Timeline for Why is independence required for two- sample proportions z test?
Current License: CC BY-SA 3.0
13 events
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| Oct 7, 2015 at 8:45 | comment | added | Erik | I tried to reproduce your simulation by generating data in the way you describe and using prop.test. I got different results. Your results surprised me, since a positive correlation between results usually means assuming independence produces conservative p-values, since Var(X - Y) = Var(X) + Var(Y) - 2*Cov(X, Y). So a positive correlation falsely set to zero will increase the variance of a difference. | |
| Oct 7, 2015 at 8:13 | history | edited | Glen_b | CC BY-SA 3.0 |
added 5 characters in body
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| Dec 30, 2014 at 0:53 | comment | added | Glen_b | I urge you not to simply accept my simulation results, though. Generate your own, in a way that matches your sample size and has a realistic amount of dependence for your problem. Firstly, you don't know that I didn't make a mistake (and if we both get similar results, you can be more confident about both), and secondly you'll see how much effect it has in a situation much closer to the one you face. | |
| Dec 30, 2014 at 0:45 | comment | added | Glen_b | Sorry, I misspoke above ... not conservative --- quite the opposite! | |
| Dec 30, 2014 at 0:44 | history | edited | Glen_b | CC BY-SA 3.0 |
fixes, added simulation results
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| Dec 29, 2014 at 22:10 | comment | added | grey | Let us continue this discussion in chat. | |
| Dec 29, 2014 at 22:07 | comment | added | Glen_b | I may have misunderstood (I had thought you were interested in the within-comparison). What's the specific hypothesis (or hypotheses, perhaps) you want to test? | |
| Dec 29, 2014 at 21:49 | comment | added | grey | The second variable is indeed dichotomous. Hence, I have one within (the 2 questions) and one between (additional information y/n) subjects manipulation. I searched the internet and statistics books for something like a 2x(2x2) contingency table that accounts for the partial dependency, but I haven't found a solution so far. Perhaps your idea with the extension of the McNemar test comes close to that? I also thought of calculating a chi square for two 2x2 tables (1: question 1 corr/incorr, add. info y/n; 2: the same for question 2) and then compare whether the chi square values are different. | |
| Dec 29, 2014 at 21:12 | comment | added | Glen_b | Yes, you'd probably want to use a GLMM in that situation. When you're dealing with paired 0/1 data with a covariate, it's not all that simple. If the additional covariate is dichotomous (or similarly simple in form) you might be able to do something else (construct an extension of a McNemar test perhaps), but it's not necessarily much simpler. | |
| Dec 29, 2014 at 19:28 | comment | added | grey | With respect to GLM, do you think of a generalized linear mixed model? I also thought about that, especially as I have a second, independent variable in my design. But I feel like cracking a nut with a sledgehammer to use such a procedure for my (in my opinion rather simple) questions (and I imagine that the required sample sizes are rather large...). Is it really adequate to think about such rather complex procedures with simple proportions? | |
| Dec 29, 2014 at 15:25 | comment | added | Glen_b | McNemar's test would be the usual way I think, though one might set it up as a GLM. Yes, more conservative when there's positive dependence. | |
| Dec 29, 2014 at 14:37 | comment | added | grey | Ok, so this would mean to use something like McNemar test I suppose. Do I understand you right, using a test that assumes independence would yield a more conservative result with respect to whether or not H1 is accepted? | |
| Dec 29, 2014 at 14:14 | history | answered | Glen_b | CC BY-SA 3.0 |