Let Zi =1 if unit i is included in the sample and 0 otherwise, with P(Zi = 1)=Ï€i.
Let Ri =1 if unit i responds to the survey and 0 otherwise, with P(Ri = 1)=φi
And

Assume Ri is independent of Zi for each i = 1. . . N. Let Å·R estimate the population mean

using only the respondents:

Where wi = 1/Ï€i. Show that the bias of Å·R is approximately

Where

As a consequence, the non response bias is approximately zero if either (1) φi =φU for all i, that is, the response propensity is the same for all units, or (2) the propensity to respond is uncorrelated with the response yi (Tremblay, 1986).

Transcribed Image Text:

YU VR ον φυ i= I