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.

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• I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!

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