In many cases during the course of your market research, you may be unable to reach the entire population you want to gather data about. While larger sample sizes bring you closer to a 1:1 representation of your target population, working with them can be time-consuming, expensive, and inconvenient. On the other hand, small samples risk yielding results that aren’t representative of the target population.
Luckily, you can easily identify an ideal subset that represents the population and produces strong, statistically significant results that don’t gobble up all of your resources. In this article, we'll teach how to calculate sample size with a margin of error in order to identify that subset.
Simply, the steps to find your sample size are as follow:
Define population size or number of people
Designate your margin of error
Determine your confidence level
Predict expected variance
Finalize your sample size
Follow these five steps to ensure you get the right selection size for your research needs.
Your sample size needs will differ depending on the population size or number of people you’re looking to draw conclusions on. That’s why determining the minimum number of individuals required to represent your selection is an important first step.
Defining the size of your population can be easier said than done. While there is a lot of population data available, you may be targeting a population that is difficult to measure or for which no reliable data currently exists.
Knowing the size of your population is more important when dealing with relatively small, easy-to-measure groups of people. If you’re dealing with a larger population, take your best estimate, and roll with it.
This is the first step in a sample size formula, which will yield more accurate results than a simple estimate – and accurately reflect the population.
Designate your margin of error
Random sample errors are inevitable whenever you’re using a subset of your total population. Be confident that your results are accurate by designating how much error you intend to permit: that’s your margin of error.
Sometimes called a confidence interval, a margin of error indicates how much you’re willing for your sample mean to differ from your population mean. It’s often expressed alongside statistics as a plus-minus (±) figure, indicating a range which you can be relatively certain about.
For example, say you take a sample of your colleagues with a designated 3% margin of error and find that 65% of your office uses some form of voice recognition technology at home. You can be sure that, if you were to ask your entire office, in reality as low as 62% and as high as 68% might use some form of voice recognition technology at home.
Determine how confident you can be
Your confidence level tells you how certain you can be that the total population would pick an answer within the range you designated in the second step. The most common confidence levels are 90%, 95%, and 99%. Researchers most often employ a 95% confidence level.
Don’t confuse confidence levels for confidence intervals (i.e. mean of error). Remember the distinction by thinking about how the concepts relate to each other to sample more confidentally.
In our example from the previous step, when you put confidence levels and intervals together, you can say you’re 95% certain that the true percentage of your colleagues who use voice recognition technology at home is within ± 3 percentage points from the sample mean of 65%, or between 62% and 68%.
Your confidence level corresponds to something called a z-score. A z-score is a value that indicates the placement of your raw score (meaning the percent of your confidence level) in any number of standard deviations below or above the population mean.
Z-scores for the most common confidence intervals are:
90% = 2.576
95% = 1.96
99% = 2.576
If you’re using a different confidence interval, use this z-score table to find the right value for your calculation.
Decide the variance you expect
The last thing you’ll want to consider when calculating your sample size is the amount of variance you expect to see among participant responses.
Standard deviation measures how much individual sample data points deviate from the average population.
Don’t know how much variance to expect? Use the standard deviation of 0.5 to make sure your group is large enough.