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How to interpret Homogenous Subsets output; ONEWAY & UNIANOVA

Question & Answer


Question

In the ONEWAY and GLM Univariate (UNIANOVA) procedures, I am wondering how to interpret the Homogeneous Subsets output. Is this of interest/needed for the analysis?

Answer

The Homogenous Subsets output is produced by a request for post hoc tests and addresses the same questions as the Multiple Comparisons table for post hoc analysis, i.e. which pairs of groups have significantly different means on the dependent variable. Like the Multiple Comparisons table, the Homogenous Subsets output would not be interpreted if the main effect (in the Between Subjects Effect, or ANOVA table) was not significant. Some post hoc tests are only reported as homogenous subset output (e.g. Duncan, SNK); some are only reported as multiple comparison tables (e.g. Sidak, Tamhane); and some are reported in both formats (e.g.Tukey HSD, Scheffe).

For each requested post hoc test that does provide homogenous subset results, the groups are listed in order of ascending means. The means that are listed under each subset comprise a set of means that are not significantly different from each other.

Suppose that there were 5 groups in the factor and (for convenience of illustration), that their dependent variable means were ordered as their level on the factor, i.e. group 1 had the lowest mean; group 5, the highest. Suppose that the means for groups 1, 2, and 3 appear in subset 1; groups 3 & 4, in subset 2; group 5, in subset 3. The interpretation is that:

Groups 1 and 2 are significantly different from Groups 4 & 5, because groups 1 & 2 never appear in any subset with either group 4 or group 5.

Group 3 is significantly different from group 5, but not from any other group, as it appears with groups 1 & 2 in Set 1 and with group 4 in Set 2.

Group 5 is significantly different from all other groups as it does not appear in a subset together with any of the groups.

The relevant literature seems to support the conclusion that the tests available in the multiple comparisons table generally have better properties than the homogenous subset tests and are the preferred focus for post hoc analysis.

Note also that the results from the POSTHOC subcommand in all relevant SPSS procedures (ONEWAY, GLM and UNIANOVA) are based on one-way observed means, regardless of the design involved. Comparisons among adjusted means are handled via the EMMEANS COMPARE option (see the Options dialog box in GLM Univariate, Multivariate and Repeated Measures).

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Historical Number

42093

Document Information

Modified date:
16 April 2020

UID

swg21479991