Stats.Blue

# 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: $\alpha=$ 0.05 0.01

One-Way ANOVA Table

 Source of variation df SS MS $F$-statistic $p$-value Variation Among Samples Variation Within Samples Total

 % Tukey Intervals by Label: