Suppose we have a set of data, that do not follow normal distribution. In order to make it follow the normal distribution approximately, we use Box Cox transformation. Then, we need to measure its normality possibly using QQ plot. According to wikipedia page here https://en.wikipedia.org/wiki/Normality_test, it says that
A graphical tool for assessing normality is the
normal probability plot, a quantile-quantile plot
(QQ plot) of the standardized data against the
standard normal distribution. Here the correlation
between the sample data and normal quantiles
(a measure of the goodness of fit) measures
how well the data are modeled by a normal distribution.
For normal data the points plotted in the QQ plot should
fall approximately on a straight line, indicating
high positive correlation. These plots are easy to interpret
and also have the benefit that outliers are easily identified.
My question is how to know the normal quantiles. What we have is a data set that the BoxCox transformation was applied. Is the following correct?
- Obtain standard deviation and mean of the data
- Set them as a parameter of normal distribution
Sample as many data from the normal distribution as the data we have
Compute the correlation b/w expected normal-distributed samples and observed transformed data
- Plot them