Nonnormal data
overview      

When you have nonnormal data, you can either transform the data in such a way that the normal distribution is a more appropriate model, or choose a nonnormal probability model for the data.

·    To check which distribution best fits your data, use Individual distribution identification.

·    To transform the data to follow a normal distribution

-    Box-Cox power transformation, use Individual distribution identification, Capability Analysis (Normal), Capability Analysis (Between/Within), Capability Sixpack (Normal), Capability Analysis Multiple Variables (Normal), and Capability Sixpack (Between/Within)

-    Johnson transformation, use Johnson transformation, Capability Analysis (Nonnormal), Capability Analysis Multiple Variables (Nonnormal), and Capability Sixpack (Nonnormal).

·    To use a nonnormal probability model, use Capability Analysis (Nonnormal), Capability Analysis Multiple Variables (Nonnormal), and Capability Sixpack (Nonnormal).

This table summarizes the differences between the models.

Normal model

Nonnormal model

Uses actual or transformed data for the histogram

Uses actual data units for the histogram

Calculates within, between/within (when both within and between subgroup variation exists), and overall capability

Calculates only overall capability

Draws a normal curve over the histogram to help you determine whether the transformation made the data
"more normal"

Draws the chosen nonnormal distribution curve over the histogram to help you determine whether the data fits the specified distribution

Which method is better? The only way to answer that question is to see which model fits the data better. If both models fit the data about the same, it is probably better to choose the normal model, since it provides estimates of both overall and within process capability.