INFERENCE FOR THE INTRINSIC SEPARATION AMONG DISTRIBUTIONS WHICH MAY DIFFER IN LOCATION AND SCALE By

The null hypothesis of equal distributions, 0 1 2:... KH F F F , is commonly used to compare two or more treatments based on data consisting of independent random samples. Using this approach, evidence of a difference among the treatments may be reported even though from a practical standpoint their effects are indistinguishable, a long-standing problem in hypothesis testing. The concept of effect size is widely used in the social sciences to deal with this issue by computing a unit-free estimate of the magnitude of the departure from 0H in terms of a change in location. I extend this approach by replacing 0H with hypotheses { 0H} that state that the distributions {}iF are possibly different in location and or scale, but close, so that rejection provides evidence that at least one treatment has an important practical effect. Assessing statistical significance under *0H is difficult and typically requires inference in the presence of nuisance parameters. I will use frequentist, Bayesian and Fiducial modes of inference to obtain approximate tests and carry out simulation studies of their behavior in terms of size and power. In some cases