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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

Stat01
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    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
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    Closely related: [What is the relationship between a chi square test and test of equal proportions?](http://stats.stackexchange.com/q/2391/930) – chl Jul 31 '13 at 16:02
  • @chl You beat me to it. – Sycorax Jul 31 '13 at 16:08
  • See [this](http://stats.stackexchange.com/questions/2391/what-is-the-relationship-between-a-chi-square-test-and-test-of-equal-proportions) question (edit: ah, @chi already mentioned it), and [this](http://stats.stackexchange.com/questions/52927/alternative-nonparametric-test-for-chi-square-test-for-independence), [this](http://stats.stackexchange.com/questions/60916/chi-square-with-unbalanced-design) ... & others. There's also some potentially relevant information [here](http://stats.stackexchange.com/questions/57104/p-value-and-confidence-interval-for-two-sample-test-of-proportions-disagree/) – Glen_b Aug 01 '13 at 00:59

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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.

Sycorax
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