One-Factor Independent Groups ANOVA

Consider a study where three doses of a new antihypertensive drug are to be compared, and three groups of subjects will each receive one dose. Such a study may be performed in earlier phase drug development to determine the most appropriate dose for subsequent larger trials. The research question, research hypothesis, and null hypothesis in this case would be  

The simple fact that there are three treatment groups means that an independent groups f-test cannot be employed that test can only handle two treatment groups. In this case, a one-factor independent groups ANOVA is appropriate. From now on, the one-factor part of the name will be left off, since our examples focus on designs where only one source of influence is being investigated. 

As noted in Section 7.5, the test statistic in ANOVAs is called F, and the test is sometimes called the F-test. The name pays respect to Sir Ronald Fisher, the statistician who developed this approach. Similarly to the calculation of the test statistic t in a f-test, F is calculated as a ratio, as follows  

F = effect variance = between treatment groups variance error variance within treatment groups variance 

Analogously to f, Fhas to reach a certain size to attain statistical significance. This size is dictated by the associated degrees of freedom in each instance, and in turn the degrees of freedom are dictated by the total number of subjects participating in the study. To attain significance, F must always be greater than 1, which means 

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As noted in Section 7.5, one-factor independent groups ANOVA can also be used in cases where the independent groups f-test is appropriate. The term independent groups is derived in exactly the same way as was independent groups f-test, in that independent groups of subjects are employed. The term one-factor relates to the fact that, in our ongoing example, there is only one factor that is of interest that factor is type of treatment administered. A factor is an influence that one wishes to study it is of interest to know whether the factor is a systematic source of influence on, and therefore a systematic source of variance in, the data collected in a study. An equivalent designation is not necessary in the case of the f-test, since it can only be used when there is just one factor of interest. 

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