Why do pairwise comparisons

This service is more advanced with JavaScript available. Editors: Alex C. Contents Search. Pairwise Comparisons. How to cite. Synonyms Follow-up tests ; Mean differences ; Planned comparisons ; Post hoc tests. Alternatively, comparisons i. This is a preview of subscription content, log in to check access. Assuming that ANOVA detects a significant effect of smoking on the pulmonary health, we can go a step further and examine whether specific population groups differ significantly from one another.

For this purpose, we need to test the differences between pairs of groups. Pairwise multiple comparisons tests , also called post hoc tests , are the right tools to address this issue. Pairwise multiple comparisons tests involve the computation of a p-value for each pair of the compared groups.

The p-value represents the risk of stating that an effect is statistically significant while this is not true. As the number of pairwise comparisons increases, and therefore the number of p-values, it becomes more likely to detect significant effects which are due to chance in reality.

Therefore, it becomes less likely to draw erroneous inferences. Note that the p-value penalization procedure differs from one post hoc test to another.

ANOVA and multiple pairwise comparison tests examine different questions. The computations made to provide the answers rely on different methodologies. It is therefore possible that the results generated are contradictory in some cases. Here are some suggestions why post-hoc tests may appear non-significant while the global effect is significant.

The list below is not exhaustive. Other situations exist. An unfortunate common practice is to pursue multiple comparisons only when the hull hypothesis of homogeneity is rejected. But we do not know the form of the inequality. Questions concerning the reason for the rejection of the null hypothesis arise in the form of: "Which mean s or proportion s differ from a standard or from each other?

One popular way to investigate the cause of rejection of the null hypothesis is a Multiple Comparison Procedure. These are methods which examine or compare more than one pair of means or proportions at the same time.

Note : Doing pairwise comparison procedures over and over again for all possible pairs will not, in general, work. This is because the overall significance level is not as specified for a single pair comparison. The ANOVA uses the F test to determine whether there exists a significant difference among treatment means or interactions.