Rhode Island 110 100.0 100.0 60 100.0 100.0 

South Carolina 110 97.2 98.3 110 97.2 98.8 

South Dakota 190 98.4 98.1 140 99.3 99.7 

Tennessee 120 100.0 100.0 120 99.2 99.2 

Texas 300 98.6 98.0 220 96.4 97.6 

Utah † — † † — †

Vermont 190 85.0 93.7 120 86.8 97.0 

Virginia 110 97.4 97.4 110 100.0 100.0 

Washington 130 99.2 100.0 130 100.0 100.0 

West Virginia 150 92.5 89.5 120 91.5 91.0 

Wisconsin 130 65.4 70.7 130 74.6 82.6 

Wyoming 170 97.6 97.2 80 96.3 97.1 

— State assessment data not available.

† Not applicable.

1

 Rounded to the nearest 10 for confidentiality. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2007 Mathematics Assessments. U.S. Department of Education, Office of Planning, 

Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-Level State 

Assessment Score Database (NLSLSASD) 2008. 

A-3 

 

 

 

 

 

 

 

 

 

APPENDIX B 

CHANGES IN STATES’ ASSESSMENTS BETWEEN 2005 AND 2007 

Tables B-1 and B-2 summarize selected changes in states’ assessments between the two NAEP 

administrations of 2005 and 2007. Their source is the 2007 Survey of State Assessment Program 

Characteristics, a survey designed to provide contextual information to document general state 

assessment program information, mainly from the section covering changes that were made to 

state assessments between the 2004-05 and 2006-07 school years. States were instructed to 

indicate whether they had added grades, eliminated grades, changed cut scores, changed the time 

of year when the test was administered, changed the assessment items significantly, used an 

entirely new assessment, realigned the assessment to new content standards, changed the 

proficiency standards, changed the accommodation policy, changed the re-test policy, or 

changed test contractors. Additionally, states could indicate that there were no significant changes 

to the state assessment between 2004-05 and 2006-07 or, if applicable, to describe any changes 

in further detail. 

States were also asked to indicate whether the following statement was true or false for grades 4 

and 8 Reading/Language Arts and Mathematics: 

The reported 2006–07 state assessment results for 4th- and 8th-grade Reading and Mathematics are 

directly comparable with the 2004–05 reported results. 

Finally, states were asked to indicate whether there were any policy or legislative changes in the 

administration of the Reading/Language Arts and Mathematics assessments or in the reporting of 

outcomes between 2004-05 and 2006-07 that would have an impact on the interpretation of 

school- or state-level results when comparing across years. Table B-3 summarizes these responses. 

State profiles tabulating the survey results are available at 

http://nces.ed.gov/nationsreportcard/studies/statemapping.asp. 

B-1 
Table B-1. Selected changes to state reading assessments between the 2004–05 and the 2006–07

administrations, by state 

Changed the Changed Entirely 

Added Eliminated Changed time of assessment different 

State/jurisdiction grades grades cut scores administration items assessment 

Alabama 

Alaska 

Arizona 

Arkansas 

California 

Colorado

Connecticut   

Delaware  

District of Columbia   

Florida

Georgia  

Hawaii    

Idaho   

Illinois   

Indiana

Iowa 

Kansas    

Kentucky   

Louisiana 

Maine     

Maryland

Massachusetts   

Michigan    

Minnesota  

Mississippi

Missouri   

Montana  

Nebraska   

Nevada 

New Hampshire     

New Jersey 

New Mexico

New York  

North Carolina

North Dakota

Ohio

Oklahoma 

Oregon  

Pennsylvania   

Rhode Island

South Carolina

South Dakota  

Tennessee

Texas

Utah  

Vermont 

Virginia  

Washington 

West Virginia 

Wisconsin 

Wyoming     

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

B-2
Table B-1. Selected changes to state reading assessments between the 2004–05 and the 2006–07

