Tukey's HSD

Definition

Tukey's Honestly Significant Difference (Tukey's HSD) is a statistical test used in the context of one-way ANOVA to determine which specific means in a group of means are significantly different from each other. It is a post-hoc test that is applied after a significant ANOVA result to identify where the differences lie among the group means.

5 Must Know Facts For Your Next Test

1. Tukey's HSD is a conservative post-hoc test, meaning it has a lower Type I error rate compared to other post-hoc tests.
2. Tukey's HSD compares all possible pairwise comparisons of group means and controls the family-wise error rate.
3. The test statistic used in Tukey's HSD is the Studentized Range Statistic, which takes into account the number of groups being compared.
4. Tukey's HSD is appropriate to use when the assumptions of one-way ANOVA are met, including normality, homogeneity of variance, and independence of observations.
5. The results of Tukey's HSD are typically presented in the form of a letter-based grouping, where groups that share a letter are not significantly different.

Review Questions

• Explain the purpose of Tukey's HSD in the context of one-way ANOVA.
  • The purpose of Tukey's HSD in the context of one-way ANOVA is to determine 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 as a post-hoc test to identify the pairwise comparisons of group means that are statistically significant. This helps researchers understand the nature of the differences between the groups and draw more meaningful conclusions from the analysis.
• Describe the key features that make Tukey's HSD a conservative post-hoc test.
  • Tukey's HSD is considered a conservative post-hoc test for several reasons. First, it controls the family-wise error rate, which is the probability of making at least one Type I error (false positive) when conducting multiple pairwise comparisons. This is achieved by using the Studentized Range Statistic, which takes into account the number of groups being compared. Additionally, Tukey's HSD has a lower Type I error rate compared to other post-hoc tests, meaning it is less likely to detect a significant difference when there is none. This conservative approach helps researchers avoid making erroneous conclusions about the differences between group means.
• Evaluate the appropriate use of Tukey's HSD in the context of one-way ANOVA and the implications of violating its assumptions.
  • Tukey's HSD is appropriate to use in the context of one-way ANOVA when the assumptions of the test are met, including normality, homogeneity of variance, and independence of observations. If these assumptions are violated, the results of Tukey's HSD may be compromised, leading to inaccurate conclusions about the differences between group means. For example, if the assumption of homogeneity of variance is violated, the Studentized Range Statistic used in Tukey's HSD may not be valid, resulting in increased Type I or Type II errors. In such cases, alternative post-hoc tests, such as Games-Howell or Dunnett's test, may be more appropriate. Researchers should carefully evaluate the assumptions of one-way ANOVA and select the most suitable post-hoc test to ensure the validity and reliability of their findings.

Related terms

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

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

Pairwise Comparisons:

Comparisons made between all possible pairs of group means to identify which ones are significantly different.