How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions. A larger sample group can yield more accurate study results — but excessive responses can be pricey.

Learn How to Determine Sample Size

Consequential research requires an understanding of the statistics that drive the range of sample size decisions you need to make. A simple equation will help you put the migraine pills away and sample confidently knowing that there is a high probability that your survey is statistically accurate with the correct sample size.

## Sample size variables based on target population

Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need:

1. Population Size — How many total people fit your demographic? For instance, if you want to know about mothers living in the US, your population size would be the total number of mothers living in the US. Not all populations sizes need to be this large. Even if your population size is small, just know who fits into your demographics. Don’t worry if you are unsure about this exact number. It is common for the population to be unknown or approximated between two educated guesses.
2. Margin of Error (Confidence Interval) — No sample will be perfect, so you must decide how much error to allow. The confidence interval determines how much higher or lower than the population mean you are willing to let your sample mean fall. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval. For example, it will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”
3. Confidence Level — How confident do you want to be that the actual mean falls within your confidence interval? The most common confidence intervals are 90% confident, 95% confident, and 99% confident.
4. Standard of Deviation — How much variance do you expect in your responses? Since we haven’t actually administered our survey yet, the safe decision is to use .5 – this is the most forgiving number and ensures that your sample will be large enough.

## Calculating sample size

Okay, now that we have these values defined, we can calculate our needed sample size. This can be done using an online sample size calculator or with paper and pencil.

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:

• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576

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 the sample size calculator or into this equation:**

Necessary Sample Size = (Z-score)2 * StdDev*(1-StdDev) / (margin of error)2

Here is an example of 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
384.16
385 respondents are needed

## Voila!

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.

*Credit to SJSU

**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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