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| Titel: |
Efficiency of t-Test and Hotelling's T2-Test After Box-Cox Transformation |
| Auteur: |
Freeman, Jade Modarres, Reza |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 35 (2006) nr. 6 pagina's 1109-1122 |
| Jaar: |
2006-07-01 |
| Inhoud: |
Early investigations of the effects of non-normality indicated that skewness has a greater effect on the distribution of t-statistic than does kurtosis. When the distribution is skewed, the actual p-values can be larger than the values calculated from the t-tables. Transformation of data to normality has shown good results in the case of univariate t-test. In order to reduce the effect of skewness of the distribution on normal-based t-test, one can transform the data and perform the t-test on the transformed scale. This method is not only a remedy for satisfying the distributional assumption, but it also turns out that one can achieve greater efficiency of the test. We investigate the efficiency of tests after a Box-Cox transformation. In particular, we consider the one sample test of location and study the gains in efficiency for one-sample t-test following a Box-Cox transformation. Under some conditions, we prove that the asymptotic relative efficiency of transformed t-test and Hotelling's T2-test of multivariate location with respect to the same statistic based on untransformed data is at least one. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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