- 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.

Group/Treatment Names (optional): | |||

Sample data goes here (enter numbers in columns): |

Use labels to group data (in Beta): | ||

Level of Significance: | $\alpha=$ |

**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: |