The tests following two-factor ANOVA without replication are similar to those following two-factor ANOVA with replication, except that clearly, no tests for the interaction of factors are necessary.
In particular, we will show how to perform Contrasts and Tukey’s HSD tests for the data in Example 1 of Two Factor ANOVA without Replications. This analysis shows that there is a significant difference in the Rows factor, but not in the Columns factor, and so it is appropriate to pinpoint where the differences lie in the Rows factor. For completeness, we also show how to perform follow-up testing on the Columns factor, even though this isn’t really necessary.
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