administrations, by state—Continued

Realigned to Changed Changed 

new content proficiency accommodation Changed Changed test No significant 

State/jurisdiction standards standards policy re-test policy contractors changes 

Alabama 

Alaska

Arizona

Arkansas 

California

Colorado 

Connecticut  

Delaware 

District of Columbia  

Florida 

Georgia   

Hawaii    

Idaho   

Illinois 

Indiana 

Iowa

Kansas  

Kentucky   

Louisiana

Maine    

Maryland 

Massachusetts

Michigan   

Minnesota   

Mississippi 

Missouri  

Montana

Nebraska

Nevada

New Hampshire   

New Jersey

New Mexico 

New York  

North Carolina 

North Dakota 

Ohio 

Oklahoma

Oregon 

Pennsylvania   

Rhode Island 

South Carolina 

South Dakota

Tennessee 

Texas 

Utah  

Vermont

Virginia   

Washington

West Virginia

Wisconsin

Wyoming    

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

B-3 
Table B-2. Selected changes to state mathematics assessments between the 2004–05 and the 


2006–07 administrations, by state 

Changed the Changed Entirely 

Added Eliminated Changed time of assessment different 

State/jurisdiction grades grades cut scores administration items assessment 

Alabama 

Alaska 

Arizona 

Arkansas 

California 

Colorado

Connecticut   

Delaware  

District of Columbia   

Florida

Georgia  

Hawaii    

Idaho   

Illinois    

Indiana

Iowa 

Kansas    

Kentucky   

Louisiana 

Maine     

Maryland

Massachusetts  

Michigan    

Minnesota   

Mississippi

Missouri   

Montana  

Nebraska   

Nevada 

New Hampshire     

New Jersey 

New Mexico

New York  

North Carolina   

North Dakota

Ohio 

Oklahoma 

Oregon  

Pennsylvania   

Rhode Island

South Carolina

South Dakota  

Tennessee

Texas

Utah  

Vermont 

Virginia  

Washington 

West Virginia 

Wisconsin 

Wyoming     

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

B-4
Table B-2. Selected changes to state mathematics assessments between the 2004–05 and the 


2006–07 administrations, by state—Continued

Realigned to Changed Changed 

new content proficiency accommodation Changed Changed test No significant 

State/jurisdiction standards standards policy re-test policy contractors changes 

Alabama 

Alaska

Arizona

Arkansas 

California

Colorado 

Connecticut  

Delaware 

District of Columbia  

Florida 

Georgia   

Hawaii   

Idaho   

Illinois 

Indiana 

Iowa

Kansas  

Kentucky   

Louisiana

Maine    

Maryland 

Massachusetts

Michigan   

Minnesota   

Mississippi 

Missouri 

Montana

Nebraska

Nevada

New Hampshire   

New Jersey

New Mexico 

New York  

North Carolina  

North Dakota 

Ohio

Oklahoma

Oregon 

Pennsylvania   

Rhode Island 

South Carolina 

South Dakota 

Tennessee 

Texas 

Utah  

Vermont

Virginia   

Washington

West Virginia

Wisconsin

Wyoming    

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

B-5 
Table B-3. Comparability of the 2007 state assessment results in reading and mathematics at 

