Tukey's HSD

Definition

Tukey's Honestly Significant Difference (HSD) is a statistical test used to identify which specific group means are significantly different from each other following a significant one-way ANOVA result. It is a post-hoc test that provides a way to control the familywise error rate when making multiple comparisons.

5 Must Know Facts For Your Next Test

1. Tukey's HSD is used after a significant one-way ANOVA to determine which specific group means are statistically different from each other.
2. It controls the familywise error rate by adjusting the p-values for multiple comparisons, reducing the likelihood of false positive results.
3. Tukey's HSD compares all possible pairs of group means and identifies which differences are large enough to be considered statistically significant.
4. The test statistic used in Tukey's HSD is the Studentized Range Statistic, which takes into account the number of groups and the sample size.
5. Tukey's HSD is considered a conservative post-hoc test, as it is less likely to detect significant differences compared to other multiple comparison procedures.

Review Questions

• Explain the purpose of Tukey's HSD in the context of a one-way ANOVA analysis.
  • Tukey's HSD is a post-hoc test used after a significant one-way ANOVA result to determine which specific group means are statistically different from each other. It helps identify the pairwise differences between group means that are large enough to be considered significant, while controlling the familywise error rate. This is important because the one-way ANOVA only tells you that at least one group mean is different, but it does not specify which groups are different.
• Describe how Tukey's HSD differs from the F-Ratio calculated in the one-way ANOVA.
  • The F-Ratio calculated in the one-way ANOVA is used to determine if there is a significant difference between any of the group means. It compares the variance between the groups to the variance within the groups. In contrast, Tukey's HSD is a post-hoc test that is used after a significant ANOVA result to identify which specific group means are significantly different from each other. Tukey's HSD uses the Studentized Range Statistic to make pairwise comparisons and control the familywise error rate, whereas the F-Ratio is the overall test statistic for the one-way ANOVA.
• Explain why Tukey's HSD is considered a conservative post-hoc test compared to other multiple comparison procedures.
  • Tukey's HSD is considered a conservative post-hoc test because it is less likely to detect significant differences between group means compared to other multiple comparison procedures, such as the Bonferroni correction. This is because Tukey's HSD takes into account the number of groups and the sample size when calculating the Studentized Range Statistic, which is used to determine the critical value for identifying significant differences. By adjusting the p-values more conservatively, Tukey's HSD reduces the likelihood of making Type I errors (false positives) when performing multiple comparisons, but it may also be less sensitive in detecting true differences between groups.

Related terms

One-Way ANOVA: A statistical test used to determine if there are significant differences between the means of three or more independent groups.

F-Ratio: The test statistic calculated in an ANOVA that compares the variance between groups to the variance within groups.

Familywise Error Rate: The probability of making one or more false discoveries, or Type I errors, when performing multiple statistical tests.