Are only the p-values relevant when testing the regression coefficients of a logistic regression? Does the z-value of a coefficient give any further information about the significance of the coefficient?

I know how the z-values are to be estimated, but I have some difficulties with interpreting it for each coefficient, so I am not sure if it gives any information about its significance.

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    $\begingroup$ The $z$-value is directly linked to the $p$-value. The two-sided $p$-value for each regression coefficient is calculated as $2\cdot \Phi(-|z|)$ where $\Phi$ denotes the CDF of the standard normal distribution. $\endgroup$ – COOLSerdash Feb 27 '15 at 21:44
  • $\begingroup$ COOLSerdash's comment covers the central issue; I'd only add that the two tailed $p$-value is monotonic in $|z|$ and so the only additional information you can get from $z$ that you can't see in $p$ would be its sign (which doesn't relate to significance in the two-tailed case). $\endgroup$ – Glen_b -Reinstate Monica Feb 27 '15 at 22:49

In a logistic regression, are you sure you aren't using chi-square values instead of z-values? I've always seen Wald (if asymptotics are appropriate) and likelihood ratio chi-square values used to measure statistical significance in logistic regression.

Either way, the p-value corresponding to a chi-square value for a logistic regression coefficient has the same interpretation as the p-value corresponding to an F-value for a linear regression coefficient.

In logistic regression, the p-value corresponding to the calculated chi-square value is the probability of seeing a chi-square value at least as high as the calculated chi-square value for the equivalent model without that coefficient.

  • $\begingroup$ You can get z-values as asymptotically normal test statistics ($\hat\beta/\hat{\sigma}_\beta$) for individual coefficients. $\endgroup$ – Glen_b -Reinstate Monica Feb 27 '15 at 22:51
  • $\begingroup$ @Glen_b You're right, sorry. I was thinking of the Wald chi-square statistic instead of the Wald normal statistic. $\endgroup$ – Brandon Sherman Feb 27 '15 at 23:35

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