I am trying to understand if there were differences between control and experimental groups toward intercultural learning.
Can two-tailed Mann-Whitney U test and one-way ANOVA on ranks be used in the same analysis? I read that one-way ANOVA on ranks extends the Mann–Whitney U test.
What are the benefits and drawbacks of using either one of these, or the combination of both?
Thanks in advance.
ANOVA applies to normal data, while MW works for all data; To apply ANOVA, you need to check the normality. However, confidence intervals in ANOVA are more contracted than MW. P-values in ANOVA are lower than the MW test. You can implement both of them to fortify your results.
As Babak Jamshidi said, ANOVA is only for normal data as it’s a parametric test, while the MW is a non parametric test. An alternative to ANOVA for non parametric data is the Kruskal-Wallis test
@Jamie Wallis you are right. But I meant to say the results o a parametric test can be supported by a nonparametric. In this case, you can say that without presumptions, the result remains is valid.
I think some of the responses have missed something essential in the question. The question is about anova on ranks. A one-way anova on ranks can be used without considering if the conditional distribution of the data is normally distributed. Basically, it's been determined that the test statistic follows the desired distribution in this case. In fact, this test will be quite similar to the Kruskal-Wallis test. I have some R code below you can run iteratively to see this. (This can be run at https://rdrr.io/snippets/ ). Or see: https://lindeloev.github.io/tests-as-linear/simulations/simulate_kruskall.html .
As to the question, there's no reason why you can't use different statistical tests in the same study. I don't think there are any major advantages or disadvantages of using any of these tests. My suggestion is to use the Kruskal-Wallis test rather than the one-way anova on ranks. This is just to avoid confusion on the part of the reader. An appropriate post-hoc test for K-W is the Dunn (1964) test.
One advantage of a two-sample test (e.g. M-W), is that you get a statistic that gives directionality. For M-W, you might get a z value (depending on your software). Typically, if this is negative, the second group is larger than the first. And vice-versa. And there are easy to understand effect-size statistics for the two-sample case.
If you have a two-sample situation, it won't matter much if you use M-W or K-W. The results might be slightly different depending on the software implementation.
Y = rnorm(30,20,5)
R = rank(Y)
Group = c(rep("A", 10), rep("B", 10), rep("C", 10))
Data=data.frame(Group, Y, R)
kruskal.test(Y ~ Group, data=Data)
summary(aov(R ~ Group, data=Data))
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