Validating an Index of Selection Bias for Proportions in Non-Probability Samples

Fast online surveys without sampling frames are becoming increasingly important in survey research. Their recruitment methods result in non-probability samples. As the mechanism of data generation is always unknown in such samples, the problem of non-ignorability arises making vgeneralisation of calculated statistics to the population of interest highly questionable. Sensitivity analyses provide a valuable tool to deal with non-ignorability. They capture the impact of different sample selection mechanisms on target statistics. In 2019, Andridge and colleagues proposed an index to quantify potential (non-ignorable) selection bias in proportions that combines the effects of different selection mechanisms. In this paper, we validate this index with an artificial non-probability sample generated from a large empirical data set and additionally applied it to proportions estimated from data on current political attitudes arising from a real non-probability sample selected via River sampling. We find a number of conditions that must be met for the index to perform meaningfully. When these requirements are fulfilled, the index shows an overall good performance in both of our applications in detecting and correcting present selection bias in estimated proportions. Thus, it provides a powerful measure for evaluating the robustness of results obtained from non-probability samples.