Anova Ftest in a oneway analysis of variance is used to assess whether the expected values of a quantitative variable within several predefined groups differ from each other. For example, suppose that a medical trial compares four treatments. The ANOVA Ftest can be used to assess whether any of the treatments is 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 Ftest is that we do not need to prespecify which treatments are to be compared, and we do not need to adjust for making multiple comparisons. The disadvantage of the ANOVA Ftest, among others, is that if we reject the null hypothesis.
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