By testing i found my data is non-normal so i can't apply t-test moving toward non-parametric test(mann whitney -U) the assumption that both distribution have same shape is violated although it is non normal,ordinal scale so which test I enter image description hereshould chose to apply on data

  • $\begingroup$ If it is relevant for the underlying hypothesis you want to test (i.e. it actually addresses the question of interest), the t-test should be fine on that; as would a WMW $\endgroup$
    – Glen_b
    Jul 17, 2018 at 3:55
  • $\begingroup$ Ho: There are not significant gender differences in loneliness among university students. $\endgroup$
    – user214769
    Jul 18, 2018 at 4:10
  • $\begingroup$ 1. I mean the research hypothesis rather than the null; 2. btw hypotheses shouldn't mention significance at all. They're positions on questions about (notional) populations. 3. You need to be more precise about what kind if differences you're interested in. For example, what if females were more polarized (either very lonely or not lonely at all) while males were more in the middle, but the averages and medians were about the same. Is that different (for your hypothesis) or not? $\endgroup$
    – Glen_b
    Jul 18, 2018 at 4:14

1 Answer 1


If the hypothesis you want to test is ‡

Ho: The probability that an observation in Group1 is greater than an observation in Group2 is 0.50 (Stochastic equality)

then there is no assumption that the distributions are similar in shape.

The assumptions listed by Conover † are:

1) Both samples are random samples from their respective populations.

2) In addition to independence within each sample, there is mutual independence between the two samples.

3) The measurement scale is at least ordinal.

The assumption about the shape of the distributions comes in to play only if you would like to test a hypothesis about the location difference (difference in median, say) between the two Groups.

‡ My phrasing for the hypothesis

† Conover, W.J. 1999. Practical Nonparametric Statistics, 3rd ed. Section 5.1.

  • $\begingroup$ thank you sir that means if i use mean in hypothesis then their is no use of that assumption.This assumption applies when we consider median??? $\endgroup$
    – user214769
    Jul 18, 2018 at 3:44
  • $\begingroup$ The mean is also a measure of location, so testing it with WMW also assumes distributions of the same shape and spread. This is easy to visualize: If you have two histograms that look the same except one is shifted to the right, you can see that if there is a difference between them, it corresponds to a difference in the location (median, mean, etc.). That being said, 1) The usual hypothesis for WMW of stochastic equality may be of interest to you. Or, 2) Take the comments to your question by @Glen_b to heart. $\endgroup$ Jul 18, 2018 at 12:36

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