Warner’s original method
In 1965 Warner developed a research technique that, by protecting the anonimity of the respondent had to lead to a reduction of non-respons and social desirability in answering sensitive questions. The respondent is given two statements, for instance:
A chance game (for instance with dice, playing cards or coins) now decides which of the two statements is answered with ‘true’ or ‘untrue’. Since only the respondents know which statements they answered, individual answers have no meaning, the answer ‘true’ might refer to both statements. From the answers of more respondents it is however possible to estimate the true prevalence in the population π of the attitudes towards capital punishment, which is given by
in which λ is the observed answer proportion ‘true’ and p is the probability of answering the first statement. The variance of πis given by
The variance increases with decreasing sample size n and with p approaching 1/2. The method of Warner is less efficient than regular direct questioning, where the variance is given by
The extra variance
is due to the errors in the answers produced by the chance mechanisme. This means that the method of Warner needs larger samples than direct questioning to obtain the same reliability.