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Heterogeneity of Variance in Randomized Block Experiments¹

Michigan State University², East Lansing 48824-1225

Abstract

Shukla's test for homogeneity of non-independent, intratreatment variances in randomized block experiments is clarified and simplified for practical use via a table of correction constants. A biological example is used to illustrate procedure and demonstrate the bias inherent in using the classical Bartlett test in situations with dependencies among variances. Via the example, one can see that existing heterogeneous variance is not necessarily clearly detected by the Anscombe and Tukey test for dependence of variability on level of response. Procedures for adjusting degrees of freedom in tests of means (to compensate for heterogeneous variance) are illustrated for the omnibus F test, Bonferroni t statistics for planned contrasts and the Tamhane procedure for comparing all pairs of means.

¹ Journal article number 10741 of the Michigan Agr. Exp. Sta.

² Dept. of Anim. Sci.