How to Calculate Sample Size for Your Survey
If you are searching for a sample size calculator you know the goal of a survey is to acquire conclusions from a representative sample of a target population. But one problem of designing a survey is figuring out just how many participants to include to have a sample that can truly represent the population. Statistics solves this problem, giving survey designers a clear-cut way of calculating the number of participants needed in a survey for the survey to be “valid” in science’s eyes. This method of calculating sample size for your survey is easy enough for even the first-time survey-creator to implement.
Choose the alpha level and corresponding confidence level
The alpha level is the probability of rejecting the null hypothesis of the survey (usually that there is no difference between the groups you wish to investigate) assuming that the null hypothesis is actually true.
In most sciences, 0.05 is the standard alpha level. However, alpha levels 0.01 and 0.1 are not uncommon. If you do not know which alpha level to choose, set alpha = 0.05. The confidence level will be 100 minus the alpha value. If the alpha is 0.05 the confidence level is 0.95 or 95%.
Choose the margin of error
The margin of error represents how precise your results will be. Technically, the margin of error represents the difference of proportion from the true proportion that is acceptable to the researcher. If you want the difference of the absolute value of the range, run a confidence interval test.
The margin of error is the range of a confidence interval. In the social sciences, 0.05 is an acceptable margin of error. You can change the margin of error depending on your precision needs. If you have no preference, choose e = 0.05 as the default.
Estimate the standard deviation
If you have previous studies researching what you are currently researching than you can use the standard-deviation reported in that study. However, it is often the case that there is no prior research for your topic of interest. In this case, for the sake of being conservative, set the standard deviation, p = 0.5.
Please note if you are going to use a distribution value other than 0.5 you have the replace p2 with p(1-p) in the initial sample size calculator equation below.
Find the z-score for the confidence level
You can find this value by using a t-table, which is available in most introductory statistics books. The bottom two rows include the most frequently used confidence levels, along with their z-scores.
Use the alpha value or the confidence level to look up the corresponding value while assuming the degrees of freedom value in the table is large (this way your estimate will still be conservative).
For example, you will find that for an alpha level of 0.05, the corresponding z-score in the table assuming a large degrees of freedom value is 1.96. So, z = 1.96.
- Sample population = 1,000
- Margin of error = ± 5%
- 95% confidence interval = (𝜇 + 2𝜎)
- 𝜇 – Population parameter mean
- 𝜎 – Standard deviation
Calculate the initial sample size estimate
Simply calculate N = ( z 2 × p 2 ) / e 2
Calculate the final sample size estimate
Divide N by 1 + (N / population), where “population” is the size of the population