Modifying the t and ANOVA F Tests When Treatment Is Expected to Increase Variability Relative to Controls

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Abstract
When similar experimental units are assigned randomly to two groups, one to receive a "treatment," the other to serve as a control, the homogeneity of variance assumption underlying the pooled t test is valid under the null hypothesis of no treatment effect. Thus power, and not validity, of the pooled t should be the concern in such experiments, espeically if treatment ma affect variability as well as mean response. We focus on studies where there is a biological basis (e.g., toxicological studies) for expecting a treatment effect on mean response to be accompanied by an increase in variance. To detect a change in mean response in such experimental situations, we propose a simple modification of the pooled t that is also valid under Ho: "no treatment effect," but which can have substantially better power than the pooled t. This modification can also be applied to other procedures for testing equality of means when there are two or more "treatment" groups in addition to the control.

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