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.

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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 QI Macros

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:

Chart Templates Top Menu

Within this template, there are 2 template options:

Proability Plot Tabs

  1. Probability Plot (Z)
  2. 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:

Normal Probability Plot Chart

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

Half Normal Probability Plot Chart

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:

Kolmogorov Smirnov Chart


Why Choose QI Macros Statistical Software for Excel?

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