Data Normality Tests in Excel

Is Your Data Normal?

Statistical analysis (e.g., ANOVA) may rely on your data being "normal" (i.e., bell-shaped), so how can you tell if it really is normal?

The two tests most commonly used are:

The Anderson-Darling values shown are:

  • A-squared = 0.270
  • p value= 0.648
  • 95% Critical Value = 0.787
  • 99% Critical Value = 1.092
p value <= a Reject the null hypothesis
p value > a Cannot reject the null hypothesis - the data is normal.
A-squared > critical value 
Reject the null hypothesis
A-squared <= critical value 
Cannot reject the null hypothesis - the data is normal.

"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.

Using the p value:  p = 0.648 which is greater than alpha (level of significance) of 0.01. So we cannot reject the null hypothesis (i.e., the data is normal).

Using the critical values, you would only reject this "null hypothesis" (i.e., data is non-normal) if A-squared is greater than either of the two critical values. Since 0.270 < 0.787 and 0.270 < 1.092, you can be at least 99% confident that the data is normal.

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Normal Probability Plot Method

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.
  • QI Macros probability plot also calculates  R².
normal probability plot

Normal Probability Plots in QI Macros Add-in for Excel

QI Macros has several tools that will run a Probability Plot for you. They include:

Example of QI Macros XmR chart Template

probability plot and histogram in the QI Macros

Just by looking at the histogram (bell shaped) and probability plot, you can see that this data is fairly normal.

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