In order to have confidence that your survey results are representative, it is critically important that you have a large number of randomly-selected participants in each group you survey. So what exactly is "a large number?" For a 95% confidence level (which means that there is only a 5% chance of your sample results differing from the true population average), a good estimate of the margin of error (or confidence interval) is given by 1/√N, where N is the number of participants or sample size (Niles, 2006).

The following table shows this estimate of the margin of error for sample sizes ranging from 10 to 10,000. (For more advanced students with an interest in statistics, the Creative Research Systems website (Creative Research Systems, 2003) has a more exact formula, along with a sample size calculator that you can use. For most purposes, though, the 1/√N approach is sufficient.)

Sample Size (N) |
Margin of Error (fraction) |
Margin of Error (percentage) |

10 | 0.316 | 31.6 |

20 | 0.224 | 22.4 |

50 | 0.141 | 14.1 |

100 | 0.100 | 10.0 |

200 | 0.071 | 7.1 |

500 | 0.045 | 4.5 |

1000 | 0.032 | 3.2 |

2000 | 0.022 | 2.2 |

5000 | 0.014 | 1.4 |

10000 | 0.010 | 1.0 |

You can quickly see from the table that results from a survey with only 10 random participants are not reliable. The margin of error in this case is roughly 32%. This means that if you found, for example, that 6 out of your 10 participants (60%) had a fear of heights, then the actual proportion of the population with a fear of heights could vary by ±32%. In other words, the actual proportion could be as low as 28% (60 - 32) and as high as 92% (60 + 32). With a range that large, your small survey isn't saying much.

If you increase the sample size to 100 people, your margin of error falls to 10%. Now if 60% of the participants reported a fear of heights, there would be a 95% probability that between 50 and 70% of the total population have a fear of heights. Now you're getting somewhere. If you want to narrow the margin of error to ±5%, you have to survey 500 randomly-selected participants. The bottom line is, you need to survey a lot of people before you can start having any confidence in your results.

## Bibliography

- This webpage calculates the sample size required for a desired confidence interval, or the confidence interval for a given sample size:

Creative Research Systems, 2003. "Sample Size Calculator," Retrieved June 28, 2006 from http://www.surveysystem.com/sscalc.htm. - This website has information on statistics and statistical tests, written for the non-mathematician:

Niles, Robert, 2006. "Robert Niles' Journalism Help: Statistics Every Writer Should Know," RobertNiles.com. Retrieved June 28, 2006 from http://www.robertniles.com/stats/.