Editing F-test (section)

===Multiple-comparison ANOVA problems===
The ''F''-test in one-way analysis of variance ([[ANOVA]]) is used to assess whether the [[expected value]]s of a quantitative variable within several pre-defined groups differ from each other. For example, suppose that a medical trial compares four treatments.  The ANOVA ''F''-test can be used to assess whether any of the treatments are on average superior, or inferior, to the others versus the null hypothesis that all four treatments yield the same mean response.  This is an example of an "omnibus" test, meaning that a single test is performed to detect any of several possible differences.  Alternatively, we could carry out pairwise tests among the treatments (for instance, in the medical trial example with four treatments we could carry out six tests among pairs of treatments).  The advantage of the ANOVA ''F''-test is that we do not need to pre-specify which treatments are to be compared, and we do not need to adjust for making [[multiple comparisons]].  The disadvantage of the ANOVA ''F''-test is that if we reject the [[null hypothesis]], we do not know which treatments can be said to be significantly different from the others, nor, if the ''F''-test is performed at level α, can we state that the treatment pair with the greatest mean difference is significantly different at level α.