Two tests were applied to the same group of people. Both tests are binary (with 0 and 1 responses). I need to test the null hypothesis that the proportion of response 1 is equal in both tests.
prtest tests the difference between two proportions in Stata. The paired design needs to specify the cluster() and rho() options. How do I obtain the rho() for my data?
I understand SPSS version 27 has an option of doing this. But I want to know how this can be done using Stata.
Hello Inaamul Haq. I suggest that you take a look at the -mcc- command, or -mcci- for the immediate version. You can see an example of the latter here:
- https://www.statology.org/mcnemar-test-stata/
Notice that the output shows both approximate and "exact" p-values for McNemar's test. HTH.
EDIT. Referring to Sal's post below, my suggestion assumes that you have a unique identifier for each individual, allowing you pair the two responses.
You can do what is known as a t-TEst of proportions. Alternatively, a chi-sq would test the same hypothesis for a 2 x 2 table.
The answer so far are disagree. Whether something akin to McNemar's test or something akin to a chi-square test of association would be appropriate partially depends on whether the responses for each individual were recorded for Test 1 and for Test 2 so that the response for each can be tied to a specific identified individual.
Bruce Weaver Thanks for the response. While I'm aware of the McNemar test, it won't display confidence intervals for the difference between proportions. I figured out using a paired t-test as an alternative, but I wonder if it would work for small samples. Specifically, I am interested in obtaining Confidence Intervals for my difference in proportions. Please guide.
Salvatore S. Mangiafico my data is paired. I have a unique identifier for each individual, and each individual receives both tests.
The t-Test will "work" for small samples, but with a small sample it is likely to produce wide confidence intervals.
It sounds like something akin to McNemar's test make sense for your setup. But the hypothesis tested isn't exactly about the proportion of one response in each Test. It might be practically equivalent, though.
If you want a confidence interval for the difference in proportions, I would recommend calculating that directly. I doubt implementations of McNemar's test won't report that confidence interval. Below I have some R code to calculate this kind of confidence interval.
Example from: https://rcompanion.org/handbook/H_02.html , with the caveat that I wrote it.
You can run this at: https://rdrr.io/snippets/ , without installing R
### Please read documentation at: https://cran.r-project.org/web/packages/PropCIs/PropCIs.pdf
### Compare 7 out of 21 and 13 out of 17.
### Ignore the fact that data are paired
(7/21) - (13/17)
library(PropCIs) diffscoreci(7, 21, 13, 17, conf.level=0.95)
wald2ci(7, 21, 13, 17, conf.level=0.95, adjust = "Wald")
### For matched pairs
### 5 and 23 are off-diagonal counts, 45 is sample size
### "Difference in proportions" is calculated as (b - c )/ n
(23 - 5) / 45
library(PropCIs)
diffpropci.mp(5, 23, 45, conf.level=0.95)
diffpropci.Wald.mp(5, 23, 45, conf.level=0.95)
Salvatore S. Mangiafico Thanks for the R code.
I actually use Stata for most of the analysis. So would love to hear a Stata solution.
If I use the xtgee with family(gaussian) link(identity) corr(independent) vce(robust) i(id), I get some results. But I suppose this is again as good as doing the paired t-test.
Though I think I have a solution for my current problem - paired t-test as suggested by David L Morgan as I have a fairly large sample, I would love to hear a difference in proportions solution rather than a difference in means solution.
Waiting for your comments.
EDIT. Oh, I guess mcc as suggested by @Bruce Weaver does offer a 95% CI for difference in proportions.
Thank you all for your time. Much appreciated.
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