Written by Scott Smith, Ph.D. April 8, 2013
How many responses do you really need? This simple question is a never-ending quandary for researchers. A larger sample can yield more accurate results — but excessive responses can be pricey.
Consequential research requires an understanding of the statistics that drive sample size decisions. A simple equation will help you put the migraine pills away and sample confidently.
Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need:
Okay, now that we have these values defined, we can calculate our needed sample size.
Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:
If you choose a different confidence level, use this Z-score table to find your score.
Next, plug in your Z-score, Standard of Deviation, and confidence interval into this equation:*
Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²
Here is how the math works assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.
((1.96)² x .5(.5)) / (.05)²
(3.8416 x .25) / .0025
.9604 / .0025
385 respondents are needed
You’ve just determined your sample size.
If you find your sample size is too large to handle, try slightly decreasing your confidence level or increasing your margin of error – this will increase the chance for error in your sampling, but it can greatly decrease the number of responses you need.
*This equation is for an unknown population size or a very large population size. If your population is smaller and known, just use the calculator above or read page 3 of this document.
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