# Chi square vs. Z-test on stratified 'bin' data

I have some data that look like: These data show between case (spinal cord injury) and control the number of drugs that patients in these populations were prescribed at any given time. I'm looking for a p-value to determine that the cases were prescribed more than >= 5 drugs at a significantly higher rate than the controls. It doesn't really matter to the study that someone is on 30 drugs, just that it's more than five. What's the best test to use to get a p value that the cases are prescribed >=5 drugs vs. the controls?

EDIT:: CASE N = 11571 CONTROL N = 9494

• How do the columns sum to 100? – Ellis Valentiner Dec 18 '13 at 14:57
• @EllisValentiner That's 100%, apologies for that confusion. The total Ns are CASE = 11571 and CONTROL = 9494 – wootscootinboogie Dec 18 '13 at 14:59

If you are only interested in $<5$ vs. $\geq 5$ drugs prescribed, then you can collapse your table like such:

# Drugs | Case  | Control
-------------------------
<5  |  4172 |   5957
>=5  |  7399 |   3537


then you can perform a chi-square test ($\chi^2 = 1487, df=1, p < 2.2e-16$). Since the $\chi^2$ test is significant, you have evidence that your case and control conditions differ in the number of drugs prescribed. I'd then calculate the odds ratio, which shows that those in the control condition had about 2.9867 (2.8234, 3.1601) times the odds of $\geq 5$ drugs relative to the case condition.

• Thanks for the help. How do you make the nice math-y script? – wootscootinboogie Dec 18 '13 at 15:17
• You can place math TeX/LaTeX between $ and $. Example try $\geq 5$, $\frac{1}{4}$, or $5^2$ – Ellis Valentiner Dec 18 '13 at 15:22
• @wootscootinboogie if you click on the little question mark at the top right of the box in which you type a question or answer, it takes you here which gives you at least some basic information about how to make your posts look more like what you want. (If you haven't used LaTeX before, there's a lot of online guides available.) – Glen_b Dec 18 '13 at 20:07