I am trying to figure out the best way to report the results of a logistic regression in an APA paper. My understanding is that the odds ratio is the most important for interpretation so I don't think I should report the Beta. For significance, do I state the Wald like I would in a comparison (e.g. t(N-2) = #.##, p < .##). Thanks.
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$\begingroup$ This should probably go to a different SE site (maybe Academia or Psychology & Neuroscience, I don't know for sure). $\endgroup$ – gung - Reinstate Monica♦ Jul 16 '16 at 15:28
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1$\begingroup$ At any rate, a Wald statistic is not distributed as t; it is a standard normal. I would think an acceptable form would be "exp(beta) = #.##, CI = (#.##, #.##), p = #.###". $\endgroup$ – gung - Reinstate Monica♦ Jul 16 '16 at 15:30
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1$\begingroup$ We do have a "reporting" tag, and I think generally reporting results is considered to be on-topic here. $\endgroup$ – Silverfish Jul 16 '16 at 17:01
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If you have hundreds of records in the run, then the standard normal distribution $N(0,1)$ approximates the $t_{\nu}$, and you could use Z-scores for the test statistic, that is $Z_j=\beta_j/s.e.(\beta_j)$. If $\textrm{abs}(Z_j) \geq 1.96$, then the $OR$ is significantly different from unity. By the way, the $OR$ for variable $j$ is simply $\exp\{\beta_j\}$. We almost always use $Z$ when reporting everything, for example: "results were significant $(Z=2.01, P=0.04)$." If you have small sample sizes then you are constrained to using $t$-variates for $\nu=1$ d.f.. The Wald $\chi^2_{\nu}$ statistic is merely $Z^2$, since for a 1 d.f. test, $1.96^2=3.84$.
