For completeness we now present another non-parametric replacement for one-way ANOVA, namely Mood’s Median Test. This test is essentially an extension of the Sign Test to two or more variables. We have already described this test for two independent variables in Mood’s Median Test for Two Samples.
The Kruskal-Wallis test has more power and is preferred to Mood’s Median Test since it takes into account the ranking of data whereas Mood’s Median Test just takes into account whether a data element is larger or samller than the median.
Example 1: Repeat Example 1 of Kruskal-Wallis Test using Mood’s Median Test.
The approach, as shown in Figure 1, is exactly the same as that described in Mood’s Median Test for Two Samples where we have one column in the contingency table for each independent variable.
Figure 1 – Mood’s Median Test
We see that the p-value = 0.100196 > .05 = α, and so the null hypothesis is not refuted. We conclude there is not significant difference between the three creams being tested. This is different from the result obtained from Kruskal-Wallis.
Real Statistics Functions: The Real Statistics Pack provides the following functions:
MOODS_STAT(R1) = the chi-square test statistic for Mood’s Median test where R1 contains the sample data.
MOODS_TEST(R1) = the p-value statistic for Mood’s Median test where R1 contains the sample data.
As we can see from Figure 1, χ2 = MOODS_STAT(A4:C13) = 4.60125 and p-value = MOODS_TEST(A4:C13) = 0.100196.