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