Family-wise Type I Error:
In multiple comparison procedures, family-wise type I error is the probability that, even if all samples come from the same population, you will wrongly conclude that at least one pair of populations differ.
If is the probability of comparison-wise type I error, then the probability of family-wise type I error is usually calculated as follows:
where C is the total number of pairwise comparisons for k populations:
For example, for k=4 populations, there are C=6=4(4-1)/2 pairs of populations; and for we have from the formula - - that is, the probability of family-wise type I error is much higher than the probability of comparison-wise type I errors.
See also: Bonferroni adjustment.