grades 4 and 8 with the 2005 reported results, by state 

 Reading Mathematics 

State/jurisdiction Grade 4 Grade 8 Grade 4 Grade 8 

Alabama Yes Yes Yes Yes

Alaska Yes Yes Yes Yes

Arizona Yes Yes Yes Yes

Arkansas Yes Yes Yes Yes

California Yes Yes Yes Yes

Colorado Yes Yes Yes Yes

Connecticut No No No No

Delaware No No No No

District of Columbia No No No No

Florida Yes Yes Yes Yes

Georgia No No Yes Yes

Hawaii No No No No

Idaho No No No No

Illinois No Yes No No

Indiana Yes Yes Yes Yes

Iowa Yes Yes Yes Yes

Kansas No No No No

Kentucky No No No No

Louisiana Yes Yes Yes Yes

Maine No No No No

Maryland Yes Yes Yes Yes

Massachusetts Yes No Yes No

Michigan No No No No

Minnesota No No No No

Mississippi Yes Yes Yes Yes

Missouri No No No No

Montana No No No No

Nebraska No No No No

Nevada No Yes No Yes

New Hampshire No No No No

New Jersey Yes Yes Yes Yes

New Mexico Yes Yes Yes Yes

New York No No No No

North Carolina Yes Yes No No

North Dakota Yes Yes Yes Yes

Ohio Yes Yes No Yes

Oklahoma No No No No

Oregon No No No No

Pennsylvania No Yes No Yes

Rhode Island Yes Yes Yes Yes

South Carolina Yes Yes Yes Yes

South Dakota Yes Yes Yes Yes

Tennessee Yes Yes Yes Yes

Texas Yes Yes Yes Yes

Utah Yes No Yes Yes

Vermont Yes Yes Yes Yes

Virginia No No No No

Washington Yes No Yes No

West Virginia No No No No

Wisconsin Yes Yes Yes Yes

Wyoming No No No No

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP) 2007 Survey of State Assessment Program Characteristics. 

B-6
 

 

 

 

 

 

APPENDIX C 

SUPPLEMENTARY TABLES 

Tables C-1 through C-4 are equivalent to tables 19 through 22, respectively, but with the 

additional results for states with changes in their state assessments between 2005 and 2007. 

Tables C-5 and C-6, for reading and mathematics, respectively, list the number of states 

according to the statistical significance of the difference D and by whether changes in the state’s 

own assessments between 2005 and 2007 were deemed to affect the direct comparability of the 

2005 and the 2007 reported results. 

For the states with both years of data that are comparable according to state assessment staff, 

tables C-7 through C-10 list selected changes to state assessments between 2005 and 2007, by 

whether reports of achievement changes from 2005 to 2007 in the state test and NAEP agree. 

C-1 
Table C-1. NAEP and state assessment percentages meeting the state grade 4 reading proficient

