A note on post-stratification when analyzing binary survey data subject to non-response

In this paper we follow up two notes of Thomsen (1973, 1978) and present some results on the estimation effect of post-stratification when analyzing binary survey data subject to non-response. Using an alternative parameterisation and assuming that the non-response depends on the variable of interest which can not be fully observed, we show that the relative reduction in the bias can be estimated from the response group alone. In addition, the relative bias and variance reduction are both shown to be approximately equal, under certain conditions, to one minus the square of the correlation coefficient between the auxiliary and object variable among the respondents.