Variance of Mantel statistic

Calculation of expected value and permutational variance for the Mantel statistic for use in an asymptotic approximation of the t-test; see Mantel (1967) for more details.

, sum of all matrix elements

, sum of the square of all matrix elements

, sum of the product of each element and its transpose element

, sum of the square of the row sums

, sum of the square of the column sums

, sum of the product of each row sum and corresponding column sum

, square of the sum of all matrix elements

Mantel statistic  

Expected Mantel statistic  

Permutational variance of Mantel statistic

Asymptotic approximation of t-test,