LECTURE 14 NORMS, SCORES, AND EQUATING EPSY 625

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

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

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

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)

RAW SCORE TIME OF TESTING IN GRADE UNITS SAMPLE A GRADE 1 SAMPLE B GRADES 1-2 SAMPLE C GRADE

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

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

Test Equating Horizontal equating: parallel forms Equipercentile: match scores for each percentile score (eg. 1%ile on form A to 1%ile on B) FORM A FORM B

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