The null hypothesis in a one-factor between-subjects ANOVA is that all the population means are equal:

H

Unfortunately, when the analysis of variance is significant and the null hypothesis is rejected, the only valid inference that can be made is that at least one population mean is different from at least one other population mean. The analysis of variance does not reveal which population means differ from which others. Experimenters usually are interested in more information. They want to know precisely where the differences lie. Consequently, further analyses are usually conducted after a significant analysis of variance. These further analyses almost always involve conducting a series of significance tests. This causes a very serious problem: the more significance tests that are conducted, the greater the chance that at least one of them will produce a Type I error. The probability that a single significance test will result in a Type I error is called the per- comparison error rate (PCER).