Anderson Darling Normality Test

Is Your Data Normal?

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

Anderson Darling p-value and Critical Value Method

QI Macros add-in for Excel contains a Normality Test which uses the Anderson-Darling method. The output includes the Anderson-Darling statistic, A-squared, and both a p-value and critical values for A-squared.

Note: Excel does not do an Anderson Darling test;
QI Macros adds this functionality.

QI Macros adds a new tab to Excel's menu. To run a normality test using QI Macros:

  1. Just select your data, then click on QI Macros menu and select Statistical Tools, Descriptive Statistics - Normality Test:

    descriptive-statistics-normality-test-2

  2. QI Macros will run an Anderson-Darling Normality Test and other descriptive statistics giving both numerical and graphical representations of the data:

    Anderson Darling test results in QI Macros

Watch this Video to See How It Works

Interpreting the Anderson Darling test results

See how....

The Anderson-Darling values shown are:

  • A-squared = 0.270
  • p value= 0.648
  • 95% Critical Value = 0.787
  • 99% Critical Value = 1.092
If
Then
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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Another Example

Using Cells D1:D41 (after deleting the blank row) from the XbarR.xls in c:\qimacros\testdata, you would get the following result. Notice how the normality plot curves at the right so that some of the points are farther from the line. Using Anderson-Darling we discover that the data is considered normal at one level (99%), but not at another (95%).

data normality test example from QI Macros

Using the p value p = 0.016 which is greater than alpha of 0.01 (0.01 < 0.016 < 0.05), we can reject the null hypothesis (i.e., the data is normal) at alpha = 0.05, but not at alpha = 0.01.

Using the critical values, . Since 0.787 <0.932 < 1.092, you would reject the null hypothesis at 95% but not reject it at 99%.

Frankly, the double negatives of "not rejecting the null hypothesis" makes my brain tired. All I really want to know is: "Is my data normal?" So, in summary:

  • if the dots fit the trend line on the normal probability plot, then the data is normal
  • if p > alpha then the data is normal
  • if A-squared < Critical Value, then the data is normal.

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