Tukey's HSD Test

Definition

Tukey's Honestly Significant Difference (HSD) test is a statistical method used in the context of one-way ANOVA to identify which specific means (group averages) are significantly different from each other. It is a post-hoc test that provides a pairwise comparison of means, controlling for the overall Type I error rate.

5 Must Know Facts For Your Next Test

1. Tukey's HSD test is a conservative post-hoc test that controls the familywise error rate, reducing the likelihood of making a Type I error.
2. The test compares all possible pairwise comparisons of group means and identifies which differences are statistically significant.
3. Tukey's HSD test assumes that the sample sizes are equal across groups and the variances are homogeneous.
4. The test statistic used in Tukey's HSD is the Studentized Range Statistic, which takes into account the number of groups and the degrees of freedom.
5. Tukey's HSD is often preferred over other post-hoc tests, such as the Bonferroni correction, because it maintains a higher statistical power while still controlling the Type I error rate.

Review Questions

• Explain the purpose of Tukey's HSD test in the context of one-way ANOVA.
  • The purpose of Tukey's HSD test in the context of one-way ANOVA is to identify which specific group means are significantly different from each other. After a significant ANOVA result indicates that at least one group mean is different, Tukey's HSD is used to perform pairwise comparisons of the group means and determine which pairs are statistically significant. This allows researchers to pinpoint the exact differences between the groups, providing more detailed insights than the overall ANOVA test alone.
• Describe the key assumptions required for the valid use of Tukey's HSD test.
  • Tukey's HSD test has several key assumptions that must be met for the results to be valid. First, the test assumes that the sample sizes are equal across the groups being compared. Second, it assumes that the variances of the groups are homogeneous, meaning the group variances are approximately equal. Finally, Tukey's HSD relies on the normality assumption, requiring that the data within each group follows a normal distribution. If these assumptions are violated, the validity and reliability of the Tukey's HSD test results may be compromised.
• Explain how Tukey's HSD test controls the familywise error rate and the significance of this feature.
  • Tukey's HSD test is designed to control the familywise error rate, which is the probability of making at least one Type I error when conducting multiple pairwise comparisons. By controlling the familywise error rate, Tukey's HSD ensures that the overall Type I error rate remains at the specified significance level (e.g., α = 0.05) across all the comparisons, even though multiple tests are being performed. This is important because conducting numerous pairwise comparisons without an adjustment, such as the Tukey method, would lead to an inflated overall Type I error rate and increase the likelihood of false positive findings. The ability of Tukey's HSD to maintain the desired significance level while providing higher statistical power than other post-hoc tests makes it a preferred choice for researchers conducting one-way ANOVA analyses.

Related terms

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

Post-Hoc Test: A statistical test performed after a significant ANOVA result to determine which specific group means differ from each other.

Type I Error:

The error that occurs when the null hypothesis is true, but is incorrectly rejected, leading to a false positive result.