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Sample Size Determination

Sample size determination refers to the process of selecting the number of units to be counted or measured in a statistical analysis. In a basic sense, when trying to determine the required sample size a researcher is asking “How many units need to be sampled in order to obtain accurate results?” Furthermore, there is a formula which can be used to estimate the required sample size needed to represent a particular target population1.


Sample Size = (Z-score)2 – σ*(1 – σ) / (margin of error)2

In this formula,
σ = standard deviation

By analyzing the above formula, it is evident that there are some variables about the target population which need to be determined in order to calculate for the required sample size. In some cases, the confidence interval that a researcher wants to work within may call for a sample size which is too large. Thus, if a researcher is willing to allow for a greater margin of error, the necessary sample size will be smaller. Larger sample sizes will always allow for more accurate results to be obtained.

In any statistical analysis, working with the most appropriate sample size is critical for obtaining results which will be representative of the target population. In order to do so, understanding population measures such as the z-score, margin of error and standard deviation, is needed as they are all a part of the formula for sample size determination. Essentially, the quality of the final results depends upon the accuracy of the sample size used.




1. Qualtrics. (April 8, 2013). Determining Sample Size: How to Ensure You Get the Correct Sample Size. Retrieved from:

Image Credit: Flickr. (October 2008). World Population Growth. Retrieved from:



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