# 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

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.

### 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 Plots in QI Macros Add-in for Excel

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

- Descriptive Statistics
- Capability Suite of Six Charts
- XmR, XbarR and XbarS Chart Templates

**Example of QI Macros XmR Chart Template**

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

### Probability Plot Template

QI Macros also offers a Probability Plot template, found in the Chart Templates drop-down menu:

Within this template, there are 2 template options:

- Probability Plot (Z)
- Probability Plot (%)

In each of these templates, you will find a Normal Probability Plot chart, a Half-Normal Probability Plot chart and a Kolmogorov-Smirnov Test.

A Normal Probability Plot graphs z-scores (standard scores) against your data set. It also provides you with a visual representation of whether your data set is a normal distribution:

A Half Normal Probability Plot graphs your distribution to evaluate which factors are important vs. which are unimportant:

Kolmogorov-Smirnov (KS) is a Goodness-of-Fit Test that is used to indicate if a sample comes from a population with a specific distribution:

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