A post hoc test, also known as an a posteriori test, is a statistical analysis performed after the initial analysis of variance (ANOVA) to determine where the significant differences lie between the groups being compared. It is used in the context of one-way ANOVA to identify which specific groups differ from one another.
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Post hoc tests are necessary after a significant one-way ANOVA result to determine which specific group means differ from one another.
Post hoc tests adjust for the increased likelihood of a Type I error that occurs when making multiple comparisons.
Common post hoc tests used in one-way ANOVA include Tukey's Honest Significant Difference (HSD), Bonferroni, and Dunnett's test.
The choice of post hoc test depends on factors such as the number of groups, the assumption of equal variances, and the desired control over the family-wise error rate.
Post hoc tests provide more detailed information about the nature and location of the significant differences found in the initial one-way ANOVA.
Review Questions
Explain the purpose of conducting a post hoc test after a significant one-way ANOVA result.
The purpose of a post hoc test after a significant one-way ANOVA result is to determine which specific group means differ from one another. The initial one-way ANOVA only indicates that at least one group mean is significantly different, but it does not provide information about the nature or location of these differences. Post hoc tests are necessary to identify which group comparisons are statistically significant, allowing for a more detailed understanding of the differences between the groups.
Describe how post hoc tests address the issue of multiple comparisons in one-way ANOVA.
When conducting multiple statistical comparisons, such as in one-way ANOVA, the likelihood of making a Type I error (false positive) increases. Post hoc tests address this issue by adjusting the significance level to control the family-wise error rate, which is the probability of making one or more Type I errors across all the comparisons. Common post hoc tests, such as Tukey's HSD, Bonferroni, and Dunnett's test, use different approaches to maintain the desired overall significance level and provide more reliable conclusions about the differences between the group means.
Evaluate the factors that influence the choice of post hoc test in the context of one-way ANOVA.
The choice of post hoc test in one-way ANOVA depends on several factors, including the number of groups being compared, the assumption of equal variances, and the desired control over the family-wise error rate. For example, Tukey's HSD is commonly used when all pairwise comparisons are of interest and the assumption of equal variances is met, while Dunnett's test is preferred when comparing each group to a control group. The Bonferroni correction is a more conservative approach that can be used when the number of comparisons is large. Considering these factors helps researchers select the most appropriate post hoc test to draw reliable conclusions from the one-way ANOVA results.
A statistical test used to determine if there are any significant differences between the means of three or more independent groups.
Multiple Comparisons: The process of making several statistical comparisons simultaneously, which can increase the likelihood of a Type I error (false positive).
Family-Wise Error Rate: The probability of making one or more Type I errors when performing multiple statistical tests.