XLSTAT: Distribution sampling & normality tests in Excel

Purpose

In this article we will demonstrate how to:

1. Generate a sample from a Normal distribution and one from a uniform distribution.

2. Perform normality tests on both samples using XLSTAT Cloud.

 

Dataset for Example

We want to generate two samples, the first one sampled in a Normal N(2,2) distribution (mean = 2, standard deviation (sigma) = 2), the second one in a Uniform distribution, bounded between -1.5 and 5. To do that, we use the Distribution sampling tool available in the Preparing data section.

Setting up the a distribution sampling

After opening XLSTAT Cloud, click on Distribution sampling in the Preparing data menu:

The Distribution sampling interface appears.

Select the Theoretical distribution to use and define its parameters.

Then enter the number and the size of the sample to generate.

The dialog box displayed below corresponds to the generation of a sample of 1000 cases from a normal N(2,2) distribution.

The computations begin once you have clicked on the Run button, and the sample is then displayed.

A second sample is then generated using a Uniform distribution bounded between -1.5 and 5 .

In the Outputs tab, deactivate the Display the report header option. In the Options tab select the cell next to the top of the column associated with the first sample in the field Range. This will allow you to generate the new sample next to the other one

Click on Run in order to display the second sample.

Setting up Normality tests

The next step is to test the normality of the two samples. Click on Normality tests in the Describing data menu:

The user interface of Normality tests appears.

Select the two samples in the Data field and activate the Sample labels .

In the Outputs tab, activate the Q-Q plots and P-P plots to visually assess sample normality.

The computations begin once you have clicked on the Run button, and the results are displayed on a new sheet.

Interpreting the Results

Results are shown first for the first sample, then the second.

The initial output is the Q-Q plot for the first sample, comparing its cumulative distribution function (x-axis) to that of a theoretical normal distribution with the same mean and standard deviation (y-axis).

If the sample is normal, points align along the bisecting line; deviations indicate non-normality.

We can see here that the empiric cdf is very close to the bissecting line.

The Shapiro-Wilk and Jarque-Bera tests both fail to reject normality for the first sample (p > α), with Shapiro-Wilk being more stringent.

For the second sample, the Q-Q plot shows two major deviations, suggesting the distribution is likely not normal.

This gap is confirmed by the normality tests (see below) which allow to assert with no hesitation that we need to reject the hypothesis that the sample is normally distributed.

Conclusion

The tests for our example did not reject the normality assumption for the first sample, and allowed us to reject it for the second sample. 
 NOTE: your data is NOT stored when you use the XLSTAT-Cloud add-in.