Introduction to Tests Supplementing a One-factor Between-Subjects ANOVA (1
of 2)
The
null hypothesis in a one-factor
between-subjects ANOVA is that all the
population
means are equal:
H
0:
µ
1 = µ
2 = ... = µ
a.
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).