Matrix Correlations

Matrix Correlations

• Mantel Test generalized regression technique that examines associations of inter-individual distances based on one characteristic with those calculated from a second characteristic. This is a distribution-free (non-parametric) test. Moreover, one of these matrices can be artificially constructed to reflect a particular hypothesis (see below right)
• R-statistic: comparable to Spearman's Rho statistic for matrices. It is a Mantel's test performed on within-matrix ranks instead of the original variables. Ranks are averaged in case of ties.
• Kendall's Tau: sum of the number of cells in which thhe values change in the same direction, minus the number of cells in which they change in opposite directions. Kc = S |(X_ij-X_ik)(Y_ij-Y_ik)|

Uses

• measure the correlation between two matrices

How this is done

• calculate sample Z as the sum of products for corresponding elements in the two distance matrices. Z_s = SSx_ijy_ij For a complete example use the following worksheet.
• create a probability density function with random permutations of rows and columns for the second matrix and calculate a Z value for each permutation
• test significance using t-Value with infinte df: t = (Z_s - Mean(Z_p)) / SD(Z_p)