Mantel test

Mantel test is part of:

  • Pro Core statistical software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
    Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
  • Data and results shared seamlessly
    Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
  • Modular
    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
  • Affordable
    Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
  • Accessible - Available in many languages
    Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
  • Automatable and customizable
    Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.

Use of the Mantel test

A Mantel test measures and tests the linear correlation between two proximity matrices (simple Mantel test) or between two matrices while taking into account the linear correlation with a third matrix (partial Mantel test).

Simple Mantel test:

Mantel proposed a first statistic to measure the correlation between two proximity (similarity or dissimilarity) and symmetric A and B matrices of size n:

Z(AB) = ∑(i-n...n-1) ∑(j-i+1...n) aij bij

In the case where the matrices are not symmetric, the computations are possible.

While it is not a problem to compute the correlation coefficient between two sets of proximity coefficients, testing their significance cannot be done using the usual approach that is used to test correlations: to use the latter tests, one needs to assume the independence of the data, which is not the case here. A permutation test has been proposed to determine if the correlation coefficient can be considered as showing a significant correlation between the matrices or not. It can be one- or two-sided.

The Mantel test consists of computing the correlation coefficient that would be obtained after permuting the rows and columns of one of the matrices. The p-value is calculated using the distribution of the r(AB) coefficients obtained from S permutations. In the case where n, the number of rows and columns of the matrices, is lower than 10, all the possible permutations can easily be computed. If n is greater than 10, one needs to randomly generate a set of S permutations in order to estimate the distribution of r(AB).

Partial Mantel test

A Mantel test for more than two matrices has been proposed: when we have three proximity matrices A, B and C, the partial Mantel statistic r(AB.C) for the A and B matrices knowing the C matrix is computed as a partial correlation coefficient. In order to determine if the coefficient is significantly different from 0, a p-value is computed using random permutations.

Tutorials

Screenshots