Do You Brush Your Teeth Every Day?

Sometimes we want to gather data about embarrassing, socially questionable or illegal behaviours, where people may not feel comfortable telling the truth.  In this problem, we explore one way of tackling this.

A survey company wants to find out what proportion (or percentage) of people brush their teeth every day.

Why might this be an ineffective survey question?

The survey company decides to try something different. They give the interviewee a fair 6-sided die and ask them to roll it without showing the interviewer.

They then ask the following question, explaining that the interviewer will not be able to know whether or not their answer is honest:
 

• Will this allow the survey company to work out the approximate proportion of people who brush their teeth every day? 
  You could try this case: the company surveys 1200 people; 500 answer "Yes" and 700 answer "No".
   
• What would be different if the question read: "If you rolled a 6, please answer the next question honestly..."?
   
• What would be different if the question read: "Secretly flip a coin.  If you got heads, please answer the next question honestly, otherwise please LIE"?
   
• How effective do you think this method would be?  How could you work it out?

This is just one approach to obtaining data about difficult topics.  There are many other approaches used by professional statisticians, including the Capture-Recapture method explored in Counting Fish, where different types of survey or other data sources are compared to try to fill in gaps and to improve the quality of the collected data.


This resource is part of the collection Statistics - Maths of Real Life