Testing Normality of Data Transformed by Maximum Likelihood Box Cox
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913509059592192 |
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| author | Hawkins, Douglas M |
| author_facet | Hawkins, Douglas M |
| contents | Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from resubstitution bias following Box-Cox transformation, and indicates normality much too often. The work reported here extends this by adding the Shapiro-Wilk statistic and the two-parameter Box Cox transformation, all of which show severe bias. We also develop a recalibration to correct the bias in all four settings. The methodology was motivated by finding reference ranges in biomarker studies where parametric analysis, possibly on a power-transformed measurand, can be much more informative than nonparametric. Setting environmental standards illustrates another potential application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing Normality of Data Transformed by Maximum Likelihood Box Cox Hawkins, Douglas M Methodology 62 Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from resubstitution bias following Box-Cox transformation, and indicates normality much too often. The work reported here extends this by adding the Shapiro-Wilk statistic and the two-parameter Box Cox transformation, all of which show severe bias. We also develop a recalibration to correct the bias in all four settings. The methodology was motivated by finding reference ranges in biomarker studies where parametric analysis, possibly on a power-transformed measurand, can be much more informative than nonparametric. Setting environmental standards illustrates another potential application. |
| title | Testing Normality of Data Transformed by Maximum Likelihood Box Cox |
| topic | Methodology 62 |
| url | https://arxiv.org/abs/2407.19329 |