How To Calculate Sample Size?

The sample size references the total number of respondents included in a study, and the number is often broken down into sub-groups by demographics such as age, gender, and location so that the total sample achieves represents the entire population. Determining the appropriate sample size is one of the most important factors in statistical analysis.

In this article we will discuss about what is sample size and how to calculate sample size?

What is a Sample Size?

Sample size is a frequently-used term in statistics and market research, and one that inevitably comes up whenever you’re surveying a large population of respondents. It relates to the way research is conducted on large populations.

A sample size is a part of the population chosen for a survey or experiment. For example, you might take a survey of dog owner’s brand preferences. You won’t want to survey all the millions of dog owners in the country (either because it’s too expensive or time consuming), so you take a sample size. That may be several thousand owners. The sample size is a representation of all dog owner’s brand preferences. If you choose your sample wisely, it will be a good representation.

When you survey a large population of respondents, you’re interested in the entire group, but it’s not realistically possible to get answers or results from absolutely everyone. So you take a random sample of individuals which represents the population as a whole.

The size of the sample is very important for getting accurate, statistically significant results and running your study successfully.

  • If your sample is too small, you may include a disproportionate number of individuals which are outliers and anomalies. These skew the results and you don’t get a fair picture of the whole population.
  • If the sample is too big, the whole study becomes complex, expensive and time-consuming to run, and although the results are more accurate, the benefits don’t outweigh the costs.

Sample size formula with example

The sample size formula is determined in two steps. First, we calculate the sample size for the infinite population and second we adjust the sample size to the required population. The sample size formula can be given as:

  • S = Sample size for infinite population
  • Z = Z score
  • P = Population proportion (Assumed as 50% or 0.5)
  • Q= (1-Population proportion(P))
  • M = Margin of error

Note: Z score is determined based on the confidence level.

How to determine sample size?

As we have defined all the necessary terms, let us briefly learn how to determine the sample size using a sample calculation formula known as Andrew Fisher’s Formula.

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

1. Determine the population size (if known).

How many people are you talking about in total? To find this out, you need to be clear about who does and doesn’t fit into your group. Don’t worry if you’re unable to calculate the exact number. It’s common to have an unknown number or an estimated range.

2. Determine the confidence interval.

If you’ve ever seen a political poll on the news, you’ve seen a confidence interval and how it’s expressed. It will look something like this: “68% of voters said yes to Proposition Z, with a +/- 5% margin of error.” The question is how much error you allow. The margin of error, also known as the confidence interval, is expressed in terms of mean values. You can control how much difference you allow between the mean of your sample and the mean of your population.

3. Determine the confidence level.

This is a separate step from the confidence interval of the same name in Step 2. It’s about how confident you want to be that the actual mean is within your margin of error. The most common confidence intervals are 90% sure, 95% sure, and 99% sure.

4. Determine the standard deviation (a standard deviation of 0.5 is a safe choice where the figure is unknown)

Since you haven’t conducted your survey yet, a standard deviation of 0.5 is a safe choice to ensure your sample size is large enough.

A low standard deviation means that all values cluster around the mean number, while a high standard deviation means that they are spread out over a much larger range with very small and very large outliers.

5. Convert the confidence level into a Z-Score. This table shows the z-scores for the most common confidence levels:

Confidence levelz-score
80%1.28
85%1.44
90%1.65
95%1.96
99%2.58

 6. Put these figures into the sample size formula to get your sample size.

Plug in your Z-score, standard of deviation, and confidence interval into the sample size calculator or use this sample size formula to work it out yourself:

Here is an example calculation:

Say you choose to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, you just need to substitute the values in the formula:

= ((1.96)2 x .5(.5)) / (.05)2

= (3.8416 x .25) / .0025

= 0.9604 / .0025

= 384.16

Your sample size should be 385.