Hi all,

What is box - cox transfromation ? Why are we converting the non-normal data to normal data when we are having non -parametric tests to perform analysis.

Please let me know if it necessary to convert my data to normal when it is non normal.

Regards

Anish Mohandas

Dear Anish,

There are several approaches to solve any problem. You will have to pick the most appropriate one depending on your situation.

Box-Cox transformation is a group of transformations that help with transformation of the data from Non-normal to Normal. This transformation includes, among others, taking the reciprocal of the data set, or taking the square of the data set, or taking the logarithm of the data etc. in order to make it Normal. Box-Cox tries different combinations and then picks the transformation that best makes the data Normal. There is NO guarantee that if you apply the Box-Cox transformation, your data will become Normal.

One application of Box-Cox transformation is in Control Charts for Individuals (example I-MR Chart). In order to use I-MR charts, data has to be Normal. If it is not Normal, then you may try using a Box-Cox to make it Normal before using the I-MR chart.

When you are doing Hypothesis testing and say comparing two populations, it may be preferable to use Non-parametric distributions rather than apply Box-Cox transformations (please see one of my earlier posts on this topic).

Hope this helps.

SJ.