# Surveying embarrassing questions

## Background

When you want to collect information on individuals, with the objective of deducing something about the population, there are several issues to contend with:

• Are you talking to the right people (have you done a good job of sampling);
• Do you have enough people to make good predictions (sample size, power)?
• Have you posed the questions carefully (experimental design)?
• Will the respondents answer truthfully?
• Have you provided anonymity, so that individuals have faith that their answers won't be discovered and shared?
• Will the respondents take your questions seriously, and answer them honestly?

These are just some of the issues we face when we want to collect information in order to make deductions about populations of interest. Polls are one such situation, where we hope that a small sample of would-be voters will inform us about the tendency of the whole.

## Providing cover for respondents

There are many methods to help provide anonymity to respondents:

• anonymous surveys
• using fill-in dots, rather than hand-written information (so that hand-writing won't be recognized)
• asking respondents to use the internet and anonymous computers to provide information

We propose the following mathematical relationship between anonymity and truth (a direct relationship):

```The more assured the respondent is that there is anonymity, the more truthful the answer.
```

• Do you have the embarrassing medical problem of multiple $(\ge 2)$ siblings?