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Tukey Pairwise Multiple Comparisons

  • Tukey Pairwise Multiple Comparisons can be used when One-Way ANOVA rejects $H_0$ and we need to perform a follow-up analysis to help us determine which means actually differ. If One-Way ANOVA does not reject $H_0$, then comparison procedures such as these are not necessary.

  • Since Tukey Pairwise Multiple Comparisons are a follow-up analysis to One-Way ANOVA, all the guidelines for using One-Way ANOVA must be met. For your convenience, we have listed these below.

  • We have $I$ independent SRSs, one from each of $I$ populations. We measure the same response variable for each sample.

  • The $i$th population has a Normal distribution with unknown mean $\mu_i$. One-way ANOVA tests the null hypothesis that all the population means are the same.

  • All the populations have the same standard deviation $\sigma$, whose value is unknown.

  • The results of the ANOVA $F$-test are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation.

Variable Names (optional):
Sample data goes here (enter numbers in columns):
Level of Significance: $\alpha=$

One-Way ANOVA Table

Source of variationdfSSMS$F$-statistic$p$-value
Variation Among Samples
Variation Within Samples

% Tukey Intervals by Label: