Nonparametric Comparisons For Each Pair Using Wilcoxon Method

[#1]

Hi,

Could you please let me know the "Nonparametric Comparisons For Each Pair Using Wilcoxon Method" is comparing Median value or Mean Rank? 

If it is comparing Mean Rank than which test is available in JMP to compare Median value between two independent groups. However one group have sample size less than 20. 

Thanks

[#2]

If you select the "?" tool, and then go to the display output for the Wilcoxon statistic and click on it, you will get the Help screen for the different tests.  Here is the section on the Wilcoxon statistic

Wilcoxon Test

Performs a test based on Wilcoxon rank scores. The Wilcoxon rank scores are the simple ranks of the data. The Wilcoxon test is the most powerful rank test for errors with logistic distributions. If the factor has more than two levels, the Kruskal-Wallis test is performed. For information about the report, see The Wilcoxon, Median, Van der Waerden, and Friedman Rank Test Reports. For an example, see Example of the Nonparametric Wilcoxon Test.

The Wilcoxon test is also called the Mann-Whitney test.

[#3]

Thanks,

Actually my hypothesis is that There is no difference for median value between two independent groups.

So, in this situation Wilcoxon is looking mean rank or rank score. So, is there any other test available in JMP to see my question?

Thanks

[#4 · Accepted solution]

The option directly below the Wilcoxon selection is the Median Test.  The below is taken from the Help screen from the Nonparametrics Tests

Median Test

Performs a test based on Median rank scores. The Median rank scores are either 1 or 0, depending on whether a rank is above or below the median rank. The Median test is the most powerful rank test for errors with double-exponential distributions.

[#5]

If I understand "my hypothesis is that there is no difference for median value between two independent groups" correctly, then the null hypothesis is that there is a difference. This situation is sometimes referred to a equivalence test, although it is really still a hypothesis test. It is just that they usual null hypothesis (i.e., no difference) and alternative hypothesis (i.e., difference) are reversed.

The case of deciding about the equivalence of the mean of two groups is based on two one-sided tests (TOST) with t-tests. Perhaps you could apply one-side non-parametric tests in the same way.

(The underlying issue is that a hypothesis test is one way. Failing to reject the null hypothesis means that you still assume the null hypothesis. You can't say that the null hypothesis is significant.)

[#6]

Thanks! I think this is answer of my query. Could you please let me know how can I do "one-side non-parametric tests" in JMP?

I am looking the way to perform "one-sided Wilcoxon-test" in JMP. 

Thanks 

[#7]

Sorry, but I do not know how to perform one-tailed non-parametric tests with JMP. I checked but I could not find them in the Oneway platform.