Graduate Thesis Or Dissertation
 

Testing for location after transformation to normality

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/rv042x085

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  • In the problem of testing the median using a random sample from a certain distribution, and if no other parametric family is suggested, the t-test is known to be the optimal procedure when this distribution is normal. If the sample appears to be non-normal, one has the choice either to consider a non-parametric approach or to try to correct for non-normality before applying the t-test. In this thesis we investigate the effect of applying certain power transformations as an action to correct for non-normality before applying the t-test. Also we investigate the effect of applying a power transformation then trimming a certain proportion from the data on each tail as a double action to correct for non-normality. This problem is first considered by Doksum and Wong (1983), who apply the Box-Cox power transformations to positive, right-skewed data when testing for the equality of distributions of two independent samples. In the present work we provide results for the one-sample case using two alternatives to the Box-Cox power family which are applicable to all data sets. Whenever it can be assumed that the data is a random sample from a symmetric distribution with heavy tails, it is shown that the John-Draper family of modtlus power transformations, with the transformation parameter being positive and smaller than 1 , is appropriate to correct for non-normality and the t-test based on the transformed data is asymptotically more efficient and has better power properties than the t-test based on the data in its original scale. -When the data is thought to have a skewed distribution and can assume negative as well as positive values, a new family of transformations, referred to as the two-domain family, is introduced. It is shown that the t-test based on the data after applying this new transformation is also asymptotically more efficient and has better power properties than the t-test in the original scale. A simulation study shows that trimming a certain proportion on each tail of the data transformed by one of the above two transformations then applying the t-test to the trimmed samples yields a considerable gain in power compared to the t-test in the original scale.
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