Variables can be called as “sensitive”, when the mechanisms leading to nonresponse and untruthful answering are “not at random”, meaning that these mechanisms depend on the values of the variable. Such respondents' behavior may result in strongly biased estimators of population parameters. Randomized response questioning designs may help to reduce such a behavior.
In the talk a certain family of such designs will be presented: The standardized multistage randomized response strategy for the estimation of proportions. This family of techniques includes several previously published methods as special cases and extends its statistical properties to all probability sampling designs. It can be described in the following way: At the first h-1 of h stages a survey unit is asked with probability pi1 (i=1,..., h-1) the question on membership of the group, of which the relative size is to be estimated. With the remaining probability the unit is directed to the next stage of the questioning design. Finally, at the h-th stage the unit is asked with a probability ph1 the same question as above. With probability ph2 the respondent is asked the question on membership of the complementary group. With ph3 the survey unit is asked a question on membership of a group, which is completely non-sensitive. With a probability of ph4 the respondent is instructed to say only “yes” and with the remaining probability ph5 to say only “no”.
Comparing the performance of the different designs included in this family it is important to measure the privacy protection offered by the procedures as objectively as possible, because only the comparison of strategies with the same level of privacy protection is relevant for the practice. The question of privacy protection is almost ever neglected in papers particularly of designs with more than one stage.
Keywords: Randomized response technique; Estimation of proportions; Probability sampling methods; Privacy protection
Biography: Andreas Quatember is Assistent Professor at the Department of Applied Statistics of the Johannes Kepler University Linz in Austria. He wrote a well-known book in the german speaking countries on basics in statistics, of which the translated title is “Statistics without being afraid of formulae”. His research is focused on data quality in sample and population surveys and therefore randomized response questioning designs are part of his work.