As providers of sample, we are often asked what sample size is needed for a study. The answer to this question is complicated – not only because the statistical formula to calculate sample size is complicated, but also because there are other factors that determine base size – primarily quotas and the level of risk of the study.
(Keep in mind that this is a rough guideline.)
For the true statistical method of calculating sample, you will need to know the following variables:
How big is the true population of the group you’re surveying? Generally in market research, we deal with rather large population sizes and use a constant for this input. When using statistical probability, the same sample size can be used to represent the opinions of 100,000 people or many million. That’s why you generally see political polls as small as 500 try to predict a presidential election in the United States, which has a population well over 300 million.
How certain do you want to be that the results are accurate? Typically, the following confidence levels are utilized, although you can really pick any number:
For the formula, the confidence level corresponds to a z-score. Here are the z-scores for the above confidence levels:
The z-score is the number of standard deviations a given proportion is away from the mean.
A percentage that tells you how much you can expect your survey results to reflect the views of the overall population. The smaller the margin of error, the closer you are to having the exact answer at a given confidence level. The margin of error is often mentioned when discussing presidential polling as the poll is +/- 3%.
Typical margins of error are:
Measures how much variance you expect in the data. We typically use .5 as a constant.
There are a couple of things to watch for when calculating sample size:
Does having a statistically significant sample size matter? Generally, the rule of thumb is that the larger the sample size, the more statistically significant it is—meaning there’s less of a chance that your results happened by coincidence.
Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²
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