Statistical Considerations in Choosing a Test Reliability ...

ACT Research Report Series

2012 (10)

Statistical Considerations in Choosing a Test Reliability Coefficient

David Woodruff Yi-Fang Wu December 2012

For additional copies, write: ACT Research Report Series P.O. Box 168 Iowa City, IA 52243-0168

? 2012 by ACT, Inc. All rights reserved.

Statistical Considerations in Choosing a Test Reliability Coefficient

David Woodruff Yi-Fang Wu

Abstract

The purpose of this paper is to illustrate alpha's robustness and usefulness, using actual

and simulated educational test data. The sampling properties of alpha are compared with the

sampling

properties

of

several

other

reliability

coefficients:

Guttman's

2

,

4

,

and

6

;

test-

retest reliability; as well as congeneric reliability. The comparisons are based on different sample

sizes and test models comprising dichotomous item and polytomous item tests. It is concluded

that alpha is indeed a lower bound to reliability except under the assumption of essential-tau-

equivalence; however, it is robust to violations of this condition, and its values are competitive

with other coefficients' values based on splitting a test into parallel halves or repeating a test to

estimate test-retest reliability. Because it is not always possible to construct parallel half-tests or

obtain test-retest data, it is very useful to have reliability coefficients, such as alpha, which are

free of these constraints.

ii

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