The original concepts of analysis of variance came from the work of Sir Ronald A. Fisher, an English statistician. This technique, better known as ANOVA, has become one of the most commonly used research methods for testing differences among several population means. If only two populations are in question, ANOVA can be used; however, a two-sample t test would be much easier to test for equality of two population means.
Now suppose five populations are in question. If the two-sample t test were used, we would need to test ten possible combinations (five items taken two at a time). This would be possible; however, if we chose α = 0.05 for each test, this means the probability of committing a Type I error in any particular test is 0.05. What can we conclude about the hypothesis that all means are equal if each of the ten individual tests has a 0.05 probability of a Type I error?