Algorithms (Friedman ANOVA)

The procedure below draws on NAG algorithms.

The scores in each column are ranked,r_{ij}\,\! denoting the rank within block j\,\! of the observation in treatmentj\,\!i\,\!. Average ranks are assigned to tie scores.

  1. The ranks are summed over each treatment to give rank sums t_i=\sum_{j=1}^n r_{ij}, for i=1,2,...,k\,\!
  2. Friedman test statistic FR\,\!is calculated as FR=\frac{12}{nk(k+1)}\sum_{i=1}^k\left\{t_i-\frac{1}{2}n(k+1)\right\}^2

The significance level is compared to the x^2\,\! distribution with k-1\,\! degrees of freedom, where k is the total number of samples

For more details of the algorithm, please refer to nag_friedman_test (g08aec)