01-30-2015 08:44 PM
I am new to modelling. I am confused, can Z Score be used to compare percentages if the percentage is coming from a binary (0,1) response variable?
I have a campaign selling TV with response 1 who bought TV and 0 who havn't bought TV. Let's say response for Treatment group is 2.1% and Control group is 1.8%. I have seen people calculating Z Score to compare the two percentages to see if they are significantly different from each other or not.
I understand that we are comparing percentages, which is numeric but they are coming from binary response which is not numeric; its a categorical variable. We fail to validate assumptions required for Z Score / t-test.
According to my understanding, we should be using only Chi-Square test in the above example and Z Scores will be incorrect.
Am I wrong?
01-30-2015 10:21 PM
You can use a z-score if you use a continuity correction.
There are problems with doing this though, because you'll still end up with CI's that are below zero or one and then you can use a Wilson (sp?) correction instead.
02-02-2015 10:49 AM
One might ask if you meant to test a proportion. If you look in many statistics books you'll find a "large sample" normal approximation is used for either a binomial distribution, n>20 or so, or Chi-square, n>100.
And with SAS generally you can accomplish these without having to go to a raw z-score unless you want to.