# Box Cox Transformation

At most times, while dealing with data, I assume that the underlying distribution is normal. Also, I have found that most common statistical measures assume normal distribution of data. But we know that data distributions are not always normal. In simple words, it means that we need to plot the data always so as to confirm the underlying distribution. With plotting,  sometimes we also find that a small transformation ( like $x^2 , log(x)$) results in normal distribution. This means that data transformations can make our life simple and allow us to use statistical measures intended form normally distributed data.

Box Cox Transformation: George Box and Sir David Cox came out with a transformation formula which uses different values between -5  and 5  of a parameter ($\lambda$) to perform transformation. In other words, this formula finds the best value at which data can be represented normally.

$\displaystyle { x }_{ \lambda }^{ ' } = \frac { { x }^{ \lambda } - 1 }{ \lambda }$

$\lambda=0$ results in log transformation.  It is not guaranteed that data will always get transformed to normal distribution.

Reference: