1

I have the same scenario here: Test for significant difference in ratios of normally distributed random variables

Suppose I have to compare a metric that is a ratio of two sample means for men and women. $$ H_{0}: \frac{\overline{X}_{men}}{\overline{Y}_{men}}> \frac{\overline{X}_{women}}{\overline{Y}_{women}} $$ What is the test statistic of this hypothesis? I was not able to figure out what kind of distribution it is. I have tried to use permutation test and it worked fine but I have a lot sample means for different group to compare with and permutation test performs pretty slow. Thanks!

bbbbbliu
  • 43
  • 3
  • Nonparametric approach, like Wilcoxon test, maybe? – Łukasz Deryło Aug 22 '17 at 07:10
  • I'll try to study Wilcoxon test. And I just think of log transformation. Is this a right approach? – bbbbbliu Aug 22 '17 at 16:28
  • Averages are random variables, while statistical hypotheses apply only to parameters. Do you want to test E(X)/E(Y), or (more likely) E(X/Y)? These are two different questions. – Zahava Kor Aug 22 '17 at 16:36
  • X/Y should be a Cauchy distribution if I'm not mistaken? But what I want to test is E(X)/E(Y) and not E(X/Y). So I need a nonparametric approach to test it like @ŁukaszDeryło mentioned? – bbbbbliu Aug 22 '17 at 17:00

0 Answers0