I am using Logistic Regression and found while checking the output tables that some variables have their Beta coefficient statistically significant based on Wald statistic derived from the (Variables in the equation output) . The same variable may not have significant scores on Rao’s Efficient Score statistic derived from (Variables not in the equation output) How to deal with such discrepancy in results?
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See [Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?](http://stats.stackexchange.com/q/144603/17230). – Scortchi - Reinstate Monica Mar 16 '16 at 09:59
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If we are talking about a $p$-value of .049 and .051 or similarly small differences, then I would not make too much of those differences. The boundary of 5% is arbitrary anyhow.
You should also keep in mind that both tests are based on an asymptotic arguments, so in principle they apply to an infinitely large sample. For simple models as sample of 50 or a 100 can be close enough to infinity. In more complex models you may need a lot more observations before the $p$-values mean what they should mean. The likelihood ratio test tends to be a bit more stable in small samples, but that test is also based on a similar asymptotic argument, so that too will produce incorrect estimates of the $p$-value if the sample is too small.
Maarten Buis
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It depends on the exact model (e.g. how many variables, are there interactions, ...) and your data (e.g. how common are the successes and the failures) whether 400 is enough or not. – Maarten Buis Mar 16 '16 at 10:47