In our focus to test for data normality so that most parametric tests can be run, we sometimes get ahead of ourselves and perform modifications to existing data in order to normalize said data. For instance, the dataset 4.5, 1.8, 9.3, 6.1, 8.2, 13.9, 23.5, 3.2, 56.8, 80.7 is subjected to BizStats’ Box–Cox Transformation and the resulting data becomes 0.55492, 1.03910, 1.30106, 1.52037, 1.72135, 1.80337, 2.05196, 2.34839, 2.78224, 2.93490. In fact, the before- and after-transformation results look rather astounding. The original data rejects normality with a p-value of 0.0017 versus the post-transformation p-value of 0.9691, with a very high normality fit. However, the data completely loses its efficacy and meaning with such a drastic change. Nonetheless, there are applications in Six Sigma, such as computing the process capability, that require such a transformation in order to obtain valid estimates.
