Sample size is the number of units or observations in an experiment, such as people, animals, plants, or products. Choosing the right sample size is crucial for obtaining valid and reliable results, as well as minimizing costs and time. In this article, you will learn how to calculate sample size for experiments using some basic statistical methods and concepts.
The first step to calculate sample size is to define your goal or research question. What are you trying to test or measure in your experiment? What is the main outcome or variable of interest? How do you plan to analyze and interpret the data? Your goal will help you determine the type of experiment, the design, and the hypothesis.
Establishing clarity in the experiment’s objectives sets the groundwork. Without a defined goal, you’re essentially aiming in the dark. It’s similar to setting off on a journey without knowing your destination - while the journey might be interesting, it’s unlikely you’ll arrive where you want.
The effect size is a measure of how large or significant the difference or relationship between two groups or variables is. For example, if you are testing a new drug versus a placebo, the effect size is the difference in the mean response between the two groups. The larger the effect size, the smaller the sample size needed to detect it. You can estimate the effect size based on previous studies, literature, or expert opinions.
Effect size isn’t just a statistical estimation but a gauge of the practical importance of results. It’s essential to realize that statistical significance doesn’t always equate to real-world relevance. An experiment could find a statistically significant result with a trivial effect size, making the practical application of findings limited.
The significance level, also known as alpha, is the probability of rejecting the null hypothesis when it is true. In other words, it is the risk of making a false positive error or finding an effect that does not exist. The common value for the significance level is 0.05, which means that there is a 5% chance of making a false positive error. The power, also known as beta, is the probability of rejecting the null hypothesis when it is false. In other words, it is the ability of the experiment to detect a true effect. The common value for the power is 0.8, which means that there is a 20% chance of making a false negative error or missing an effect that exists. The lower the significance level and the higher the power, the larger the sample size needed.
Confidence and reliability are both established based on the risk analysis. The higher the risk, the more conservative one has to be.
These parameters aren’t conventional numbers but guardrails against potential pitfalls in experimental research. A too high significance level might lead you to spot patterns where none exist, whereas setting power too low could make you overlook genuine effects. It is balancing between being overly skeptical and overly optimistic.
The variability and error are factors that affect the precision and accuracy of the measurement or outcome. The variability is the natural variation or diversity in the population or sample, such as age, gender, weight, or preferences. The error is the random or systematic deviation from the true value, such as measurement error, sampling error, or human error. The higher the variability and error, the larger the sample size needed to reduce them and increase the confidence in the results.
The final step to calculate sample size is to use a formula or a calculator that applies to your type of experiment and design. There are different formulas and calculators for different scenarios, such as comparing means, proportions, correlations, or rates. You can find them online or in textbooks or software. You will need to input the parameters that you have estimated or chosen in the previous steps, such as the effect size, the significance level, the power, and the variability or error. The formula or calculator will then output the sample size required for your experiment.