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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

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    $\begingroup$ 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. $\endgroup$ – Sycorax Jul 31 '13 at 15:36
  • $\begingroup$ @DJE I agree, but this is how they evaluate customer satisfaction here. $\endgroup$ – Stat01 Jul 31 '13 at 15:42
  • $\begingroup$ 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. $\endgroup$ – Sycorax Jul 31 '13 at 15:49
  • $\begingroup$ @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? $\endgroup$ – Stat01 Jul 31 '13 at 15:54
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    $\begingroup$ Closely related: What is the relationship between a chi square test and test of equal proportions? $\endgroup$ – chl Jul 31 '13 at 16:02
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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.

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