![]() Another indication is that the group histograms or QQ plots look similar (although not necessarily indicating normality). H 1: the group population medians are not equalĪn indication that the population distributions have the same shape (except that possibly there is a shift to the right or left among them) is that the box plots are similar, except that the box and whiskers among them may be at different heights. H 0: the group population medians are equal When the group samples have the same shape (and so presumably this is reflective of the corresponding population distributions), then the null hypothesis can be viewed as a statement about the group medians. H 1: At least one of the group populations is dominant over the others when one element is drawn at random from each group population, the largest (or smallest, or second smallest, etc.) element is equally likely to come from any one of the group populations H 0: the group populations have equal dominance i.e. A group is dominant over the others if when one element is drawn at random from each of the group populations, it is more likely that the largest element is in that group. The Kruskal-Wallis test is actually testing the null hypothesis that the populations from which the group samples are selected are equal in the sense that none of the group populations is dominant over any of the others.
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