FAQ: One-sample proportion z-test -- Implementation Issue?

[Nolataari]

In the case of one-sample test, the function proportions_ztest(count, nobs, value=None, alternative='two-sided', prop_var=False) from statsmodels.stats.proportion calculates the variance based on the sample proportion, unless prop_var is specified, like so:

    if prop_var:
        p_pooled = prop_var
    var_ = p_pooled * (1 - p_pooled) * nobs_fact

However, explicitly specifying prop_var is redundant, since in my opinion it should be picked up by the parameter value. I personally do not see a reason why the variance should be calculated by default using the sample proportion instead of the null hypothesis value.

I am keen to hear your opinion on this.

[josef-pkt]

Both versions are legitimate, it is the difference between wald tests (parameters estimated from the sample without null hypothesis restrictions) and score/LM test (parameters estimated under the null hypothesis restrictions). I followed the documentation of SAS or SPSS or some other package in this. (I don't remember which ones I looked at.)
see also the related number of possibilities to compute confidence intervals for a proportion.

e.g.
http://support.sas.com/documentation/cdl/en/procstat/67528/HTML/default/viewer.htm#procstat_freq_details37.htm section "Equality Test"

The problem is that the score test has better small sample behavior than the wald test. However, at the time I mainly translated formulas to code and hadn't read yet much about the small sample behavior of those hypothesis test and related statistics.