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I have conducted a survey and would like to assess whether men compared to women differ in their attitudes. At a glance, the means differ quite much, which is why I wanted to prove it statistically.

For this reason, I conducted a Mann-Whitney test, as my dependent variables are ordinal and the distributions are non-normal. However, now I am not sure how to interpret the results. As mentioned above, I ideally want to make a statement that attitudes between men and women differ significantly (and that men/women show a more positive attitude towards something).

Now, if I display the mean ranks for both groups and find a significant p, can I derive such a statement depending on the size of the mean ranks?

I found a study of my professor in which he put the mean/SE of two groups next to the Mann-Whitney U and p-value and concluded that they are significantly lower/higher. However, I also read multiple times that this is not how the Mann-Whitney U test works and should be interpreted. Long story short - how can I prove that the attitudes are significantly different and more/ less positive between two groups?

Thanks so much!

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    $\begingroup$ "At a glance, the means differ quite much, which is why I wanted to prove it statistically." You generally need to fix the test you are using before knowing the data. If you run tests only if it looks like you have a difference (or conditionally on any decision based on your data), you already have invalidated any test and you can't "prove" anything. So generally looking at the data and then trying to find significance for something that you see in the data is not how proper testing works. $\endgroup$ Commented Sep 5, 2023 at 10:27

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One thing you can do is ordinal logistic regression, where attitude is the dependent variable and sex is an independent variable. You will have to check the assumptions of the model, but this is a good starting point.

One advantage of a regression model over anything that just compares the two groups on one variable (whether t or Mann Whitney or whatever) is that you can include covariates. For research on people and attitudes, this is often a good idea; e.g. you might want to include age, race/ethnicity, or other demographic variables, depending on what you are asking about (is it attitudes about Donald Trump? Peanut butter? Shakespeare? Elon Musk? Or what?)

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  • $\begingroup$ Hi and thanks for the quick reply! This a great idea and I will apply it once I am going to test my hypotheses. For now, I am just trying to describe my sample and as I saw differences in the means among gender, I thought it would be interesting to mention that (and prove significance through the means of a Mann-Whitney Test, instead of just reporting the means). So in a way, I am just looking for a way to describe a difference in the means, which I thought a Mann-Whitney test is good for. $\endgroup$
    – ber1495
    Commented Sep 5, 2023 at 11:25
  • $\begingroup$ I am not sure, but I assume in that case an ordinal logistic regression would be too much, given no hypotheses? Is it maybe better to not report and compare the means between gender, but just report the general mean of the sample? Thanks! $\endgroup$
    – ber1495
    Commented Sep 5, 2023 at 11:28
  • $\begingroup$ Both the Wilcoxon test and its generalization the proportional odds ordinal logistic model can be interpreted as provided evidence that responses in one group tend to be larger than responses in the other group. This is summarized by the concordance probability. $\endgroup$ Commented Sep 5, 2023 at 11:47

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