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Chapter 5: Test Scores as Composites
•
Test battery: collection of two or more separate tests designed to be administered
to the same examinees. Separate score is computed for each test.
o
Example: GRE
separate score for verbal, quantitative, and analytic.
•
Composite test score
: total score created by summing two or more subtest scores.
•
Item score
: number of points assigned to an individual’s response to a given item.
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Total score: usually determined by summing the item scores.
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Every test score is a composite.
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Scoring for most items can be classified as either dichotomous or
nondichotomous.
•
Variability of responses displayed by the group for an item: calculate the variance
of that set of item responses.
•
Item difficulty:
(p)
the proportion of examinees who answer an item correctly.
o
P of 0.85: an item answered correctly by 85% of the examinees.
o
Thus, the easier item actually has the higher item difficulty value.
•
Dichotomous variables:
when all values are restricted to 0 or 1, the mean of item
will be equivalent to the number of persons with a score of 1 on item (pj = mean j)
•
When items are dichotomous, variance formula
pjqj
, where qj = 1 pj
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Total test score variance > sum of item variances
o
Total test variance is not determined by individual item variances.
•
For any pair of variables taken on the same sample,
covariance
the correlation
of those two variables multiplied by their standard deviations.
•
There will always be
one variance term for each item and a pair of covariance
terms for each pair of items (2pjSiSj)
•
Total variance of a composite
: determined jointly by the variance of individual
test items and by the covariance of all pairs of those items.
•
Composite variance for a test with
n
items will have
n
variance terms and
n(n
1) covariance terms. However, there are only n(n1)/2 UNIQUE
covariance terms.
•
Variance: individual differences
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 Fall '09
 Lissitz

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