Stan/All:
This is great feedback and I plan to follow your suggestion and compare the confidence intervals. This seems to be the most straight forward solution to the problem. Since this is non-normal data, I believe that I should use the “one sample sign test” to obtain each distributions confidence interval correct?
By the way, I did go back and re-look at the help screens within Minitab as suggested. Try the following yourself: (open the program, click 1. help (from the top tool bar), 2. Statguide, 3. Help topics, 4. Nonparametic, and then 5. click on any of the following tests (Mann-Whitney, Kruskal-Wallis, Mood’s Median, and Friedman). You will find the Summay screen for each of these tests assumes that the two distributions should have the “same shape” and “equal variances”.
I contacted Minitab tech support and they are consulting with their Phd. Statistician on the issue. The person I spoke with did however pass along some information from one of their references that I thought might be worth sharing. The reference was the “Third Edition – Handbook of Parametric and Nonarametric Statistical Procedures by David J. Sheskin (pg.757-758):
“Various sources (e.g., Conover (1980, 1999), Daniel (1990), and Marascuilo and McSweeney (1977)) note that the Kruskal-Wallis one-way analysis of variance by ranks is based on the following assumptions: a) Each sample has been randomly selected from the population it represents; b) The k samples are independent of one another; c) The dependent variable (which is subsequently ranked) is a continuous random variable. In truth, this assumption, which is common to many nonparametric tests, is often not adhered to, in that such tests are often employed with a dependent variable which represents a discrete random variable; and d) The underlying distributions from which the samples are derived are identical in shape. The shapes of the underlying population distributions, however, do no have to be normal. Maxwell and Delaney (1990) point out that the assumption of identically shaped distributions implies equal dispersion of data within each distribution. Because of this, they note that, like the single-factor between-subjects analysis of variance, the Kruskal-Wallis one-way analysis of variance by ranks assumes homogeneity of variance with respect to the underlying population distributions. Because the latter assumption is not generally acknowledged for the Kruskal-Wallis one-way analysis of variance by ranks, it is not uncommon for the sources to state that violation of the homogeneity of variance assumption justifies use of the Kruskal-Wallis one-way analysis of variance by ranks in lieu of the single-factor between-subjects analysis of variance. It should be pointed out, however, that there is some empirical research which suggests that the sampling distribution for the Kruskal-Wallis test statistic is not as affected by violation of the homogeneity of variance assumption as is the F distribution (which is the sampling distribution for the single-factor between-subjects analysis of variance).”
The Mann-Whitney U test and found the exact same paragraph as above (except it compared the Mann-Whitney to the t test for two independent samples). (pg. 423-424)
The section covering the Friedman two-way analysis of variance by ranks test assumptions said nothing about variance. (pg. 845-846)
that the Kruskal-Wallis one way analysis of variance test by ranks does assume homegeneity of variance with respect to the underlying population distributions. However, it is not uncommon for the sources to state thatalso indicated that violation of this HOV assumption may at times be considered justified by some in lieu of the single-factor between -subjects analysis of variance.
By the way, technical support is also going to look at why their help sceens vary on this subject.
Thanks to all for your help on this one.
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