How do you determine the sample size for your hypothesis test?

1 Define Goals

Before you dive into calculations, clearly define your hypothesis test goals. This includes understanding what you're trying to prove or disprove and identifying the key metrics that will inform your decision-making process. Your goals will influence the level of precision you need and, consequently, your sample size . For instance, if you're testing a new product feature's impact on user engagement, your goal might be to detect a certain percentage increase in usage. The more specific your goals, the easier it will be to determine the sample size that will provide meaningful results.

2 Significance Level

The significance level , often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true. In simpler terms, it's your tolerance for making a false positive error. A common choice for α is 5%, but this can be adjusted based on how critical the decision is. For high-stakes decisions, you might opt for a lower α to minimize the risk of error. The significance level directly affects the sample size—the lower the α, the larger the sample size required to achieve the same level of confidence in your results.

3 Effect Size

Effect size is a measure of how strong a relationship you expect to find between variables or how big a difference you expect between groups. Determining this requires subject matter expertise and a clear understanding of what constitutes a meaningful difference in your specific context. If you expect a small effect size , you'll need a larger sample to detect it. Conversely, if you expect a large effect, you might get away with a smaller sample. It's a balancing act between expectations and practical limitations like time and cost.

4 Power Analysis

Power analysis is a statistical method used to determine the minimum sample size required to detect an effect of a given size with a certain degree of confidence. Essentially, it tells you how likely your test is to detect an actual effect when there is one (statistical power). Typically, you aim for a power of 80% or higher, meaning there's an 80% chance of finding a true effect. Conducting a power analysis involves inputting your significance level, effect size, and desired power to calculate the appropriate sample size.

5 Practical Considerations

Beyond statistical requirements, practical considerations must also be taken into account when determining sample size. These include constraints such as budget, time, and operational resources. For example, if you're conducting a survey, you must consider the cost of reaching out to respondents and the response rate. Sometimes, despite what statistics suggest, you may be limited by what's feasible in practice. It's important to strike a balance between statistical rigor and real-world constraints.

6 Validate Assumptions

Lastly, it's important to validate the assumptions that underpin your sample size calculations. These include the distribution of your data, variance within your data, and the homogeneity of your population. If your assumptions are incorrect, your sample size may be inadequate or unnecessarily large. It's wise to review your assumptions with stakeholders or colleagues who can provide additional insights or catch potential oversights. Validating assumptions helps ensure that your hypothesis test is set up for success.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?