To deal with this problem, multiple pairwise comparisons tests involve p-value corrections: p-values are penalized (= their value is increased) as the number of comparisons increase. For example, given a significance level alpha of 5%, we would likely find 5 significant p-values by chance over 100 significant p-values. 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. The p-value represents the risk of stating that an effect is statistically significant while this is not true. Pairwise multiple comparisons tests involve the computation of a p-value for each pair of the compared groups. What is the multiple comparisons problem? Pairwise multiple comparisons tests, also called post hoc tests, are the right tools to address this issue. For this purpose, we need to test the differences between pairs of groups. Smoking is the factor involving 4 population groups (non-smokers, passive smokers, light smokers and heavy smokers).Īssuming 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 example, we may study how smoking affects pulmonary health. The aim of ANOVA is to detect whether a factor has a significant effect on a dependent variable globally. A few words on pairwise multiple comparisons tools Why do we need to use multiple pairwise comparisons tests?
#XLSTAT MULTIVARIATE COMPARISON HOW TO#
This article explains how to interpret contradictory results between ANOVA and multiple pairwise comparisons, also referred as post hoc comparisons.