The Friedman test is an extension of the sign test for several independent samples. It is analogous to the 2-way Analysis of Variance, but depends only on the ranks of the observations, so it is like a 2-way ANOVA on ranks.
The Friedman test should not be used for only three treatments due to lack of power, and is best for six or more treatments. It is a test for treatment differences in a randomized, complete block design. Data consists of b mutually independent k-variate random variables called blocks. The Friedman assumptions are that the data in these blocks are mutually independent, and that within each block, observations are ordinally rankable according to some criterion of interest.
A Friedman test is produced using rank scores and the F table, though alternative implementations call it the Friedman Statistic and use the chi-square table. Note that when all of the treatments are not applied to each block, it is an incomplete block design. The requirements of the Friedman test are not met under these conditions, and other tests such as the Durban test should be applied.
In addition to the Friedman statistics, Kendall’s Coefficient of Concordance (W) is produced, as well as Spearman’s Rho. Kendall's coefficient of concordance can range from 0 to 1. The higher its value, the stronger the association. W is 1.0 if all treatments receive the same rankness in all blocks, and 0 if there is “perfect disagreement” among blocks.
Spearman's rho is a measure of the linear relationship between two variables. It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks. Spearman’s Rho equals 1 if there is perfect agreement among rankings; disagreement causes rho to be less than 1, sometimes becoming negative.