Can I use a two proportion z-test?

Question

I have a response, "Satisfaction" that goes on a scale from 0-10 (where 0=dissatisfied and 10= very satisfied), and I have a predictor variable that also uses the same scale. I recoded the response so that 0-5 is "not satisfied" and 6-10 is "satisfied". I did the same for the predictor variable. I used SPSS to get the frequencies for each (there are 4 different combinations). My question is, can I use a two proportion z-test to test whether there is a significant difference in the predictor at the two different levels of my response?

Thank you

In general, it's best to perform analysis with the highest resolution data available. By regrouping your 0-10 data into binary categories, you're losing out on the more textured data in the 0-10 scale. — Sycorax, Jul 31 '13 at 15:36
@DJE I agree, but this is how they evaluate customer satisfaction here. — Stat01, Jul 31 '13 at 15:42
The logical follow-up would be to ask why they collect the 0-10 data in the first place, if the data will inevitably be collapsed into binary categories during the analysis... but I understand that one is sometimes constrained by structural circumstances. — Sycorax, Jul 31 '13 at 15:49
@DJE That's a valid point, I guess they use it for other analysis. Would a two proportion z-test be appropiate in this case? — Stat01, Jul 31 '13 at 15:54
Closely related: What is the relationship between a chi square test and test of equal proportions? — chl, Jul 31 '13 at 16:02
See this question (edit: ah, @chi already mentioned it), and this, this ... & others. There's also some potentially relevant information here — Glen_b, Aug 01 '13 at 00:59

Sycorax · Accepted Answer · 2013-07-31T16:03:32.613

2

Yes. Indeed, a two-proportion z-test in this case is the same as a chi-square test on a 2x2 a contingency table where the cells are the number of events satisfying the pair of conditions. Alan Agresti, An Introduction to Categorical Data Analysis provides further information.

edited Jul 31 '13 at 16:03

answered Jul 31 '13 at 15:58

Sycorax

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Can I use a two proportion z-test?

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