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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
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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 SAMPLE C GRADE 2 18 15 12 9 6 3 0 SAMPLE A GRADE 1 SAMPLE B GRADES 1-2 1.1 1.5 1.9 2.1 2.5 2.9 TIME OF TESTING IN GRADE UNITS
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 75 99 73 98 70 97 66 96 65 95 . . 99 76 98 74 97 71 96 67 95 66 . .
Test Equating • Vertical equating: overlapping difficulties • Scores are overpredicted based on easy forms • Scores are underpredicted based on difficult forms • Chance scores are overpredicted