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# How do you choose a sample size for a survey?

Students frequently have to conduct surveys and an early topic raised with supervisors is how many samples (the sample size) are required to adequately define the subject or target population?

Sample size (n) can be calculated using statistical methods using values for the confidence level, the acceptable error (margin of error), and the percentage of the sample proportion selecting a given choice.

The confidence level of a sample is expressed as a percentage and describes the extent to which it is representative of the target population. For example, if you have a confidence level of 95%, and you were to conduct a survey 100 times, the survey would yield the same result 95 times out of 100 times. In practice, confidence levels of 95% are frequently used. Confidence levels of 99% and 90% are also used. As confidence level increases so do the number of samples, cost, and time.

The margin of error (e), measured in percentage terms,  indicates the extent to which the results of the sample population are indicative of the overall population. In many student projects, a margin of error of 5% is commonly used. As the margin of error decreases (e.g. going from 5% to 1%) the number of samples increases as does the cost and time.

The percentage of a population, also known as sample proportion (p), selecting a given choice markedly influences the accuracy of the research findings.  This figure is not usually known before most surveys but may sometimes be estimated from previous similar research.  Its importance is apparent if you consider two situations. In the first  99% of a population selects “yes” for a study attribute and only 1% selects “no”. Under these conditions, there is a low chance of error even with a small sample. On the other hand, if only 38% of the population select “yes” and 62% select “no”, there is a much higher chance of error. Because this value is usually unknown most researchers when calculating the sample size required for a given level of accuracy will opt for caution and will normally use a value of 50%.
Sample size can be calculated using equation 1.

Equation 1. n = Z2 x p x(1 - p) / e2
Where
n: number of samples required
Z: is the z-score and is derived from the confidence limit
p: is the sample proportion. In this equation it is represented as a decimal
e: is the margin of error required. It is represented as a decimal in this equation.

Equation 1 requires the addition of a correction factor to allow for finite-size when working with small populations. Most student projects will have to work using this finite correction factor. The modified equation (equation 2) is shown below.

Equation 2. n = [Z2 * p * (1 - p) / e2] / [1 + (Z2 * p * (1 - p) / (e2 * N))]

Note the only new variable in equation 2 is N which is the size of sample population e.g. the number of employees at a cheese processing company.

The Z-score for commonly used confidence levels is given in Table 1.

 Table1. The Z-score for commonly used confidence levels Confidence Level (%) Z-Score 90 1.645 95 1.96 99 2.58

You can use the calculator below to determine your sample size. Note the number of samples required has been rounded up to the next highest number.

# Calculate sample size required for a survey

To use select confidence limit and modify or add your values to the fields below.

Select confidence level
Population proportion, %
Error limit (%)
Population size (optional) Required for research on an organisation e.g. school, company, club, university

.

Calculating the sample size is the easy part of a survey. Many student surveys on initial design will have design and logic errors. Consideration needs to be given to how, when, and where your sample will be conducted. Your survey form needs to capture the information required without directing the respondent. A good survey will have been randomised and include some similar questions worded so that you can validate previous answers. All surveys should be pilot tested and the results with subsequent modifications included for example in an appendix.