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 a is the probability of comparison-wise type I error, then the probability a_FW 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 a = 0.01 we have from the formula - a_FW=0.0585 - 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.

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