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A Test of the Equality of Standard Errors of Measurement

Green, Bert F., Jr.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Standard Error of Measurement, Statistical Significance, Reliability, Group Differences, Variance


When a psychological test has been given to more than one group of people, it has a standard error of measurement for each group. A procedure is proposed for testing the significance of group differences in the standard error of measurement. Wilks' criterion is used to insure that the tests used in ascertaining reliability and hence variance of measurement errors may be assumed parallel for each group. Votaw's criterion is a logical next step in checking the error of measurement. It is used to check whether the test scores of all the groups have the same mean, variance, and covariance. However, it is possible for the test's reliability and variance to differ widely from group to group. Therefore, Votaw's criterion is not satisfied, even though the variance of measurement errors stays the same. A modification of Neyman and Pearson's test is utilized if the tests are parallel, to see whether the error variances are the same within the limits of sampling error. (SGK)

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