What is a Sample Size?
A sample size is a part of the population chosen for a survey or experiment. It’s called a sample because it only represents part of the group of people (or population) whose opinions or behaviour that are of interest.
How big or small of a sample size do you require? 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 costly.
Consequential research requires an understanding of the statistics that drive sample size decisions. Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need:
- Population Size — How many total people fit your demographic? For instance, if you want to know about fathers living in Malaysia, your population size would be the total number of fathers living in Malaysia. It is no cause for alarm if you are unsure of this number. It is common for the population to be unknown or approximated.
- Margin of Error (Confidence Interval) — No sample will be perfect, so you need to decide how much error is acceptable. 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. It will look something like this: “87% of voters said yes to Candidate A, with a margin of error of +/- 4%.”
- 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.
- 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.
- Rate of Response — Before you start sending out your survey to 500 respondents, remember there is such a thing as response rate. Response rate is the ratio of respondents that fill in the questionnaire they received compared to the total number of surveys you send out. For instance, if you send out your survey to 500 people and you receive 250 filled in surveys, your response rate is 50%.
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:
- 90% – Z Score = 1.645
- 95% – Z Score = 1.96
- 99% – Z Score = 2.576
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
That’s it! 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.
*Z-Table Score obtained from 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 or read this article.