**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:**

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

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

### Watch this Video to See How It Works

### Interpreting the Anderson Darling test results

#### 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.

### 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%).

**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.

### Why Choose QI Macros Statistical Software for Excel?

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- Works Right in Excel
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