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Notes on Topic 13:
One-Way Analysis of Variance

    Post Hoc Tests

    ANOVA Hypotheses:

    You will recall, that in ANOVA the null and alternative hypotheses are:

    When the null hypothesis is rejected you conclude that the means are not all the same. But we are left with the question of which means are different?

    T-Tests can't be used

    We can't answer this question in the obvious way (using T-Tests on the various pairs of groups) because we would get too "rosy" a picture of the significance (for reasons I don't go into). Post Hoc tests help give us an answer to the question of which means are different. The Post Hoc tests gaurantee we don't get too "rosy" a picture (actually, they provide a picture that is too "glum"!).

    Post Hoc tests

    Post Hoc tests are done "after the fact": i.e., after the ANOVA is done and has shown us that there are indeed differences amongst the means. Specifically, Post Hoc tests are done when:
    1. you reject Ho, and
    2. there are 3 or more treatments (groups).
    A Post Hoc test enables you to go back through the data and compare the individual treatments two at a time, and to do this in a way which provides the appropriate alpha level.

    Two Post Hoc tests are commonly used (although ViSta doesn't offer any Post Hoc tests):

    • Tukey's HSD Test (thats HSD for Honestly Significant Difference). This test can be used only when the groups are all the same size. It determines a single value that is the minimum difference between a pair of groups that is needed for the difference to be significant at a specific alpha level.
    • Scheffe's Test is very conservative. It involves computing an F-Ratio that has a numerator that is a mean-square that is based on only the two groups being compared (the denominator is the regular error variance term).