1. LECTURE 14 NORMS, SCORES, AND EQUATING EPSY 625

2. NORMS Norm: sample of population Intent: representative of population Reality: hope to mirror population characteristics (no means to get representative samples, except NAEP)

3. NORMS Norming study Construct test Pilot items Construct test(s) Testlets/item packets Parallel forms Revise items/tests Test norm sample

4. Test Scores Types of scores Smoothing distributions Equating scores for different forms horizontal (same difficulty/population) vertical (different difficulty/population)

5. Types of scores Raw scores Standardized scores linear transformations of raw scores z-scores (mean=0, SD=1) T-scores (mean=50, SD=10) Stanines (mean=5, SD=2) nonlinear transformations of raw scores percentile scores smoothed standard scores grade equivalents (GEs)

6. RAW SCORE 1.11.51.92.12.52.9 TIME OF TESTING IN GRADE UNITS SAMPLE A GRADE 1 SAMPLE B GRADES 1-2 SAMPLE C GRADE 2 18 15 12 9 6 3 0

7. Smoothing Distributions Normal curve fitting trait-theoretic (ability, physical performance) Nonnormal curve fitting trait theoretic (abnormal behavior) Procedures graphical fitting mathematical curve-fitting

8. Test Equating Horizontal equating: parallel forms Equipercentile: match scores for each percentile score (eg. 1%ile on form A to 1%ile on B) IRT ability equating (mean score for ability value of -.5 on A to mean score on B) Regression/linear procedures Vertical equating: overlapping difficulties IRT ability equating Grade equivalent equating

9. Test Equating Horizontal equating: parallel forms Equipercentile: match scores for each percentile score (eg. 1%ile on form A to 1%ile on B) 7599 7398 7097 6696 6595. 9976 9874 9771 9667 9566. FORM A FORM B

10. Test Equating Vertical equating: overlapping difficulties Scores are overpredicted based on easy forms Scores are underpredicted based on difficult forms Chance scores are overpredicted