standards in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at Standard 

the standard the 2005 standard the standard Difference error of 

State/jurisdiction in 20051 in 2007 in 2007 D D 

2005 and 2007 state assessment reported results are comparable

Alabama 82.4 88.8 85.3 -3.5 * 0.86 

Alaska 79.2 81.0 80.4 -0.6 0.77 

Arkansas 53.5 53.2 57.9 4.6 * 1.05 

California 47.8 51.0 50.7 -0.3 0.73 

Colorado 86.0 86.0 85.7 -0.3 0.78 

Florida 70.8 76.2 69.5 -6.7 * 0.75 

Indiana 72.3 76.6 76.1 -0.4 0.97 

Iowa 77.3 82.9 81.5 -1.3 1.29 

Louisiana 65.4 62.7 67.1 4.4 * 1.63 

Maryland 82.0 86.4 86.9 0.5 1.00 

Massachusetts 48.3 53.4 56.3 2.8 1.46 

Mississippi 88.1 91.2 90.1 -1.2 0.65 

New Jersey 81.0 88.2 81.7 -6.5 * 0.92 

New Mexico 50.3 57.6 55.7 -1.9 1.31 

North Carolina 82.4 84.5 85.0 0.5 0.74 

North Dakota 76.5 79.6 81.8 2.2 * 1.12 

Ohio 76.6 81.4 81.6 0.2 1.13 

South Carolina 34.7 36.2 42.4 6.2 * 1.21 

Tennessee 87.9 89.8 87.6 -2.2 * 0.79 

Texas 80.6 81.6 83.5 1.9 * 0.81 

Washington 79.6 79.4 75.1 -4.3 * 1.11 

Wisconsin 82.8 83.3 79.5 -3.8 * 0.95 

2005 and 2007 state assessment reported results are not comparable

Connecticut 66.4 69.1 68.4 -0.6 1.06 

Georgia 86.5 91.2 85.2 -6.0 * 0.68 

Hawaii 56.4 62.3 54.6 -7.6 * 1.14 

Idaho 86.9 88.0 80.4 -7.6 * 0.77 

Kentucky 67.0 70.1 71.7 1.6 1.29 

Maine 52.8 54.4 67.1 12.7 * 1.13 

Michigan 83.4 85.3 87.4 2.0 * 0.98 

Montana 80.6 83.9 79.9 -4.0 * 0.90 

New York 70.5 70.8 68.4 -2.4 * 1.14 

Oklahoma 82.2 86.3 90.9 4.6 * 0.97 

West Virginia 80.4 80.8 83.2 2.4 * 0.97 

Wyoming 46.9 49.7 76.9 27.1 * 0.91 

* Difference is statistically significant at p < .05. 

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-2
Table C-2. NAEP and state assessment percentages meeting the state grade 8 reading proficient 

standards in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

2005 and 2007 state assessment reported results are comparable

Alabama 69.3 69.1 71.4 2.3 * 1.07 

Alaska 81.8 81.3 79.3 -2.0 * 0.93 

Arizona 63.2 63.6 62.8 -0.9 1.06 

Arkansas 57.6 58.0 63.8 5.8 * 1.22 

California 39.2 41.1 41.9 0.8 0.82 

Colorado 85.9 87.9 87.0 -0.9 0.87 

Florida 43.5 46.9 50.7 3.7 * 0.78 

Illinois 72.5 73.0 80.8 7.8 * 1.22 

Indiana 66.3 70.0 68.5 -1.5 0.96 

Iowa 72.3 74.1 72.8 -1.3 1.17 

Louisiana 54.0 55.0 60.5 5.5 * 1.40 

Maryland 67.7 74.4 69.3 -5.1 * 1.17 

Mississippi 57.3 56.2 50.5 -5.7 * 1.14 

Nevada 52.7 52.1 57.6 5.5 * 0.98 

New Jersey 73.8 75.7 74.0 -1.7 1.13 

New Mexico 51.9 53.6 56.0 2.4 * 1.17 

North Carolina 87.6 88.1 87.9 -0.2 0.76 

North Dakota 72.2 71.4 76.5 5.2 * 1.46 

Ohio 80.1 81.4 82.2 0.8 0.89 

Pennsylvania 64.3 65.5 77.2 11.7 * 1.31 

South Carolina 30.3 30.0 24.7 -5.3 * 1.19 

Tennessee 87.4 88.0 92.5 4.4 * 0.81 

Texas 83.4 86.5 87.8 1.3 0.68 

Wisconsin 85.8 84.8 82.7 -2.1 * 0.90 

2005 and 2007 state assessment reported results are not comparable

Connecticut 76.7 77.4 75.3 -2.1 * 0.99 

Delaware 80.5 78.2 80.0 1.8 * 0.78 

Georgia 82.6 85.5 89.8 4.3 * 0.94 

Hawaii 37.3 41.0 60.4 19.4 * 1.09 

Idaho 82.0 84.6 86.1 1.5 * 0.73 

Kansas 78.0 81.2 82.1 0.9 0.93 

Maine 44.1 44.7 64.4 19.7 * 1.73 

Montana 72.2 76.7 79.2 2.6 * 1.01 

New York 48.6 47.8 57.4 9.6 * 1.08 

Oklahoma 71.2 71.3 81.4 10.1 * 1.09 

Oregon 63.7 67.6 70.5 2.9 * 1.19 

Virginia 78.2 78.4 82.0 3.6 * 1.22 

West Virginia 79.8 80.4 80.4 0.0 1.28 

Wyoming 39.0 37.7 72.8 35.1 * 1.11 

* Difference is statistically significant at p < .05.

