Proportion of Returns in Survey Research

Abstract

Formulas are given for computing, from the responses of returnees alone, the maximum and minimum values between which the mean response to a survey item must fall in the total sample. Expressions for the standard errors of these maximum and minimum mean values are provided. The difference between the maximum and minimum means, in addition to the magnitudes of their standard errors, vary inversely with the proportion of returns. It is also shown that the extent to which the responses of returnees to a survey item are representative of the responses of the total sample is a function of sample size, proportion of returns, and proportion of returnees responding to the item in a specified direction. Formulas are derived for computing (1) the probability that the difference between the proportion of returnees who respond in a specified direction and the proportion of the total sample responding in that direction will be equal to or greater than an acceptable value, and (2) the minimum proportion of returns required to be fairly confident that the responses of returnees are representative of the responses of the total sample.