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Family-wise Type I Error (Graphical)

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 Math image is the probability of comparison-wise type I error, then the probability Math image of family-wise type I error is usually calculated as follows:

Math image

where C is the total number of pairwise comparisons for k populations:

Math image

For example, for k=4 populations, there are C=6=4(4-1)/2 pairs of populations; and for Math image we have from the formula – Math image – 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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