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-


Level State Assessment Score Database (NLSLSASD) 2008.

C-3 
Table C-3. NAEP and state assessment percentages meeting the state grade 4 mathematics 

proficient standards in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

2005 and 2007 state assessment reported results are comparable

Alabama 74.0 77.3 78.7 1.4 1.29 

Alaska 70.7 71.3 76.7 5.3 * 1.20 

Arkansas 52.9 55.3 64.8 9.5 * 1.09 

California 51.4 51.2 57.3 6.1 * 0.76 

Colorado 89.7 90.1 90.1 0.0 0.67 

Florida 63.1 68.9 69.7 0.8 1.09 

Georgia 74.5 77.4 78.9 1.5 0.95 

Indiana 72.3 79.9 77.0 -2.9 * 1.13 

Iowa 79.5 82.6 82.2 -0.4 1.04 

Louisiana 62.6 61.7 61.3 -0.4 1.48 

Maryland 78.1 79.5 86.3 6.9 * 1.28 

Massachusetts 38.5 47.0 48.6 1.5 1.78 

Mississippi 78.8 79.3 81.0 1.8 1.06 

New Jersey 80.7 84.5 85.3 0.8 0.98 

New Mexico 38.6 46.7 46.1 -0.5 1.07 

North Dakota 80.1 82.3 80.4 -1.9 * 0.85 

South Carolina 38.9 39.8 41.7 1.9 1.07 

Tennessee 86.8 88.3 89.2 0.9 0.82 

Texas 81.7 82.5 84.9 2.3 * 0.88 

Washington 60.5 62.9 56.9 -5.9 * 1.14 

Wisconsin 74.1 75.6 76.1 0.5 1.33 

2005 and 2007 state assessment reported results are not comparable

Connecticut 78.2 78.5 79.2 0.6 0.89 

Hawaii 29.6 36.2 48.9 12.7 * 0.92 

Idaho 90.6 89.2 82.2 -7.0 * 0.76 

Kansas 85.3 86.8 86.2 -0.6 1.08 

Maine 39.8 42.3 61.2 19.0 * 1.18 

Michigan 73.0 72.6 87.3 14.7 * 1.24 

Missouri 40.9 48.2 44.3 -3.8 * 1.49 

Montana 79.8 82.3 67.8 -14.5 * 1.07 

New York 86.6 89.1 80.9 -8.2 * 0.72 

North Carolina 91.5 92.0 66.5 -25.4 * 0.84 

Ohio 65.2 69.2 78.2 9.1 * 1.44 

Oklahoma 73.7 78.1 83.2 5.1 * 1.33 

West Virginia 74.7 80.8 78.4 -2.4 * 1.14 

Wyoming 39.2 41.0 87.0 46.0 * 0.92 

* Difference is statistically significant at p < .05. 

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-4
Table C-4. NAEP and state assessment percentages meeting the state grade 8 mathematics 

