Detecting outliers with Mandel’s h and k statistics with XLSTAT

Dataset for testing differences between samples with Mandel's statistics

An Excel sheet with both the data and the results can be downloaded by clicking here.

Four samples have been obtained from two different distribution: 3 with a normal distribution with mean 0 and variance 2 and one with a normal distribution with mean 0 and variance 5 .We suppose that each sample is related to the results of a laboratory. We wish to test if there are differences between laboratories' results.

Goal of this tutorial

We would like to detect if means and variances are homogeneous using the h and k statistics of Mandel. You can find some detail on these statistics here.

Setting up a h and k Mandel's statistics analysis

To start the Madel's h and k statistics go to the menu Testing outliers / Mandel's h and k statistcs.

mandel statistics menu

In the General tab, select the data. Four columns should be selected with the option one column per group.

mandel statistics dialog box general

When ready click on OK.

Results of a h and k Mandel's statics

In the following table, we can see the h and k statistics for each laboratory.

mandel statistics result

In the following graphic, the h statistics are displayed together with the critical value. We can see that none of the values are outside the critical interval.

mandel statistics plot

The same graphic is available for the k statistic. It also shows that none of the laboratory obtain an outlying k statistic.

mandel statistics k plot

We have shown that there is no outlying laboratory in this study.

Click here for other tutorials.

About KCS

Kovach Computing Services (KCS) was founded in 1993 by Dr. Warren Kovach. The company specializes in the development and marketing of inexpensive and easy-to-use statistical software for scientists, as well as in data analysis consulting.

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