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Post hoc analysis applies to tests of differences among sample statistics when the specific hypothesis to be tested has been suggested by the values of the statistics themselves. Perhaps the most common statistic to be tested is the sample mean in experiments involving three or more means. In such cases, it is most common to begin with the testing of an analysis of variance (ANOVA) F test. A nonsignificant F test implies that the full null hypothesis of the equality of all population means is plausible. Consequently, no additional testing would be considered.

Suppose a significant ANOVA F test is found in an experiment involving k = 4 means. If the last two means are greater than the first two means, a researcher might want ...

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