proficient standards in 2007 based on 2005 standards, by state 

State percent at NAEP percent at State percent at 

the standard the 2005 standard the standard Standard 

State/jurisdiction in 20051 in 2007 in 2007 Difference D error of D 

2005 and 2007 state assessment reported results are comparable

Alaska 65.1 67.2 70.0 2.9 * 1.12 

Arizona 60.5 63.1 60.2 -2.9 * 1.12 

Arkansas 33.7 36.3 48.4 12.1 * 1.34 

Colorado 74.1 78.7 77.6 -1.0 0.94 

Florida 58.2 60.8 64.1 3.4 * 0.92 

Georgia 68.7 71.9 82.5 10.6 * 1.35 

Indiana 70.2 72.2 71.5 -0.7 1.23 

Iowa 75.6 77.6 75.6 -2.0 1.09 

Louisiana 56.3 62.3 58.7 -3.6 * 1.37 

Maryland 53.0 60.4 58.4 -2.0 1.22 

Mississippi 52.5 54.4 53.6 -0.8 1.13 

Nevada 51.1 49.6 53.8 4.1 * 0.89 

New Jersey 63.9 67.8 68.5 0.7 1.10 

New Mexico 23.6 28.5 29.7 1.2 0.92 

North Dakota 65.5 70.6 68.0 -2.6 * 1.28 

Ohio 62.7 65.0 74.0 9.0 * 1.22 

Pennsylvania 62.4 68.9 69.7 0.8 1.16 

South Carolina 23.8 25.7 19.9 -5.7 * 1.18 

Tennessee 87.8 90.8 88.5 -2.3 * 0.91 

Texas 60.9 67.4 71.9 4.5 * 0.99 

Wisconsin 74.9 75.4 74.4 -1.0 1.16 

2005 and 2007 state assessment reported results are not comparable

Connecticut 75.9 77.3 80.6 3.3 * 0.99 

Delaware 56.3 58.8 62.9 4.1 * 1.29 

Hawaii 20.4 23.8 25.7 1.9 * 0.79 

Idaho 69.8 71.4 72.2 0.8 0.97 

Illinois 54.2 56.1 80.4 24.3 * 1.10 

Kentucky 37.1 42.6 49.9 7.3 * 1.21 

Maine 29.0 33.6 50.6 17.0 * 0.98 

Massachusetts 41.6 49.1 47.1 -2.0 1.18 

Michigan 61.4 60.7 68.6 8.0 * 1.29 

Missouri 15.3 18.8 43.0 24.3 * 1.27 

Montana 71.3 71.6 59.7 -11.9 * 1.18 

New York 56.2 56.9 59.4 2.5 * 1.27 

North Carolina 83.9 85.3 65.9 -19.3 * 0.98 

Oklahoma 67.5 71.0 79.8 8.8 * 1.29 

Oregon 65.3 66.5 73.2 6.7 * 1.26 

Virginia 82.8 84.3 79.7 -4.6 * 1.08 

West Virginia 70.6 71.9 71.6 -0.3 1.04 

Wyoming 36.8 44.5 62.1 17.6 * 1.59 

* Difference is statistically significant at p < .05.

1

 This matches the NAEP percentage meeting 2005 standard in 2005, by definition.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal School-


Level State Assessment Score Database (NLSLSASD) 2008.

C-5 
 

 

 

 

0 0 0

 

 

 

 

0 0 0

0

 

Table C-5.	 Number of states according to the comparability of state-reported results between 

2005 and 2007, by the statistical significance of the discrepancy between NAEP and 

state measures of gains in grades 4 and 8 reading 

Grade 4 Grade 8 

2005 and 2007 state assessment reported 2005 and 2007 state assessment reported 

results results 

Difference D Comparable Not comparable Comparable Not comparable 

Not statistically significant 11 2 9 2 

Statistically significant 11 10 15 12 

Total 22 12 24 14 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

Table C-6.	 Number of states according to the comparability of state-reported results between 

2005 and 2007, by the statistical significance of the discrepancy between NAEP and 

state measures of gains in grades 4 and 8 mathematics 

Grade 4 Grade 8 

2005 and 2007 state assessment reported 2005 and 2007 state assessment reported 

results results 

Difference D Comparable Not comparable Comparable Not comparable 

Not statistically significant 13 2 9 3 

Statistically significant 8 12 12 15 

Total 21 14 21 18 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-6 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table C-7.	 Selected changes to state reading assessments between 2005 and 2007, by whether 

reports of grade 4 reading achievement changes from 2005 to 2007 in the state test 

and NAEP agree, by state 

Changed Changed Used Changed Changed Changed Changed No 

Changed time of assessment different content proficiency accommodation test significant 

State/jurisdiction cut scores administration items assessment standards standards policy contractors changes 

