I want to analyze the quantitative data between two independent groups. The number of samples in each group is 6 and the distribution is not normal distribution. The U test is used to find the difference of distribution between two small groups and also for finding the difference of means between two small groups. It make me confused because my data is small in size and also not distributed normally.
What should I do?
The Size of the effect and the statistical significance go hand-in-hand.
To be more specific, if we talk about a small sample, then, if the difference obtained (which in turn is a measure of the size of the effect) is not statistically significant, then it's impossible to state that the difference observed is not due to chance, so calculating only the effect might be misleading as it might be considered just a random, chance-derived result.
The benefit of reporting only the effect size estimate is to give a raw idea about the results and provide a starting point for other research that will use larger samples.
On the other hand, when talking about small samples, if the effect size is large enought, then the probability of the MWU test (in this particular case) to be statistically significant is large enough.
I would do the following:
1. See if it is possible to increase the number of observations
2. run MWU for statistical significance
3. Calculate effec size with CI
4. Report MWU result, report ES result.
the reason you don't get normality may be coz n is small. You can perform a U test, but keep in mind that it works with ranks rather than with your raw data, so you lose information in the process. Try to transform you data, just in case a t-test may be applied
hi,
Mann–Whitney U test, which is a non-parametric test, can be used on non-normal distributions and has greater efficiency than the t-test on non-normal distributions.
The problem with small sample is that the p-value might suffer, although there is a debate about that.
For more info check (nice discussion in the comments too): http://allenfleishmanbiostatistics.com/Articles/2012/01/13-p-values-in-small-samples/
cheers, Kostas
Brishna, I agree with all my peers on the appropriateness of MW U test for non-normally distributed samples. As a non-parametric tool it is really designed for such (as an alternative to t-test of difference carried out for the normally distributed). Also, I have reservations on whether you can make your already collected data normally distributed.
If you can't collect more data, you might consider abandoning the significance testing approach and focusing on effect size estimation. You're unlikely to have enough statistical power to produce significant evidence against a null hypothesis with only six observations per group unless differences are quite large and consistent. You might find an estimate of the size of the difference and its corresponding confidence interval more useful than a mere "fail to reject" result, which seems the foregone conclusion of any significance test, if differences in your samples are really unclear enough to necessitate testing. An effect size estimate would be a summary statistic regarding the degree of difference between your two groups in general, and a confidence interval would represent the range of effect size estimates you might reasonably expect to derive from replications of your study.
The Size of the effect and the statistical significance go hand-in-hand.
To be more specific, if we talk about a small sample, then, if the difference obtained (which in turn is a measure of the size of the effect) is not statistically significant, then it's impossible to state that the difference observed is not due to chance, so calculating only the effect might be misleading as it might be considered just a random, chance-derived result.
The benefit of reporting only the effect size estimate is to give a raw idea about the results and provide a starting point for other research that will use larger samples.
On the other hand, when talking about small samples, if the effect size is large enought, then the probability of the MWU test (in this particular case) to be statistically significant is large enough.
I would do the following:
1. See if it is possible to increase the number of observations
2. run MWU for statistical significance
3. Calculate effec size with CI
4. Report MWU result, report ES result.
Hi everyone.
what's the minimum sample size for mann whitney u test?
I currently have a window size of 50 samples and i am trying to detect a changepoint. (in mean). My population comes from a non-Gaussian distribution which i am sure of as i tested with large number samples with normal test.
Is it okay if i use the bootstrap method / permutation method to check whether there is a mean shift by having the whitney mann statistic for all the possible changepoints ?
Sergiu Chirilă
This statement, "The Size of the effect and the statistical significance go hand-in-hand." by Sergiu Chirilă is not always true for MWU test since it only consider rank of observations. you will get the same p-value for (1,1,1 vs 2,2,2) and (1,1,1 vs 9,9,9)
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