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Run Mandel’s h and k statistics to detect outliers


This tutorial will help you compute and interpret Mandel’s h and k statistics for outliers in Excel using 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 distributions: 3 from a normal distribution with mean 0 and variance 2 and one from 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.

Setting up a h and k Mandel's statistics analysis

To start the Mandel'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 statistics

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.

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