I am curious about the appropriate statistical test to compare the results from a chi-squared proportion test in R.
In the below code, using a chi-squared proportions test in R, it is shown that the difference between "1" Responses for Group A1 and A2 is significant at > 95%. The difference is 90% 1s vs 10% 1s
It is also shown that the difference between "1" Responses for Group B1 and B2 is significant at > 95%. The difference is 80% 1s vs 20% 1s
However, I am now interested in comparing the resulting differences: the difference between Group A1 and A2, against the difference between Group B1 and B2.
What is the most appropriate test of whether the 90%:10% result from comparing Group A1 and A2, is different from the 80%:20% result from comparing Group B1 and B2? Or is there a single test that should pull in all this information at once?
RESPONSE = c(1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0) GROUP = c(rep("Group A1",10),rep("Group A2",10),rep("Group B1",10),rep("Group B2",10)) Data = cbind.data.frame(RESPONSE,GROUP) table(Data) #> table(Data) # GROUP #RESPONSE Group A1 Group A2 Group B1 Group B2 # 0 1 9 2 8 # 1 9 1 8 2 #Proportion test Group A1 vs A2 prop.test(c(9,1),c(10,10)) #Proportion Group A1 = 0.9 #Proportion Group A2 = 0.1 #P-Value = 0.001745 #Proportion test Group B1 vs B2 prop.test(c(8,2),c(10,10)) #Proportion Group B1 = 0.8 #Proportion Group B2 = 0.2 #P-Value = 0.02535