Distribution comparison for two highly size-different samples

Question

I have the data for an ambulatory assessment for autonomic cardiovascular functioning and the labels for posture are really mixed (the number in parenthesis represents the code, not the number of participants):

• lying (10)
• sitting (11)
• standing (12)
• walking (13)
• sitting/ standing (15)
• sitting/ standing/ walking (16)
• standing/ walking (17)

Looking for options, I found out that some studies focus on vertical vs. horizontal postures, or even more specific supine vs. prone positions (Houtveen, Groot, & Geus, 2005; Watanabe, Reece, & Polus, 2007; van Dijk et al., 2013). Best option to still make sense of the data seems to reduce the labels to two categories. I am using SPSS to accomplish this:

• RECODE Posture_Code (10=1) (11=2) (12=2) (13=2) (15=2) (16=2) (17=2) INTO posture_2.

Using recode I highly unbalanced the sample (e.g. 18 vs. 125 in one case) so, I decided to run the nonparametric Mann–Whitney U test. Is this a valid approach and, if not, what alternatives do I have to still make use of the data? Here's what I got from the test:

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Edit: By'making use of the data' I mean to test for a main effect of posture on pre-ejection period and RSA.

Answer 1

You seem to be saying that you chose the Mann-Whitney because the sample sizes were different.

Different sample sizes alone would not cause me to do that. I can see some reason for it -- the t-test is more sensitive to the equal-variance assumption when sample sizes differ. However, if you would otherwise have been happy to use the t-test, I'd have thought that a Welch-Satterthwaite type (unequal-variance) t-test would have been the more obvious choice.

That said, the Mann-Whitney seems an excellent choice as long as it corresponds to a test of a hypothesis you are interested in (at its most general it's not a test for a difference in means, though with additional assumptions (for example, that the distributions at the null are the same, and under the alternative will differ in ways that change the mean in the same direction as $P(X>Y)$ changes), it's quite good for that purpose in a wide variety of circumstances, having excellent power at the normal and for distributions with heavier tails than the normal.

You don't really make it clear what other considerations might have entered into your decision and you don't give much detail about the hypothesis*, so it's hard to say much more.

* (though if it's really as general as you suggest then the Mann-Whitney might be a very good idea)

[As a general principle, one thing I would caution you against is seeing the test results before choosing your analysis, as here.]