In statistics, tests of the significance of pairwise differences between more than two means, often conducted after analysis of variance. Significance tests designed for comparisons between just one pair of means cannot be used for this purpose without violating the assumptions of the tests, because if three comparisons are made between three means, for example, then even if the data were completely random, the probability that one of the comparisons would be significant at p < .05 by chance alone would be greater than .05, because there would be three ways in which this could happen: Mean 1 could be significantly different from Mean 2, Mean 1 from Mean 3, or Mean 2 from Mean 3. This means that there would be inadequate protection against a Type I error. Various specialized procedures have therefore been devised for handling multiple comparisons. See also Bonferroni correction, Duncan's multiple range test, least-significant difference test, Newman-Keuls test, Scheffé test, Tukey-HSD test. Compare a priori test.