Alternative to Mann-Whitney U-test for very small samples sizes?

[Biochemist]

Hello,

I want to compare two unpaired ordinal-type data sets (histological score data) for a statistically significant difference.

Each data set consists of only 6 values and, for now, resources don't allow increasing the n number. The problem is that the Mann-Whitney U-test, which would normally be used for this kind of data, can only give p<0.05 with a sample size of more than 7 (i.e. at least .

Is there any solution or workaround to this problem? Any alternative to the Mann-Whitney U-test, which also works with n numbers of 7 or less?

[reason180]

So you have only three subjects in each of two groups, with ranks being constrained to 1-through-6? I think that since you're starting with ranks rather than interval/ordinal data, the U test is already sufficiently powerful. I'm afraid that three rank-scores per group just isn't enough for drawing inferences about the two populations.

[MAgojam]

Hey @Biochemist,
I think if you take a look here, you can find some answers.
https://stats.stackexchange.com/questio ... all-sample

Cheers,
Maurizio

[Biochemist]

Thanks for the answers.

Yes, I agree that n=3 for each of the two groups is really too small to draw any reliable conclusions about the populations. It is just that I am expected to perform and show some kind of statistical analysis even with this small sample size. I hope that sooner or later I will be able to increase it.

However, getting p<0.05 with the Mann-Whitney U-test at a total n of 6 is just impossible no matter how big the differences are between the groups. The result for the p-value is always p=0.1.

What I get from the link that you posted, Maurizio, is this: It is suggsted that replacing the test with a confidence interval or Bayesian credible interval would be alternatives. Unfortunately, I have never used Bayesian statistics so far. Wouldn't confidence intervals require at least interval-scale type data and ideally a normal distribution?

[reason180]

Would the requirement for "some kind of statistical analysis" be satisfied by sample-descriptive rather than population-inferential statistics?
For example:

"The median rank was 4.0 for Group A and 2.0 for Group B. The effect size, calculated as the rank biserial correlation (rank vs. group), was .56. Note that inferential statistics are not reported here, given the small sample size."

The screen shot, below, shows how I used jamovi to obtain the results. Alternatively you could just go ahead and include the p value, which of course will be non-significant (but given such a small sample, it should be non-significant).

tmpUntitled.png (71.08 KiB) Viewed 306 times

[Biochemist]

Thanks for the advice, reason180. I think what you suggested is the best solution for the data at hand.