## Sample Size Calculator

If you are conducting a non-conjoint quantitative survey where your objective is to gather data to make generalized statements about a larger population, then it is critical that you use the proper sample size from the target population. This sample-size (survey-size) calculator will point you in the right direction. Please see the Definitions section if you do not understand any of the terms in the calculator.

If you are conducting a conjoint or discrete-choice survey, this tool may not be relevant. Please see the following article for other things you need to consider when determining sample size: Sample Size Issues for Conjoint Analysis Studies (2009).

 What margin of error can you accept? % What confidence level do you need? % What is the population size? What is the response distribution? % Your recommended sample size is: 377

Below are some scenarios that illustrates what happens to your margin of error and confidence levels if you do not use the recommended sample sizes.

 With a sample size of: Your margin of error would be: 9.78% 6.89% 5.62%
 With a confidence level of: Your sample size would need to be: 267 377 643

## Definitions

Margin of Error. The margin of error is the amount of random sampling error that you can tolerate. If 90% of respondents answer yes, while 10% answer no, you may be able to tolerate a larger amount of error than if the respondents are more evenly split, such as 45-55. The larger the margin of error, the less confidence you should have that the survey results accurately reflect the whole population. A lower margin of error requires a larger sample size. 5% is a common choice.

Confidence Level. The confidence level is the amount of uncertainty you can tolerate. It refers to the percentage of all possible samples that can be expected to include the true population parameter. For example, suppose that you have 20 yes-no questions in your survey. With a confidence level of 95%, you would expect that for one of the questions (1 in 20), the percentage of people who answer yes would be more than the margin of error away from the true answer. The true answer is the percentage you would get if you exhaustively interviewed everyone. A higher confidence level requires a larger sample size. Most researchers use the 95% confidence level.

Population. This term refers to the total observations that can be made. If you are studying the natural hair color of men, the population is all of the men in the entire world. Fortunately, because of probability theory, we don't have to survey all men--just a representative sample. The sample size doesn't change much for populations larger than 20,000. Therefore, if you don't know the size of your population, use 20,000.

Response Distribution. For each question, what do you expect the results will be? If the sample is skewed highly one way or the other, the population probably is, too. If you don't know, use 50%, which is the most conservative assumption and provides the largest sample size.

Formula. In this calculator, the sample size n and margin of error E are given by:

 x = Z( c/ 100) 2 r(100- r) n = N x/ ((N-1)E2 + x) E = Sqrt[ (N - n)x/ n(N-1)]

In the equations above, N is the population size, r is the fraction of responses that you are interested in, and Z ( c/100) is the critical value for the confidence level c. This calculation is based on the normal Gaussian distribution, and assumes you have more than about 30 samples.

## Population Confidence Level Table

As you can see from the table below, the size of the population becomes irrelevant unless the size of the sample exceeds a few percent of your target population. It other words, a sample of 400 people is equally useful in examining the opinions of a country of 250,000,000 as it would a city of 50,000. ## Sawtooth Software

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## Lighthouse Studio

Lighthouse Studio is our flagship software for producing and analyzing online and offline surveys. It contains modules for general interviewing, choice-based conjoint, adaptive choice-based conjoint, adaptive choice analysis, choice-value analysis, and maxdiff exercises.