Timeline for At What Level is a $\chi^2$ test Mathematically Identical to a $z$-test of Proportions?
Current License: CC BY-SA 3.0
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| Aug 4, 2022 at 18:49 | history | edited | ttnphns |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Sep 21, 2015 at 21:51 | vote | accept | Antoni Parellada | ||
| Sep 21, 2015 at 18:37 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 16:23 | comment | added | amoeba | I guess that one p-value is one-sided and another is two-sided; hence the difference by the factor of two. | |
| Sep 21, 2015 at 13:22 | answer | added | ttnphns | timeline score: 20 | |
| Sep 21, 2015 at 12:02 | comment | added | Antoni Parellada | The first could be a matter of rearranging terms, and splicing nomenclature, and I could tackle it later when I have time. The second is a bit more hairy. In any event, it would be great to just get a formal answer from another member I can upvote and accept. | |
| Sep 21, 2015 at 11:59 | comment | added | Antoni Parellada | Thank you! You were (predictably) correct. With the Yates correction off, one is just the square of the other. I edited the question accordingly, although a bit fast. I still would like to prove algebraically that both test statistics are the same (or one the square of the other), and understand why the p-values are different. | |
| Sep 21, 2015 at 11:57 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 11:09 | comment | added | ttnphns | Indeed, Antoni. Both tests exist with or without the Yates. Could it be that you compute one with but the other without it? | |
| Sep 21, 2015 at 11:05 | comment | added | mark999 |
In chisq.test(), have you tried using correct=FALSE?
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| Sep 21, 2015 at 11:02 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 10:24 | comment | added | Antoni Parellada | In the example on the last hyperlink the $\chi^2$ is almost the square of the z-test statistic, but not quite, and the p-values are different. Also, when you look at the formulas for the rest statistics above, is it truly immediate that they are identical? Or even one the square of the other? | |
| Sep 21, 2015 at 6:04 | comment | added | ttnphns | But these are two identical tests. Z squared is the chi-square statistic. Let you have 2x2 frequency table where columns are the two groups and the rows are "success" and "failure". Then the so called expected frequencies of the chi-square test in a given column is the weighted (by the groups' N) average column (group) profile multiplied by that group's N. Thus, it comes that chi-square tests the deviation of each of the two groups profiles from this average group profile, - which is equivalent to testing the groups' profiles difference from each other, the z-test of proportions. | |
| Sep 21, 2015 at 3:27 | history | tweeted | twitter.com/#!/StackStats/status/645801427248529409 | ||
| Sep 21, 2015 at 3:19 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 3:11 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 3:06 | history | edited | Antoni Parellada | CC BY-SA 3.0 |
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| Sep 21, 2015 at 3:00 | history | asked | Antoni Parellada | CC BY-SA 3.0 |