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I have a sample of 24 participants who gave their responses to 8 questions. I calculated their mean response. Can I use Mann Whitney to compare between 2 groups where one of them has only 2 participants and the other has 22?

Silverfish
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Mohamed Nabil
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    What are the responses? I hope something like weight, size, US-$, that you can actually calculate the mean of. It is not admissible to calculate the mean if you have some kind of Likert scale. – Horst Grünbusch Jan 07 '15 at 17:42

2 Answers2

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Did you try it ;-)? Yes, it can be done, you can even do it when one group has only one datum. However, you will have very little power to detect differences. To get the idea, it may help to read my answer here: How should one interpret the comparison of means from different sample sizes?

Community
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gung - Reinstate Monica
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    Excellent. Theoretically it can be done but the power will be very low. – Mohamed Nabil Jan 07 '15 at 17:31
  • The U-statistic is imprecise for two samples. Does SPSS switch over to an exact formula for small sizes? If not, this should not be done. – Rex Kerr Jan 07 '15 at 20:20
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    SPSS computes exact significance following Dineen and Blakesley (1973) if the sample size is small enough. See "SPSS Algorithms" document for details, chapter "Nonparametric tests". – ttnphns Jan 08 '15 at 09:19
  • Should I do the test anyway and state that its power is small or do not do it at all and state that I could not compare between the two groups because it would not be a balanced test. – Mohamed Nabil Jan 08 '15 at 13:29
  • @MohamedNabil, what you should do is a very difficult question for me to answer here. But your suggestion seems fine. – gung - Reinstate Monica Jan 09 '15 at 15:05
  • Thanks gung. I think you mean that I state I could not compare between them because it would not be a balanced test.Don't you? – Mohamed Nabil Jan 11 '15 at 09:55
  • @MohamedNabil, sorry, you had listed two options, so 'yes' isn't helpful ;-). I suppose you could do either, but I meant that the suggestion to do the test but state that its power will be little above 5%. – gung - Reinstate Monica Jan 11 '15 at 15:12
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I wouldn't treat two observations as a "group" and also a group of 22 is a very small sample size. So I would say that no matter if it is or not technically possible, the other thing is that analyzing such a small samples would give you unreliable results no matter what method of analysis would you use. By "unreliable" I mean here that it is hard to extrapolate the results estimated using a sample of two on the population. This kind of data qualifies rather for a qualitative research and treating the two individuals as case studies.

Tim
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  • I'd like to thank you first. So , what do you think the appropriate test to compare between these "groups" will be.Actually, I need to compare between them. – Mohamed Nabil Jan 07 '15 at 17:23
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    I beg to differ with the undifferentiated characterization of "highly unreliable." If the M-W test of size $\alpha$ rejects the null, then the conclusion is no more or less "reliable" than *any* test of size $\alpha$. It is true that this test may have little power, or it might not be robust, compared to tests with larger sample sizes: but that just shows you need to be more specific about what you mean by "unreliable." – whuber Jan 07 '15 at 17:47
  • Ok, I restated it to be more clear. – Tim Jan 07 '15 at 17:56
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    If two observations isn't a "group", what is it? Purely for mathematical purposes it appears to be a group, albeit a very small one. – Silverfish Jan 08 '15 at 11:24
  • For **practical** reasons that small group does not make sens. – Tim Jan 08 '15 at 11:48