Example of Friedman test main topic interpreting results session command see also
Example of Friedman test A randomized block experiment was conducted to evaluate the effect of a drug treatment on enzyme activity. Three different drug therapies were given to four animals, with each animal belonging to a different litter. The Friedman test provides the desired test of H0: all treatment effects are zero vs. H1: not all treatment effects are zero.
1 Open the worksheet EXH_STAT.MTW.
2 Choose Stat > Nonparametrics > Friedman.
3 In Response, enter EnzymeActivity.
4 In Treatment, enter Therapy. In Blocks, enter Litter. Click OK.
Session window output
Friedman Test: EnzymeActivity versus Therapy blocked by Litter
S = 2.38 DF = 2 P = 0.305 S = 3.80 DF = 2 P = 0.150 (adjusted for ties)
Sum of Therapy N Est Median Ranks 1 4 0.2450 6.5 2 4 0.3117 7.0 3 4 0.5783 10.5
Grand median = 0.3783 |
The test statistic, S, has a p-value of 0.305, unadjusted for ties, and 0.150, adjusted for ties. For a levels 0.05 or 0.10, there is insufficient evidence to reject H0 because the p-value is greater than the a level. You therefore conclude that the data do not support the hypothesis that any of the treatment effects are different from zero.
The estimated medians associated with treatments are the grand median plus estimated treatment effects. The sum of ranks value is the sum of the treatment ranks, when ranked within each block. These values can serve as a measure of the relative size of treatment medians and are used in calculating the test statistic. The grand median is the median of the adjusted block medians. See Methods and Formulas for more information.