Bivariate inductive statistics - ordinal and nominal variables - dependent groups

Friedman's test

Friedman's test is a nonparametric analysis that may be performed on data from a randomized block experiment. Friedman's test compares the medians of three or more dependent groups. It tests the null hypothesis that the different samples were drawn from distributions with the same median. Alternative hypothesis states that at least one median is different from the rest. Friedman's test uses ranks instead of original data (1 is assigned to lowest value etc.). The randomized block design takes account of known factors that affect outcome but are not of primary interest.

The two steps in randomized block design are:
1. Collect together homogeneous experimental units (e.g. people of same age, sex) into a block.
2. Assign treatments at random to the experimental units within a block.

Block often represents one person, who takes different medicine (treatment). In the analysis treatment is fixed factor and block is random factor. Data for the analysis must be entered so that one column is response variable, second is fixed factor and another random factor. One row represents one observation. Design with 3 treatments and 5 blocks must have exactly 3 x 5 = 15 rows.

Example: Do customers discriminate between several alternative commercials?