Statistical Tests Based on Transformed Data

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Abstract
The problem of testing hypotheses in linear models when the original data have been transformed is considered. It is assumed that the transformation involves an unknown parameter that has to be estimated from the data. For certain important testing problems it is found that the asymptotic level and power is as if λ had been assumed known. Asymptotic efficiency results show that when the Box-Cox transformation is used, tests based on transformed data have good power properties. Simulation results for transformed two-sample and linear regression testing problems show this to be true for moderate to small sample sizes as well. In particular, an α-trimmed t test based on averages of trimmed transformed variables performs very well in both light-tailed and heavy-tailed skew models when compared with the usual t test and rank tests.

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