Then a distribution-free test, the Friedman test (developed by Milton Friedman, the economist), can be used. If there is concern about the normality or variability of the distributions, or if ordinal numbers are involved, then a straightforward two-way ANOVA might yield misleading results. Hoffman, in Basic Biostatistics for Medical and Biomedical Practitioners (Second Edition), 2019 Friedman Test In this particular example, the 20 ☌ temperature was significantly different from the 27 and 32 ☌ temperatures but not the 24 ☌. A Dunn's test is used to subsequently compare the different treatments following the Friedman analysis.

In this table a value of 7.6 is necessary for α < 0.05 and 10.0 for significance at the 0.01 level. In this experiment there are four treatments with a total of six subjects and the F r = 14.90. This test results in a Friedman statistic ( F r) and the possible significance of this value is then looked up in a specific table literally called the critical values for the Friedman two-way analysis of variance by ranks statistic, which is available on the web. The magnitude of the differences with each subject is not important. Essentially what this test does is rank the swim speeds for each subject across the various water temperatures and in this way each animal is compared to itself. The H o is that the swim speed will be the same regardless of the water temperature. The question is whether or not changing the water temperature in the maze affects the swimming speed. Here is a group of six different rats with their swim speeds on different days as a result of a change in the water temperature.

Sigmaplot 11 do not test bonferroni