Many of the analysis required in the Green Belt and Black Belt Body of knowledge assumes a normal distribution. There’s a good reason for this; normal distributions have a nice, symmetrical shape that makes working with them much easier (like in an ANOVA for example!) But how do you know if your process is following a normal distribution? Use these tests to find out.

## Visual Normality Tests / Graphical Analysis

- Visual examination. Make a histogram or another bar graph. Only reject normality in the presence of “gross non-normality” – extreme departures from symmetry.
- If you see a bell curve, a distribution is approaching normal.
- Tall, thin curve = smaller standard deviation.
- Fatter, lower curve = larger standard deviation.
- You can test using a Normal Probability Plot. The probability plot transforms the data into a normal distribution and plots it as a scatter diagram.
- Normal data will follow the trend line.
- Non-normal data will have more points farther from the trend line.

- The peak of the normal curve is an indication of the average, which is the center of process variation. An average of a group of numbers is an indication of the central tendency.
- Neat interactive graphic here.

## Quantifiable Normality Tests

- Use the Chi Square Goodness of Fit test.
- Follow the Anderson-Darling Normality test or Critical Value Method.
- The output includes the Anderson-Darling statistic, A-squared, and both a p-value and critical values for A-squared.
- “Null hypothesis” is that the data is normal. The “alternative hypothesis” is that the data is non-normal. Reject the Null hypothesis (i.e., accept the alternative) when p<=alpha or A-squared>critical value.
- if p > alpha then the data is normal.
- if A-squared < Critical Value, then the data is normal

- Mean is the inverse of the Poisson distribution.
- The smaller the standard deviation, the tighter the grouping of data around the mean.