Changes in student achievement on the state test are not statistically significantly different from changes on NAEP 

Alaska 

California 

Colorado 

Indiana 

Iowa 

Maryland 

Massachusetts  

Mississippi 

New Mexico 

North Carolina   

Ohio 

Changes in student achievement on the state test are statistically significantly larger than changes on NAEP 

Arkansas  

Louisiana 

North Dakota 

South Carolina     

Texas  

Changes in student achievement on the state test are statistically significantly smaller than changes on NAEP 

Alabama  

Florida 

New Jersey       

Tennessee 

Washington 

Wisconsin 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-7 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table C-8.	 Selected changes to state reading assessments between 2005 and 2007, by whether 

reports of grade 8 reading achievement changes from 2005 to 2007 in the state test 

and NAEP agree, by state 

Changed Changed Used Changed Changed Changed Changed No 

Changed time of assessment different content proficiency accommodation test significant 

State/jurisdiction cut scores administration items assessment standards standards policy contractors changes 

Changes in student achievement on the state test are not statistically significantly different from changes on NAEP 

Arizona 

California 

Colorado 

Indiana 

Iowa 

New Jersey 

North Carolina 

Ohio 

Texas 

Changes in student achievement on the state test are statistically significantly larger than changes on NAEP 

Alabama  

Arkansas  

Florida 

Illinois   

Louisiana 

Nevada 

New Mexico 

North Dakota 

Pennsylvania     

Tennessee 

Changes in student achievement on the state test are statistically significantly smaller than changes on NAEP 

Alaska 

Maryland 

Mississippi 

South Carolina 

Wisconsin 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Reading Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table C-9.	 Selected changes to state mathematics assessments between 2005 and 2007, by 

whether reports of grade 4 mathematics achievement changes from 2005 to 2007 in 

the state test and NAEP agree, by state 

Changed Changed Used Changed Changed Changed Changed No 

Changed time of assessment different content proficiency accommodation test significant 

State/jurisdiction cut scores administration items assessment standards standards policy contractors changes 

Changes in student achievement on the state test are not statistically significantly different from changes on NAEP 

Alabama  

Colorado 

Florida 

Georgia     

Iowa 

Louisiana 

Massachusetts 

Mississippi 

New Jersey 

New Mexico 

South Carolina 

Tennessee 

Wisconsin 

Changes in student achievement on the state test are statistically significantly larger than changes on NAEP 

Alaska 

Arkansas  

California 

Maryland 

Texas 

Changes in student achievement on the state test are statistically significantly smaller than changes on NAEP 

Indiana 

North Dakota 

Washington 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-9 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table C-10.Selected changes to state mathematics assessments between 2005 and 2007, by 

whether reports of grade 8 mathematics achievement changes from 2005 to 2007 in 

the state test and NAEP agree, by state 

Changed Changed Used Changed Changed Changed Changed No 

Changed time of assessment different content proficiency accommodation test significant 

State/jurisdiction cut scores administration items assessment standards standards policy contractors changes 

Changes in student achievement on the state test are not statistically significantly different from changes on NAEP 

Colorado 

Indiana 

Iowa 

Maryland 

Mississippi 

New Jersey 

New Mexico 

Pennsylvania     

Wisconsin 

Changes in student achievement on the state test are statistically significantly larger than changes on NAEP 

Alaska 

Arkansas  

Florida 

Georgia     

Nevada 

Ohio 

Texas 

Changes in student achievement on the state test are statistically significantly smaller than changes on NAEP 

Arizona 

Louisiana 

North Dakota 

South Carolina 

Tennessee 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), 2005 and 2007 Mathematics Assessments. U.S. Department of Education, Office of 

Planning, Evaluation and Policy Development, EDFacts SY 2006-07, Washington, DC, 2008. The National Longitudinal SchoolLevel State Assessment Score Database (NLSLSASD) 2008. 

C-10 

www.ed.gov ies.ed.gov