Sample Size Calculator: Easily Calculate the Sample Size

What Do the Parameters of the Sample Size Calculator Mean?

The margin of error and confidence level are absolutely necessary to calculate the sample size. The sample size can be calculated even without knowing the size of the total population. But what do these terms actually mean?

Margin of Error

The margin of error defines the tolerance of your measurements and determines how much the true value in the population may differ from the value measured in your survey.

For example, if your survey shows that 60% of respondents prefer brand X, a margin of error of 5% means that the share of brand X fans in the population may vary by 5% up or down from your measured 60%. This means the true value lies somewhere between 57% (60 minus 5% of 60) and 63% (60 plus 5% of 60). This range is also called the confidence interval.

Smaller margins of error require larger samples.

Confidence Level

The confidence level, also known as the level of confidence, indicates how sure you want to be that the survey results are representative of the population. In other words, it defines the probability that the values derived from the survey lie within the confidence interval when generalized to the population.

A confidence level of 95% means the following:

If we conducted the same survey 100 times, we would correctly estimate the confidence interval in 95 of those cases, meaning the actual values of the population would lie within the “measured value +/- margin of error” range. In 5 cases, however, the actual value would lie outside this range, making the survey results non-transferable to the population.

In the example above, we can say: We are 95% confident that the percentage of people who prefer brand X in the population lies between 57% and 63%.

Higher confidence levels require larger sample sizes.

Population Size

The population size, or total population, refers to the number of people you want to make statements about based on your survey results.

If the survey results are supposed to represent the employees in your company, then the population size equals the number of all employees in your company. If the results should apply to the whole of Germany, the population would be about 83 million.

The smaller the population, the smaller the required sample size for a representative survey.

In many cases, the population size is unknown. That’s not a major issue. In such cases, the sample size can be calculated assuming an “infinite population.” This means you’ll have to survey a few more participants, but you’ll also be confident that your results are representative.

Required Sample Size

The required sample size is the minimum number of participants you need to survey in order for the results to be considered representative of the population.

The more people you survey, the more “representative” your results become. So it’s not a problem if you survey more participants than required.

It’s a different story if you survey fewer participants than the minimum required sample size. In that case, you lose the basis for claiming that the insights from your survey can be generalized to the population. Neither the margin of error nor the confidence level can help here—if the minimum sample size is not reached, they become meaningless.

Does My Survey Have to Be Representative?

The answer to this question is simple: It depends on the purpose of your survey!

If you want to gain a comprehensive understanding of the entire population in order to make generalizations or important decisions, then you should definitely aim for representativeness.

This is the case, for example, in market research studies that collect information about target markets to segment them, assess how a new product might be received by potential customers, or evaluate consumer reactions to advertising messages. If the survey is not representative, you cannot transfer the insights to the population, and you won’t know whether the market will respond in the same way your survey results suggest.

Similarly, in employee surveys—especially before planned restructuring—and in opinion and election polls, representativeness should be pursued.

If you are only collecting feedback or looking for ideas and suggestions from employees or customers, representativeness is not particularly important. It is also not required for qualitative studies.

How Can I Calculate the Sample Size Myself?

The sample size calculator presented in this article is suitable for most survey projects and provides reliable estimates of sample size in the majority of practical cases.

The calculator assumes that you don’t have prior knowledge about the distribution of the variable of interest (e.g. share of dissatisfied consumers) in the population before starting your survey. However, if you do have such information (e.g. from previous studies or data from the federal statistical office), the required sample size may be slightly smaller.

To calculate the sample size in such cases and/or if you want to learn more details about how sample sizes are calculated, read our technical article on Sample Size Calculation.

Date: 23.11.2020
Author: Dr. Paul Marx
This text is protected by copyright. All rights reserved.

You might also be interested in:

• Sample Size Calculation: Technical Details Explained Simply
• Materials from the course “Principles of Survey Research”
• Margin of Error Approach to Determining Sample Size
• Samples