How to run Mandel’s h and k statistics to detect outliers in XLSTAT?

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

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 the computation of Mandel’s h and k statistics

• Open XLSTAT

• In the ribbon, select Testing outliers / Mandel's h and k statistics.

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

• Click on OK to begin computation.

How to interpret Mandel's h and k statistics?

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

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.

Therefore, none of the samples has a mean that is significantly different from the other ones and thus does not contain any outliers.
The same graphic is available for the k statistic. This chart shows that LAB1 has a k statistic that is above the critical interval. This means that this laboratory is an outlying one because its variance is significantly different from the variance of the other laboratories.

Conclusion

The h test statistic does not detect a sample to be significantly different from the others depending on the means. However, the k statistic reveals a significantly different variance in the first sample. We can conclude that some outliers, significantly lower and greater than in the data from the other labs, are present in the first one. Their values compensate, which explains that the mean does not differ significantly from the other ones, but the high variance reveals their presence.