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- Using Z Scores to analyze binary response? Confuse...

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01-30-2015 08:44 PM

Hi,

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?

Example:

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?

Thanks

Sachin .

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01-30-2015 10:21 PM

You can use a z-score if you use a continuity correction.

http://www.statisticshowto.com/what-is-the-continuity-correction-factor/

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.

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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.