Box Cox Transformation. The statisticians george box and david cox developed a procedure to identify an appropriate exponent lambda l to use to transform data into a normal shape the lambda value indicates the power to which all data should be raised. The box cox transformation of the variable x is also indexed by λ and is defined as equation 1 at first glance although the formula in equation 1 is a scaled version of the tukey transformation x λ this transformation does not appear to be the same as the tukey formula in equation 2.
The basic idea behind this method is to find some value for λ such that the transformed data is as close to normally distributed as possible using the following formula. The box cox transformation of the variable x is also indexed by λ and is defined as equation 1 at first glance although the formula in equation 1 is a scaled version of the tukey transformation x λ this transformation does not appear to be the same as the tukey formula in equation 2. Y λ y λ 1 λ if y 0.
Box cox normal transformation we seek a transformation of data in a sample x1 xn which results in data that is normally distributed.
Mathematics behind box cox transformation. The box cox transformation is named after statisticians george box and sir david roxbee cox who collaborated on a 1964 paper and developed the technique. Minitab will select the best mathematical function for this data transformation. In order to do this the box cox power transformation searches from lambda 5 to lamba 5 until the best value is found.
