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I have the following myData, where the response variable high-rated denotes if an application is high-rated or not, and the independent variable isWindows denotes if the application supports Windows:

high-rated   isWindows
Yes          1
Yes          0
No           1
No           1
Yes          0
....

I want to statistically compare the distribution of isWindows in high-rated app and low-rated app. Is it correct to use the Wilcoxon rank sum test (or Mann-Whitney U test) like below?

high_rated_app <- subset(myData, high-rated   == "Yes")
low_rated_app <- subset(myData, high-rated   == "No")

wilcox.test(as.numeric(high_rated_app$isWindows), 
            as.numeric(low_rated_app$isWindows))

Secondly, if the above test returns a significant p-value (< 0.05), I proceed to calculate the magnitude of difference using Cliff's delta:

library(effsize)
d <- cliff.delta(as.numeric(high_rated_app$isWindows), 
                 as.numeric(low_rated_app$isWindows))

Can I conclude with this statement: "high-rated app is statistically significantly different from low-rated app in whether an app is Windows, with an effect size of d"?

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  • $\begingroup$ If your response is categorical (isWindows), you could simply compare proportions. Why would you use a rank sum test? $\endgroup$ – Glen_b -Reinstate Monica Jan 11 at 3:37
  • $\begingroup$ @Glen_b-ReinstateMonica my response variable is high-rated. Comparing proportion means that how many % is high-rated ? $\endgroup$ – hydradon Jan 11 at 6:39
  • $\begingroup$ If your response is high-rated then you are not correctly expressing this when you write things like "I want to statistically compare the distribution of isWindows in high-rated app and low-rated app" which appears to invert the roles of DV and IV. Can you edit your question to make if very clear which is the DV and which is the IV? $\endgroup$ – Glen_b -Reinstate Monica Jan 11 at 6:42
  • $\begingroup$ @Glen_b-ReinstateMonica edited. $\endgroup$ – hydradon Jan 11 at 7:21
  • $\begingroup$ It looks like it would be more appropriate to use a chi-square test of association, and then an appropriate effect size statistic like phi, Cramer's V, perhaps odds ratio, Goodman Kruskal lambda, Tschuprow's T, and so on. ... One consideration is if you are truly thinking of one variable as the dependent and one as independent, or if you are more-or-less just interested in the association of the variables. $\endgroup$ – Sal Mangiafico Jan 11 at 16:48

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