I have performed a two-way contingency test and to "check" these results i performed two one-way Wilcoxon tests. The results differ, however. Which set of results is more accurate and the one I should use? I am working with the statistical program jmp
How exactly do you "check" the result fomr the contingency test (what? how? Fisher's exact test on a 2x2 table?) by the results of two Wilcoxon tests?
Despite the fact that I can't imagine how this should work...: shouldn't you use a binomial test rather then Wilcoxon?
Okay-thank you. Let me clarify. I have two independent variables: season and gender and one continuous dependent variable: hormone level. I wish to test if there is a significant difference between the genders at each season. My sample size for each gender is about ten. According to the Shapiro-Wilken test, I know that none of the female and male samples are normally distributed. I performed two wilcoxon tests to test for a possible difference between gender medians at each season. In addition, I performed a contingency test to perform this "all at once." The contingency test (fisher's exact test) indicates no significant difference between medians and the two wilcoxon tests indicate a significant difference between the genders at each season. I performed both just to make sure results were correct because I though one contingency test was equivalent to two wilcoxon tests. But---you are saying I should scrap all of this and use a binomial test to test for a significant difference between medians for the non normally distributed (and small sample size) data?
"I performed two wilcoxon tests to test for a possible difference between gender medians at each season." - This is tested ONLY when the distributions are symmetric, what is likely not the case.What theses tests test is the hypothesis that the probability of lower value in one group is equal to the probability of a lower value in the other group ("stochastic equivalence").
"The contingency test (fisher's exact test) indicates no significant difference between medians" - Fisher's exact test is about frequencies, not medians. How did you do this?
"you are saying I should scrap all of this and use a binomial test to test for a significant difference between medians" - Nope. I was thinking(!): if you used Fishers test, then -so I thought(!)- you are analyzing frequencies of two dichotomous (binary) variables. And if this was the case, than you could test a hypothesis about a proprotion of two frequencies using a binomial test. But right now I do not understand how you used Fisher's test with the medians. This all makes no sense to me.
My advice would be the following (after you last post):
Don't analyze concentration. Analyze the log concentrations instead, and use a standard linear model to do this. You have two factors: gender and season, and you seem to be interested in the interaction gender x season. So tha't a simple two-factorial model with interaction. You might consider checking the diagnostic residual plots for your fitted model to check if the assumption of variance homogeneity and normal distribution for the residuals is appropriate.
@Stephen: the sample size is not too small for ANOVA. It is likely that an appropriate transformation will give roughly symmetrically distributed residuals what is ok for ANOVA. Using ranks is problematic when an interaction should be analyzed. The interaction is a product term, and it is not clear (at least to me) what the meaning of a product of ranks should be. Mathematically it's fine, but I would not know how to practically interpret the coefficients. And if one says: "I give a damn on coefficients, I only want p-values, and those should be 'significant'" then would ask what these p-values are about and how I should judge how small a p-value in this case must be to be deemed "significant" (is p
@Jochen, let me preface this next question with the following: I am an undergraduate and have taken one stats class (and so, if possible, use "small" words). I tried a Fit least square model (with a 2 degree factorial of the two independent, categorical variables) Now if this is what you suggested, I must interpret the results. The analysis of variance using F distribution provides: P value < .0001. The P values of the test (which I know you are so fond of as indicated by the last post) show that the seasonal difference is insignificant, the gender difference is significant and the Season*Gender interaction is insignificant.
I wish to see if there is a significant difference between the gender hormone levels at each season (season has two levels: summer and winter). My question: is the male testosterone level sig. different from female testosterone level in winter? in summer? With that, is it possible for you to help me interpret results of fit model or tell me my other test options? My sample size is small and not normally distributed. I really appreciate your expertise!
what's your response? Conc or log(Conc)?
Have you had a look at the diagnostic residual plots?
The you write that, for instance, the gender:season interaction is significant. Well, that's not a result but rather an interpretation! That is what you interpret (from looking at a p-value, I suppose). If this interperation is justified, then you say that it is not useful to distinguish the gender-effects between seasons (or the season-effects betweem genders). But then it would make not much sense to look for gender-differences at each season separately.
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