Pierre Legendre
December 2000
Département de Sciences Biologiques
Université de Montréal
This program computes a matrix of Pearson correlations among variables, with test of significance of the correlation coefficients obtained by permuting the data in one of the two variables in each pair. The theory of this type of test is presented, for instance, in Legendre & Legendre (1998, Section 1.2). Input data file: the objects are the rows of this file; the variables are the columns. The program is presently dimensioned for 1000 objects and 101 variables. There are three types of output files: File 'Correlation.out' contains the square correlation matrix. File 'Prob.out' contains the square matrix of permutational probabilities. File 'CorrProb.out' contains both the correlations and the probabilities. Here is an example of a 'CorrProb.out' file. It contains the correlations among 5 variables made of random normal deviates. The correlation matrix is of size (5 x 5); the values on the diagonal are 1.00000. The corresponding permutational probability is printed under each correlation value. The diagonal probabilities (0.0000) were not computed; they are trivial values devoid of interest.
```
Square correlation matrix. For each correlation:
Line 1 = correlation,  line 2 = probability (    99 permutations)

1.00000  0.11873  0.00299  0.04744  0.24603
0.0000   0.3900   1.0000   0.6900   0.1000

0.11873  1.00000  0.24107  0.05241  0.09498
0.3900   0.0000   0.1200   0.7400   0.5600

0.00299  0.24107  1.00000  0.28926 -0.02828
1.0000   0.1200   0.0000   0.0500   0.8800

0.04744  0.05241  0.28926  1.00000  0.01057
0.6900   0.7400   0.0500   0.0000   0.9500

0.24603  0.09498 -0.02828  0.01057  1.00000
0.1000   0.5600   0.8800   0.9500   0.0000

```
If necessary, the output files can be transferred to a spreadsheet program where identifiers may be added to the rows and columns of the correlation matrix.

### Program availability

• Macintosh version
• Fortran source code
• Compiled versions of the program for any Macintosh computer (fat binary)
• Sample data file
• 32-bit DOS version (The executable file is a Win32 "console" executable, not a DOS executable. Therefore it cannot run under plain DOS, nor in a DOS window under Windows 3.x, only in Windows 95/98 or Windows NT consoles)
• Fortran source code
• Compiled version of the program for Win32 compatible computers
• Sample data file
Reference:
Legendre, P. & Legendre, L. 1998. Numerical Ecology, 2nd English edition. Elsevier Science BV, Amsterdam. xv + 853 pages.