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I am not that used to searching the right test statistic, however, I have some basic knowledge about hypothese testing. My question is if there is a name/standart procedure in R for testing the population proportion of a control group compared to a treatment group.

In more detail:

  • Controlgroup: Two answer options A1 and A2
  • Treatmentgroup: Three answer options A1, A2 and A3

I want to test if the answer A3 can influence the observer to choose A2.

Define P := proportion of responses that choose A2.

  • H0: P_c = P_t (P_c - P_t = 0)
  • Ha: P_c < P_t (P_c - P_t < 0)

I would use something like example three on this page: https://courses.lumenlearning.com/introstats1/chapter/comparing-two-independent-population-proportions/ But my question is, is there a name/standart procedure in R for testing such a cenario? Can u help me to choose the correct testing method for this hypothesis?

Edit 16.03.20 17:34: Thanks to Dave's answer I tried the proportion test with the prop.test package:

I have two setups to test the same effect. For setup one I have C: 48/80 A2 and T: 60/85. For setup two I have: 45/80 A2 and T: 60/85. Setup one shows no significant difference (p-val=0.1028) where setup two shows significance (p-val=0.03992) with the prop.test.

Does someone have another test that I can use? Does someone know the uniform most powerful test for this scenario?

Onerock
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    Your setup is that you want to know what proportion of subjects respond with A2 in each group. For each group, you have a count of how many responded that way, and you have a count of how many subjects there were. This is exactly how prop.test works. There are other ways of doing this kind of test, but prop.test looks like the most straightforward. Read the documentation through “?prop.test” to see how to do the one-sided test. – Dave Mar 16 '20 at 14:41
  • Thank you Dave for your contribution. It did work, however, the result is seems to be not very robust (see new Answer). Do you have more tests for recommandation? – Onerock Mar 16 '20 at 16:06
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    Why do you say it’s not robust? – Dave Mar 16 '20 at 16:32
  • I'm sorry I may have misused the term "robust" here. What I meant was that I am surprised by the large effect on the p-value due to the only 3 additional A2 selections in setup one compared to setup two. – Onerock Mar 16 '20 at 16:40
  • You don’t have a tiny sample size, but it’s not especially large, either. A couple of different responses would have an effect, as you’ve noticed. – Dave Mar 16 '20 at 17:21
  • In your first comment you mentioned other ways of doing this kind of test, can you elucidate? – Onerock Mar 17 '20 at 08:21
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    Fishers exact test (fisher.test) and a $\chi^2$ test (chisq.test) come to mind. – Dave Mar 17 '20 at 12:54
  • Your contributions helped and let me to this entery: https://stats.stackexchange.com/questions/2391/what-is-the-relationship-between-a-chi-squared-test-and-test-of-equal-proportion Which answered all remaining questions. Thank you Dave! – Onerock Mar 17 '20 at 15:41

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