Fisher's Least Significant Difference Test

When an analysis of variance (ANOVA) gives a significant result, this indicates that at least one group differs from the other groups. Yet the omnibus test does not indicate which group differs. In order to analyze the pattern of difference between means, the ANOVA is often followed by specific comparisons, and the most commonly used involves comparing two means (the so-called pairwise comparisons).

The first pairwise comparison technique was developed by Ronald Fisher in 1935 and is called the least significant difference (LSD) test. This technique can be used only if the ANOVA F omnibus is significant. The main idea of the LSD is to compute the smallest significant difference (i.e., the LSD) between two means as if these means had been the only means to ...