Asymmetric Confidence Interval with Box-Cox Transformation in R

2017-12-08
Dağ, Osman
İlk, Özlem
Normal distribution is important in statistical literature since most of the statistical methods are based on normal distribution such as t-test, analysis of variance and regression analysis. However, it is difficult to satisfy the normality assumption for real life datasets. Box–Cox power transformation is the most well-known and commonly utilized remedy [2]. The algorithm relies on a single transformation parameter. In the original article [2], maximum likelihood estimation was proposed for the estimation of transformation parameter. There are other algorithms to obtain transformation parameter. Some of them include the studies of [1], [3] and [4]. Box– Cox power transformation is given by 𝑦𝑖 𝑇 = { 𝑦𝑖 𝜆−1 𝜆 , 𝑖𝑓 𝜆 ≠ 0 𝑙𝑜𝑔 𝑦𝑖 , 𝑖𝑓 𝜆 = 0 . Here, 𝜆 is the power transformation parameter to be estimated, 𝑦𝑖 ’s are the observed data, 𝑦𝑖 𝑇 ’s are transformed data. In this study, we focus on obtaining the mean of data and a confidence interval for it when Box-Cox transformation is applied. Since the transformation is applied, the scale of the data has changed. Therefore, reporting the mean and confidence interval obtained from transformed data is not meaningful for the researchers. Besides, reporting mean and symmetric confidence interval obtained from original data becomes misleading for the researchers since the normality assumption is not satisfied. Therefore, it is pointed out that mean and asymmetric confidence interval obtained from back transformed data must be reported. We have written down a generic function to obtain the mean of data and a confidence interval for it when Box-Cox transformation is applied. It is released under R package AID with the name of “confInt” for implementation.
Citation Formats
O. Dağ and Ö. İlk, “Asymmetric Confidence Interval with Box-Cox Transformation in R,” presented at the 10th International Statistics Congress, (6 - 08 Aralık 2017), 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/85386.