Hello Santos,

The Mann-Whitney test may be used to compare two sample data sets (of equal or unequal size) for equality, and uses the rank values rather than dichotomizing the scores into frequencies of cases above/below median as does Mood's test. If you assume symmetric distributions, the Mann-Whitney becomes a test of equality of medians. If not, it's a more general test of equality of distributions (vs. the alternative that one is displaced relative to the other).

Good luck with your work.

You can use the Mood's median test for median comparisons of two samples. You can perform the median test using SPSS.

Best

Sevilay

Hello Santos,

The Mann-Whitney test may be used to compare two sample data sets (of equal or unequal size) for equality, and uses the rank values rather than dichotomizing the scores into frequencies of cases above/below median as does Mood's test. If you assume symmetric distributions, the Mann-Whitney becomes a test of equality of medians. If not, it's a more general test of equality of distributions (vs. the alternative that one is displaced relative to the other).

Good luck with your work.

Yes, use Mood's median test. You can use R too.

Mood's median test has been criticized by many for low power (and all the other issues with dichotomizing). As David Morse says, the M-W is only testing the equality of medians in specific circumstances so should not generally be used for this (Divine et al, 2018, Am Stat, gives some great examples and explanations). A good alternative is applying the inverse Normal transformations to the ranks, and then just doing a t-test. Gelman discussed this a few weeks ago in his blog. Otherwise, bootstrapping can be done. I either run a standard median bootstrap and use the BCa intervals, or use Wilcox's (not Wilcoxon) functions in WRS2 and described in his book. There are other others, but this should be a good start. In fact, this may be more info that you wanted, but stats on medians can be tricky.

Here is the webpage for the paper I mentioned: Article The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians

Hello Santos,

You can use one of the nonparametric comparison tests. Mood's median test is one of the options. You can also use Moses, MWU options. You can also report two or three test results (if there are no contradictions between them).

Good luck with your work

/* The Mann-Whitney test may with SAS*/

data new;

input group species;

cards;

1

.

.

.

;

run;

ods graphics on;

proc npar1way data=new median

plots=(medianplot);

class group ;

var species ;

run;

ods graphics off;

you can use Mann-Whitney test

You can do t-test if the values are normally distributed. If you are not sure, then Mann-Whitney U will be just fine .

I hope that helps.

Nuri Doğan , I am interested in your final parenthetic clause. If you run multiple procedures that test similar hypotheses and the answers are different, I would think it is vital to tell the readers this. Have I mis-interpretted what you said?

Seyed Abbas Rafat , Restu Arisanti Muchtar and Abid Hasan Khan . I assume you read through the other comments to make sure that your contribution was unique and saw a paper titled "The Wilcoxon-Mann-Whitney fails as a test of medians." I assume that since your comments were after this was mentioned you are disagreeing with this paper. I'd be interested to know which aspects.

Finally, back to the original question. Santos Filho , is there are reason why you are specifically interested in medians? I like some of conceptual arguments for medians (e.g., Galton, F. (1907). One vote, one value. Nature, 75, 414.), but if you are just wanting something more robust than the mean, there are lots of alternatives (e.g., comparing trimmed means).

Ok. Is the question referring to probability sampling, non-probability sampling or both scenarios?

Dear Mr. Jordan,

My field of study is human resource management, leadership, and organizational behavior so I am not used to doing laboratory research. Maybe it can be asked to other colleagues in the same field of study

Daniel Wright Dear Daniel, Thank you for your comments. I just wanted to provide the SAS code if the researcher decided to use MWM.

Article The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians

is an interesting article. However, many reviewers of scientific journals automatically request MWM test for Medians in non-normal data. Best Regards, Seyed

Santos Filho, median regression (aka., least absolute deviations regression, or quantile regression with quantile = 0.5) could be used to do this. What software do you use, or have access to?

For general purpose, you may consider to use Mann Whitney test.

Fernando Sotero, using the data set pasted below and whatever software you like, compute the medians for the two groups, and then carry out a Mann Whitney U test (aka., a Wilcoxon-Mann-Whitney test). What do you conclude about using the Wilcoxon-Mann-Whitney test as a test for a difference in medians?

Grp Y

0 5

0 5

0 5

0 5

0 5

0 5

0 7

0 8

0 9

0 10

1 1

1 2

1 3

1 4

1 5

1 5

1 5

1 5

1 5

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The data are from a Stata Journal article by Ronán Michael Conroy.

• https://www.stata-journal.com/article.html?article=st0253

An important question worth pursuing

Seldom do I see any references to using bootstrap analysis. You could do a bootstrap randomly selecting with replacement and comparing the means between the two substrate.

John Joseph Geibel , yes this is done comparing medians. See for example Rand Wilcox's textbooks on robust estimation. In second ed of Intro to RObust Estimation and Hypo Testing (the only one I have at home) it is on p. 272-273. These are available in his and Mair's WRS2 package ( https://cran.r-project.org/web/packages/WRS2/vignettes/WRS2.pdf ).

I had the privilege of knowing Bradl;y Efron and was introduced to the bootstrap by Percy Diaconus when getting my MS in statistics at Stanford - two brilliant and, generous individuals. Look for publications by Efron - there are a number of them all worth perusing.

Daniel, thanks for backup. After 40 years, I wold think that the bootstrap would have become well known because it can be used in so many ways in which Gaussian statistics is difficult, requiring transformations, etc. In many situations, I have been unable to understand results of statistics on transformed data while finding the bootstrap results much easier to interpret.

I agree with Daniel Wright.

Another idea:

Can we look at species numbers as Poisson variables? If so, would you agree to use a test that compares the parameters of the Poisson distributions as indicators of species diversity?

Dear: It is possible to use non- parametric tests, including Wilcoxon or Mann-Whitney

For general purpose, you may consider to use Mann Whitney test.

Sourangshu Ghosh, you advised using the Mann Whitney test to compare medians. That suggests to me that you missed the two most popular answers (currently) in this thread (by David Morse & Daniel Wright), and that you also missed the example I posted earlier. I repeat that example here so that you will be sure to find it.

Repeat of earlier example

Using the data set pasted below and whatever software you like, compute the medians for the two groups, and then carry out a Mann Whitney U test (aka., a Wilcoxon-Mann-Whitney test). What do you conclude about using the Wilcoxon-Mann-Whitney test as a test for a difference in medians?

Grp Y

0 5

0 5

0 5

0 5

0 5

0 5

0 7

0 8

0 9

0 10

1 1

1 2

1 3

1 4

1 5

1 5

1 5

1 5

1 5

1 5

The data are from a Stata Journal article by Ronán Michael Conroy.

• https://www.stata-journal.com/article.html?article=st0253

Sourangshu Ghosh, it is nice reading your posting once again on ResearchGate. An explanation was requested from you by my humble self why you posted a 100 percent unedited and unmodified quotation of my previous response to a questioner on Research Gate. You have still not responded to the anomaly.

Your profile shows that you are an academic staff in a University. You may do well to respond especially because the act borders on plagiarism

which is unethical on an intellectual platform.