XLSTAT: Mantel Test in Excel

 

Background

The Mantel test is useful to compute and test the linear correlation between two proximity matrices (dissimilarity or similarity). It is often used in Ecology to test if the dissimilarities between several sites, in terms abundancy of species on one side, and in terms of geophysical characteristics on the other side, can be related or not. Our example is in the field of genetics of populations.

 

Dataset for Example

The attached dataset is from a study examining whether genetic distance between insect populations across African regions is related to geographic and climatic distances. Genetic distance is measured by differences in gene frequencies for a single gene, while geographic distance includes both physical and climatic separation.

 

Setting Up

• Open XLSTAT.

• Click on the Nonparametric tests menu and select the Mantel test feature:

• Once you have clicked on the button, the dialog box appears.

In the General tab:

• Select the data corresponding to the first dissimilarity matrix (A).

• Select the data corresponding to the second dissimilarity matrix (B).

• Leave the Labels included option checked, since the row and column labels have been included in the selection,

In the Options tab:

• Select the two-tailed (r ≠ 0) option to compute a two-tailed p-value.

• Leave the Exact p-value option activated.

Note: If the matrices are larger than 4×4, the exact p-value cannot be computed. In that case, XLSTAT automatically switches to using 10,000 random permutations to estimate the p-value.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first result allows to visually verify if there is somehow a correlation between the proximities of the two matrices.

The next table gives the Mantel r statistic, and the corresponding two-tailed p-value, obtained from the 10000 permutations. We can see here that as the conclusion confirms it, we should reject the null hypothesis that there is no correlation between the matrices. As a conclusion, we can consider that the genetic and geographic distances are correlated.

A chart shows the distribution from which the p-value has been obtained.