Estimate the share of AI-assisted responses from a randomised-response question

For a question of the form "answer Yes if at least one of these is true: you have an identical twin; you are an AI agent; you used a bot, a script or an AI for some of your answers". Nobody can tell from a single Yes which statement applies, which makes it safe to answer honestly; across a sample, the known rate of the harmless statement gives the share of the others.

Usage

dq_rrt(yes, p = 0.008)

Arguments

yes

a logical or 0/1 vector, TRUE for "Yes". Missing values are dropped.

p

the probability of the harmless statement. The default is the share of people who are identical twins (about four monozygotic twin pairs per 1,000 births).

Value

A named numeric vector: n, yes_rate, the estimated share ai_share, its standard error se, and the bounds lower and upper of a 95% confidence interval.

Details

Everyone the sensitive statements apply to (share pi) answers Yes whether or not they are a twin, everyone else only if they are one (rate p), so P(Yes) = pi + (1 - pi) * p and pi = (P(Yes) - p) / (1 - p). The only assumption is that the harmless statement applies to the others at rate p. With a small sample the estimate can be below zero.

Examples

answers <- c(rep(TRUE, 12), rep(FALSE, 288))
dq_rrt(answers)
#>            n     yes_rate     ai_share           se        lower        upper 
#> 3.000000e+02 4.000000e-02 3.225806e-02 1.140495e-02 9.904366e-03 5.461176e-02