1. Session 3 ANOVA POST HOC Testing STAT 3130 Statistical Methods I

2. ANOVA – Post Hoc Testing From the previous notes, we found an F-statistic of 24.33. This equated to a very low p-value (<.001), allowing us to reject the Null Hypothesis and conclude that a difference amongst the means was present… This does not really guide our decision making – although we concluded that at least one of the plans is different, at this point we have no information regarding WHICH plan(s) is (are) different. To determine this, we need to execute a Post Hoc test.

3. ANOVA – Post Hoc Testing Post Hoc tests are a critical step in the ANOVA process because they allow us to determine WHICH plans are different from the others. There are several possible Post Hoc tests to choose from based upon the specifics of your analysis. We will look at the two most common: Fishers LSD and Tukey.

4. Both Fisher’s LSD test and Tukey’s test are commonly accepted tests amongst statisticians. You really cannot go too far wrong with either. Here are a few general points of comparison: 1.Fisher’s LSD (least significant difference) is less conservative than Tukey’s HSD (honestly significant difference). 2.Fisher’s LSD executes a series of ttests amongst the pairs, resulting in a higher Type 1 error rate, while Tukey’s HSD specifies a “family error rate” across all comparisons 3.Tukey’s HSD calculates “Tukey’s Yardstick” – any mean differences which are at least as large as the Yardstick are considered to be different. ANOVA – Post Hoc Testing

5. Additional sources for detailed information regarding Post Hoc tests: http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_glm_a0000000867.htm http://www.uwsp.edu/psych/cw/statmanual/posthocs.html http://pages.uoregon.edu/stevensj/posthoc.pdf http://practicalstats.labanca.net/index.php?title=Selecting_a_Post_Hoc_test ANOVA – Post Hoc Testing