Ling, Yan2009-10-192009-10-192009-10-19http://hdl.handle.net/2097/1845The null hypothesis of equal distributions, H0 : F1[equals]F2[equals]...[equals]FK , 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 longstanding 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 H0 in terms of a change in location. I extend this approach by replacing H0 with hypotheses H0* that state that the distributions {Fi} 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 H0* 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 a bootstrap will be employed. I will focus on tests based on independent random samples arising from K[greater than and equals]3 normal distributions not required to have the same variances to generalize the K[equals]2 sample parameter P(X1>X2) and non-centrality type parameters that arise in testing for the equality of means.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/intrinsic separation parameter (ISP)normal distributionnuisance parameterp-valueaverage p-valueparametric bootstrap testDissertationStatistics (0463)