These six rows are highlighted (in blue and red) in the figure. So, after examining all rows in the first cell, we only need to check the difference between (a) Joke 2 and Joke 3, (b) Joke 2 and Joke 4, AND (c) Joke 3 and Joke 4. The first cell compares Joke 1 with all the other three groups. The column marked "Sig" reports the significance (i.e., the p-value) of the difference (the difference is significant when p 0.05).Īs you may realize after looking at the table, there are some repetitions (albeit with changes in signs).
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The column marked "mean difference" is the difference in group means. The first large cell compares the Group 1 mean (i.e., Joke 1) with all the other three groups (Jokes 2, 3, and 4). Note the pairwise comparisons in the output above. * The mean difference is significant at the 0.05 level
#How to use phstat in excel anova pdf#
Post-hoc tests PDF Watch Instructor Video: Post-Hoc Tests in ANOVA: Excel Instructions (4:38)
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Unequal group variance (confirm by Levene's test).REGWQ or Tukey (has more power when # of comparisons are large) or Bonferroni (has more power when the # of comparisons is small).Equal sample size and group variances are similar.Depending on the statistical package used, quite a few choices are available. Different post-hoc tests have varying strengths in the trade-off between the Type I and Type II errors (remember, we can control one at a time, not both (Reference: Hypothesis Testing Lesson: Type I and Type II errors). 1 The pairwise comparisons control the familywise error rate by correcting the level of significance of each test such that the overall Type I rate α across all comparisons remains at 0.05 (i.e., 5%).
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When we use multiple comparisons, we need to be aware of familywise error rates: the probability that at least one of the comparisons will include a Type I error. We will use this test to choose the right post-hoc test. The null hypothesis in Levene's test is that all groups have the same variance, so a statistically significant Levene's test ( p-value < 0.05) implies that groups have unequal variance. Also, the choice of the post-hoc test depends on these criteria as well. Although the F-test is generally robust (meaning that even if some assumptions are violated, generally results will still be accurate), large differences in group variances can significantly affect the Type I and Type II error rates. Levene's Testīefore we proceed to the post-hoc tests, we should discuss one of the main ANOVA assumptions: that variances of each group are the same. If we do not have any a priori hypothesis as to which specific groups will differ AND we have a statistically significant one-way ANOVA result, we should perform post-hoc tests (they are called post-hoc because they are performed after the ANOVA). Post-hoc tests provide pairwise comparisons between all possible combinations of groups. However, it does not point out which specific groups differ. As we have just seen, the ANOVA F-test tells us whether there is an overall difference between the groups.