# Mann-Whitney Test with post-hoc adjustment

#### Anatomist

##### New Member
I am comparing a number of architectural characteristics in two sets of muscles using Mann-Whitney U test (sample size is too small to justify the use of parametric tests). I want to do a post-hoc adjustment of the alpha (e.g. Bonferroni, Dunn-Sidak), but SPSS (v. 21) does not show any post-hoc option for M-W test. I know how to manually do the post-hoc tests, but still want to see how the spss presents the results. If somebody could suggest a solution to this problem, it would be highly appreciated. Thank you.

#### GretaGarbo

##### Human
(sample size is too small to justify the use of parametric tests).
Where does this statement comes from? Has it been written in a textbook, or where?

#### Anatomist

##### New Member
Where does this statement comes from? Has it been written in a textbook, or where?
One of the assumptions of parametric tests is that the data are normally distributed. There are tests to check if it is indeed the case (e.g., Shapiro-Wilks, Kolmogorov-Smirnov, etc.). However, if the sample size is below 10 (which is my case), then the normality tests are rather useless (Biometry by Sokal & Rohlf; Biostatistics by Zar). In addition, I collected my samples from museum specimens all over the world; so they do not even belong to the same population.

#### Karabiner

##### TS Contributor
One of the assumptions of parametric tests is that the data are normally distributed.
This is not quite correct. For parametric tests within the
framework of the general linear model, for example,
the model residuals or data within GROUPS should
preferabily be normally distributed, not the unconditional
data.
sample size is below 10 (which is my case)
Ok, then U-test is a commopn choice. So you could
perhaps do a short research about Bonferroni correction
and then pick your pocket calculator to perform the
correction. By the way, if your number of tests is
large, Bonferroni correction could be very conservative
i.e. it may then be nearly impossble to obtain significant
results.

With kind regards

K.

#### Anatomist

##### New Member
Thank you Karabiner. Actually I've already done the post-hoc tests manually. As expected, they are conservative (post-hoc tests are designed to be so), and results are not significant. However, I wanted to know whether there was some way to do the post-hoc tests on spss. For Kruskal-Wallis, the program can perform the post-hoc tests. I am trying to find out if it whether and how it does so for Mann-Whitney.

Best regards,
A.

#### Karabiner

##### TS Contributor
You didn't perform post-hoc tests, AFAICS.
Post-hoc testing is done e.g. when an omnibus test
with multiple groups turned out significant and
then pairwise comparisons are performed (this
is the case for example with parametric ANOVA
or a Kruskal-Wallis H-test, both with k > 2 groups).
What you seemingly did was multiple testing
(several U-tests), for which protection against
inflation of type 1 error risk might be sought.

With kind regards

K.

#### Anatomist

##### New Member
Thank you again for your explanation. However, my question has been whether there is some way to do Bonferroni adjustment for Mann-Whitney on the spss, instead of having to do so manually.

Best regards,
A.

#### GretaGarbo

##### Human
One of the assumptions of parametric tests is that the data are normally distributed.
NO!

Some of the parametric test are based on the normal distribution.

But there are many other parametric distributions. Like the Poisson distribution, with a parameter that is often called "lambda". Or the binomial distribution with parmeters "p" and "n". Or the exponential distribution...

One usual test is to do likelihood ratio tests.

However, if the sample size is below 10 (which is my case), then the normality tests are rather useless (Biometry by Sokal & Rohlf; Biostatistics by Zar).
True! If the sample size is small then the power will be low to detect even large deviations from normality.

But since the OP says that, how can the OP know that his(or her) data is not normally distributed?

One should remember that the Student t-test and F-tests in analysis of variance were designed to be small sample test. Student himself used a sample size of four (n=4) in his original paper from 1908 (page 13).

But a non-parametric tests like Mann-Whitney has assumptions too, like being continuous variables, so no ties, and being sensitive to "spread" and skewness...

I collected my samples from museum specimens all over the world; so they do not even belong to the same population.
When statisticians talk about "populations" they don't refer at all to a human population or an animal population. It simply means an abstract construct like drawing units from a distribution. If the animals in this case are drawn from several (statistical) populations then it could be a case of mixed distribution, e.g. with different parameters.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Hey anatomist,

I have no idea if SPSS has a correction for post hoc test. You seem to know your basics. However, what K was gettting at was per the description of your data we don't get why you need to run post hoc tests, which are typically reserved to address pairwise comparison to combat multiplicity. From your description you don't seem to be running these. Also, since you don't seem to be running a KW test, which would typically be the cue to run more tests.

Why do you need post hoc tests?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Oh, as you probably know the easy way to do the Bonferroni Correction is just multiple your p-values times the number of pairwise comparisons you had. Perhaps you can get SPSS to output these p-values and then you can just multiply them all in a data step using the generate dataset.

#### Anatomist

##### New Member
Another way to do the Bonferroni adjustment is to divide the alpha by the number of pairwise comparisons. Either way, individual comparisons are less likely to be significant using this approach (unless the number of comparisons is very small).

#### Anatomist

##### New Member
Thank you everybody for your comments and suggestions. I think I've found what I was looking for.

Best wishes,
A.