I am testing the hypothesis using Mann-Whitney Test:
Ho: Median rating (for likert type item) for males and females is equal
Ha: Median rating is not equal VS Median rating for males is greater than that of females.
I observe that median rating for the *sample* of women is less than that of the *sample* of men so I feel I should use one tailed test but still am not sure. Could someone suggest the appropriate test?
One tailed is appropriate given your directional hypothesis. Good luck with you research.
The alternative hypothesis is supposed to be determined before the study begins and you see the findings. Was it? If it wasn't, you use the 2-tailed Mann-Whitney test. In addition, one-tailed tests have fallen out of favor over the years. You might have difficulty getting those findings published if you use a one-tailed test. I cannot think of a circumstance when I would use a one-tailed test now a days.
You satiated your null and alternative hypothesis as follow:
H0: Median rating of males and females is equal (the same)
HA: Median rating of females is different from males (not equal).
The term is ‘different/not equal‘ indicates a two tailed test.
Hello Zedix,
I agree with the other posters that, unless you had posed and justified a directional test prior to collecting the data, the only appropriate way to proceed would be to conduct a non-directional test. There are two reasons:
1. If you allow yourself to modify tests, hypotheses, or other features based on inspecting the data, then the a priori risks of type I and type II error no longer apply. Human nature being what it is, you run a far greater risk of biasing the results.
2. If your (prior to data collection) inclination was that, in fact, males would have higher ratings than females, then the null hypothesis and alternative hypothesis should have been:
Ho: Either there is no difference between male and female ratings OR females have higher ratings than males;
Ha: Males have higher ratings than females.
Good luck with your work.
Why are you using the Mann-Whitney procedure to test for differences in medians?
Divine, G. W., Norton, H. J., Barón, A. E., & Juarez-Colunga, E. (2018). The Wilcoxon-Mann-Whitney procedure fails as a test of medians. The American Statistician, 72, 278-286. doi: 10.1080/00031305.2017.1305291
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