TESTING FOR DIFFERENCES IN TEST SCORE DISTRIBUTIONS USING LOGLINEAR MODELS

In this article, I consider the problem of determining whether score d istributions on 2 or more test forms administered to samples of examin ees from a single population differ. Three statistical tests using log linear models are described for testing whether the score distribution s on alternative test forms differ. One test is the usual test for ind ependence in a 2-way table. Two alternatives to the usual test for ind ependence are presented. One alternative is to replace the saturated m odel in the usual test for independence with the column effects model. The other alternative is to base the test on polynomial loglinear mod els that have been found to fit test score distributions well. The pow er of the alternative tests can be greater than the power of the usual test for independence when the column effects model or polynomial log linear model provide an adequate description of the differences among the score distributions. Examples are provided of applying the tests o f distribution differences to deciding whether equating is needed for alternative forms of a test.