
TABLE OF CONTENTS 
TABLE OF CONTENTS 
LIST OF TABLES 
LIST OF FIGURES 
ACKNOWLEDGEMENTS 
OVERVIEW OF THIS MANUAL

1. 
Introduction


1.1 

Background 

1.2 

Rationale for the 2010 ModMSA: Mathematics 

1.3 

Eligibility Criteria for the ModMSA: Mathematics 

1.4 

Test Administration of the 2010 ModMSA: Mathematics 



Test Materials 



Test Administration Schedule 



Student Participation 



Accommodations for Assessment 



Test Format 



Security of Test Materials 

1.5 

Quality Control Procedures 

1.6 

Item Bank Construction

2. 
Test Design and Development of the 2010 ModMSA: Mathematics


2.1 

Test Design and Structure of the 2010 ModMSA: Mathematics 

2.2 

Development and Review of the 2010 ModMSA: Mathematics 



National Psychometric Council 



Content Review Committee 



Bias Review Committee 



Vision Review Committee 

2.3 

Operational Form Structure of the 2010 ModMSA: Mathematics 

2.4 

Procedures Undertaken for Item Analyses Prior to the Creation of the Operational Form 



Classical Item Analyses 



Differential Item Functioning Analyses 



Item Response Theory (IRT) Analyses 

2.5 

Items Flagged for Inspection Prior to the Creation of the Operational Forms 

2.6 

Items Selected for the 2010 Operational Tests 

2.7 

Scoring Procedures of the 2010 ModMSA: Mathematics

3. 
Central Tendency Measures and Other Classical Item Analyses of the 2010 ModMSA: Mathematics


3.1 

Measures of Central Tendency 



Standard Error of the Mean 

3.2 

ItemLevel Descriptive Statistics

4. 
Scale Creation, Equating and Raw Scores to Scale Scores Conversion via Item Response Theory (IRT) Procedures




The Rasch Model 

4.1 

Calibration and Scaling Procedures for Grades 3 to 5 

4.2 

Specifics for Creating the Base Scale for the ModMSA: Mathematics Grades 35 

4.3 

Calibration Equating the 2010 ModMSA: Mathematics Grades 68 

4.4 

Specifics of Linking and Equating the 2010 ModMSA Grades 68: Mathematics 

4.5 

Reporting Scale Scores for the 2010 ModMSA: Mathematics 



Raw Score to Scale Score Conversion Tables for the Total Score 



Raw Score to Scale Score Conversion Tables for the Subscales 

4.6 

Score Interpretation 



Scale Scores 



Performance Level Descriptors 

4.7 

Final Performance Level Cut Points for the ModMSA: Mathematics

5. 
Comparative Classical and IRT Stats Across Years for the Common Items Used in Grades 68

6. 
IRT Item Level Statistics for the 2010 ModMSA: Mathematics


6.1 

Rationale for the Use of the Rasch Model 

6.2 

Fit Statistics for the Rasch Model 

6.3 

Rasch Item Level Statistics

7. 
Test Reliability


7.1 

Precision and Reliability (Classical Methods) 



Standard Error of Measurement (SEM) of the Test 



Cronbach’s Alpha (KR20) 

7.2 

IRT Method in Measuring Precision of the Test 

7.3 

Decision Accuracy and Consistency at the Cut Scores

8. 
Test Validity


8.1 

Test Validity for the 2010 ModMSA: Mathematics 



ContentRelated Evidence 



Evidence from Item Development Methods 



Evidence from Internal Structure of the Tests 

8.2 

Unidimensionality Analysis for the 2010 ModMSA: Mathematics

9. 
Summary of Operational Test Results of the 2010 ModMSA: Mathematics


9.1 

Classical Descriptive Test Statistics (Raw Scores) 

9.2 

Scale Score Descriptive Statistics 

9.3 

Frequency of Students at Each Proficiency Level by Grade 

9.4 

Test Characteristic Curves, Test Information Functions, and Conditional Standard Errors of Measurement

10. 
References

APPENDICES

A.
 Operational Items Selected After Data Review 
B.
 Item Distractor Analyses 
C.
 Frequency Distribution Histograms of Scale Scores 
D.
 Standard Setting Report 
E.
 Alignment of the 2009 ModMSA: Mathematics Items to the State Standards 
F.
 Identifying Students for Participation in the ModMSA: Mathematics Program 
G.
 Comparability Study of Paper and Pencil, and Online Administration of the ModMSA
