What is Fisher's least significant difference (LSD) method for multiple comparisons?

Fisher's LSD method for multiple comparisons is used in ANOVA to create confidence intervals for all pairwise differences between factor level means while controlling the individual error rate to a significance level you specify.

Fisher's LSD method then uses the individual error rate and number of comparisons to calculate the simultaneous confidence level for all confidence intervals. This simultaneous confidence level is the probability that all confidence intervals contain the true difference. It is important to consider the family error rate when making multiple comparisons because your chances of committing a type I error for a series of comparisons is greater than the error rate for any one comparison alone.

Example of Fisher's LSD method

For example, you are measuring the response times for memory chips. You take a sample of 25 chips from five different manufacturers. The ANOVA resulted in a p-value of 0.01, leading you to conclude that at least one of the manufacturer means is different from the others.

You decide to examine all 10 comparisons between the five plants to determine specifically which means are different. Using Fisher's LSD method, you specify that each comparison should have an individual error rate of 0.05 (equivalent to a 95% confidence level). Minitab creates these ten 95% confidence intervals and calculates that this set yields a 71.79% simultaneous confidence level. Understanding this context, you can then examine the confidence intervals to determine whether any do not include zero, identifying a significant difference.