Each survey candidate is given a fair coin, and a private room. Alone, they flip the coin. If it comes up heads, then they answer the question honestly (writing YES if they engage in questionable practices, and NO if they do not.) If the coin comes up tails, however, they flip it once more. They then answer YES if the coin comes up heads, and NO if the coin comes up tails.

Assume that you survey 5,000 North American astronomers using this technique. You find that 1,975 of them answer YES to the survey. What is the actual fraction of astronomers who engage in questionable practices?

Of the 5,000 answers, 50% (2,500) represent the results of a fair coin toss. We thus expect that these will be evenly split between heads (1,250) and tails (1,250). Removing these obscuring data from the survey data,

Note that anonymity has been preserved for all individuals!