Before collecting a single data point, every study has to answer one question: how many participants or observations do we need? Getting that number right is one of the most important design decisions you will make.

What is sample size?

Sample size is the number of participants or observations a study needs to meet its objectives. It usually serves one of two purposes:

  • estimating a population parameter, such as a mean or a proportion, with a chosen level of confidence;
  • detecting a difference between groups, if one really exists.

Both directions of error cost something. Too many subjects raise costs and waste resources. Too few give imprecise results, can miss real differences and may lead to wrong conclusions.

How is it calculated?

The calculation depends on a handful of decisions:

  • the type of study: descriptive, comparative, correlational and so on;
  • the main objective, such as estimating a proportion or a mean, or comparing groups;
  • the significance level, usually 5%;
  • the statistical power, generally 80% or 90%;
  • the effect size you expect to detect;
  • the variability of the variable you are measuring.

Each type of study has its own formulas. Software can run the arithmetic for you, but judgment is still needed to choose the inputs, interpret the result and adapt it to your situation.

Is the number enough? Representativeness

A correct number is not enough if the sample does not represent the population you care about. To get there:

  • choose a suitable sampling method, such as random, stratified or cluster sampling;
  • avoid selection bias;
  • allow for losses and non-response by increasing the planned sample.

A well-designed sample is what makes results reliable and generalizable.

Margin of error and confidence level

Two ideas are tied directly to the sample size.

The margin of error is how far your result may be from the true population value. The smaller the margin you want, the larger the sample you need.

The confidence level describes how sure you want to be that your interval captures the true value, usually 95%. A higher confidence level also calls for a larger sample.

Together they define how precise and how reliable your results will be.

In short

An adequate sample size is an essential step of study design. It helps make results valid, accurate and applicable to the population you are studying. A careful calculation uses resources efficiently, lowers risk and improves reliability, which is why it belongs in the planning stage of any rigorous study.