I had to compare whether the two groups is somehow of the same distribution the problem is I only have 3 samples from each group in millimeters, say, Group A is 29mm, 32mm and 31mm while the other group is 35 mm in all three samples. What statistical treatment should I use? Im thinking mann whitney but not so sure... t test is possible but im not sure with the underlying assumptions... please help me with this.

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    $\begingroup$ I'd have probably leaned toward a Welch t-test, but it depends on how the variable you're measuring behaves. Can you say more about what you're doing? What's the size of measurement error in your measurements? What are you measuring? Note that you're never going to be able to obtain a two-tailed Mann-Whitney p-value below 10% with n=3 and 3. No matter how different the observations are. $\endgroup$ – Glen_b -Reinstate Monica Jan 20 '19 at 11:27
  • $\begingroup$ How can I check whether the two distributions have equal or unequal variance? Should I actually compute for their variances? Does it mean that they should be exactly equal to be equzl variance? $\endgroup$ – rosa Jan 20 '19 at 11:38
  • $\begingroup$ What if the two set of data came from 2 different population? Namely, product in company A and Company B? What is the most appropriate stats that I can use here? $\endgroup$ – rosa Jan 20 '19 at 11:45
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    $\begingroup$ "product" ... that's not enough information to say anything at all.. Please put available information into your question. Your assumptions (we cannot possibly help you with assumptions when we know so little) will be crucial. $\endgroup$ – Glen_b -Reinstate Monica Jan 20 '19 at 12:14
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    $\begingroup$ Statistical theory alone cannot provide a good answer to this question, but it's possible that an account of your measurement system and what you are measuring could resolve it. $\endgroup$ – whuber Jan 20 '19 at 15:54

With two groups of 3, significant differences in the mean or variance will have to pass the interocular trauma test - IOTT - it hits you between the eyes. Certainly you can do a test of the means (@Glen_b suggests Welch t-test, and that's a good suggestion) but how do you hope to find something significant,, regardless of whether you assume equal variances or not?

So I would say the best you can do is to present the 6 values and let people think about it for themselves.

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    $\begingroup$ You can definitely get significance (at say the 5% level) with either kind of t-test since the variances are small and the means are several standard errors apart, but the question will always be how much that means -- the p-value in the t will not be robust to the distributional assumption. With a heavier-tailed and more peaked distribution the data would provide only weak evidence of a difference. This (very small samples) is a case where a good understanding of the variable is essential, so that a suitable model may be chosen without reference to the data. $\endgroup$ – Glen_b -Reinstate Monica Jan 20 '19 at 12:29
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    $\begingroup$ Certainly you can get significant results. In fact, a Welch t test gives p = 0.039 - but isn't it intuitively obvious that the means are different? And of course I agree that knowing the variables is important. $\endgroup$ – Peter Flom - Reinstate Monica Jan 20 '19 at 12:56

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