Determining Sample Sizes for Estimating Proportions

When you decide to conduct a survey, one of the decisions you will need to make is the number of people to include in the sample. Your research supplier will help you to do this. Nevertheless, you may have some curiosity about how precise your results will be at different sample sizes. This tip will give you some idea of the amount of extra precision you will obtain (when estimating the true population proportion) as you increase your sample size.

**Definitions**

- Population Proportion: The percentage of people in the population who will respond a certain way for a given issue. This is an actual percentage which we would know if we were able to include everyone in a given population in a survey. We are attempting to estimate the population proportion by sampling a smaller group of people.
- Sample Size: The number of people in the survey.
- Margin of Error, or Precision: The "plus or minus" amount, or percentage in the case of estimating proportions.
- Confidence Level: The degree to which you are certain that the result, or estimate, you obtain from the study includes the true population percentage, when the precision is taken into account. Typical confidence levels are 80%, 90%, and 95%, although any confidence level can be used.
- Confidence Interval: The range within which we expect the true population percentage to fall for a given confidence level.

The table below shows the margin of error associated with three different sample sizes at three different confidence levels, if the true population proportion is 50%. An example of how to interpret the table is as follows:

Let's say you are conducting a poll to determine the percentage of likely voters who favor a particular candidate. If you have a sample size of 200 people, and you want to be 90% confident in the results, the margin of error would be plus or minus 5.8. If the result of the survey shows that 50% of people would vote for the candidate, the confidence interval would be 44.2% to 55.8%. You would then be able to say that you are 90% confident that the actual percentage of people who will vote for a candidate is within this range.

Margin of Error if the Population Proportion Is 50% | |||
---|---|---|---|

Sample Size | |||

Confidence Level | 100 | 200 | 500 |

80% | ±6.4% | ±4.6% | ±2.9% |

90% | ±8.2% | ±5.8% | ±3.7% |

95% | ±9.9% | ±7.0% | ±4.4% |

The further from 50% that the proportion is, the more precise will be your estimate. It is helpful to have some idea of what the result will be when choosing the sample size, since you may be able to live with a smaller sample if you suspect that the result will be much larger or smaller than 50%. The table below shows the margin of error for each of our three confidence levels and each of our three sample sizes, if the percentage who would vote for the candidate is 10% or 90%.

Margin of Error if the Population Proportion Is 10% or 90% | |||
---|---|---|---|

Sample Size | |||

Confidence Level | 100 | 200 | 500 |

80% | ±3.8% | ±2.7% | ±1.7% |

90% | ±4.9% | ±3.5% | ±2.2% |

95% | ±5.9% | ±4.2% | ±2.6% |

If you have no idea what percentage you will end up with after conducting the survey, you should assume 50%, and use the figures from the first table.

The confidence level you choose will depend upon the importance of the conclusion or decision you wish to make with the data. In reality, budgetary constraints will likely play a part, and you will find yourself making tradeoffs between the amount of precision you want and the amount for which you are willing to pay. As you can see in the above tables, doubling the sample size does not cut the margin of error in half, so there are diminishing returns as you increase sample size.

Most people are surprised to find that there is no relationship between the number of people in a population being measured and the number of people you need to sample. This means that a sample size of 200 will work as well if the population being measured is 1,000,000 as it will if the population being measured is 3000.

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