How Do You Know if a Process Is Following a Normal Distribution?

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

  • 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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