LECTURE 14NORMS, 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
1.1 1.5 1.9 2.1 2.5 2.9
TIME OF TESTING IN GRADE UNITS
SAMPLE A
GRADE 1
SAMPLE B
GRADES 1-2
SAMPLE C
GRADE 218
15
12
9
6
3
0
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 formsEquipercentile: 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 difficultiesIRT ability equating
Grade equivalent equating
Test Equating
Horizontal equating: parallel formsEquipercentile: match scores for each percentile score (eg. 1%ile
on form A to 1%ile on B)
75 99
73 98
70 97
66 96
65 95
.
.
99 76
98 74
97 71
96 67
95 66
.
.
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
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