How Do You Determine the Appropriate Sample Size for a Study?


    How Do You Determine the Appropriate Sample Size for a Study?

    When it comes to determining the right sample size for a study, insight from seasoned statisticians proves invaluable. Alongside perspectives from experts, including a President of a research consulting firm, we've gathered additional methods that touch on a range of factors. From consulting established guidelines to anticipating effect size variability, discover multifaceted approaches to sample size determination.

    • Draw Insights From Observational Studies
    • Use Historical Data for A/B Testing
    • Apply Sampling Theory and Power Calculations
    • Follow Established Sample Size Guidelines
    • Account for Project Resource Limitations
    • Anticipate Effect Size Variability

    Draw Insights From Observational Studies

    I draw insights from protected electronic health records. In these observational studies, sample size is determined by eligibility criteria defined by medical researchers. For example, you may want to study adults older than 65 who have an illness. You must draw these subjects from your already finite database. Alas, you may not have big data, as in textbooks. This is where you must learn what methods are appropriate and emphasize what interpretations are possible.

    Edie EspejoSr. Statistician

    Use Historical Data for A/B Testing

    To determine the appropriate sample size for our A/B test focused on improving conversion rates, we first identified the conversion rate as our primary metric and estimated the minimum effect size we considered significant for our business, guided by historical data. We then set our alpha at 0.05 and our power at 0.80, reflecting a 5% chance of a false positive and an 80% chance of detecting a true effect, respectively. Using these parameters, we utilized a sample size calculator, inputting our baseline conversion rate and the desired effect size to compute the necessary sample size. This methodical approach highlighted the importance of statistical parameters in ensuring the reliability and validity of our findings. Moreover, it demonstrated the vital role of historical data in grounding our expectations and refining our sample size estimates.

    Yahui ZhaoData Scientist

    Apply Sampling Theory and Power Calculations

    We use two approaches for determining sample size for a study. If we are looking to sample from a population and make generalizable results back to that population, we use sampling theory calculations (my online favorite: to determine the recommended sample size needed for a particular population size based on the confidence level we need (i.e., 90%, 95%), the margin of error we can accept (i.e., 4%, 5%), and the response distribution (i.e., 50%, 45%). When you survey a sample of the population, you don't know that you've found the correct answer, but you do know that there is a 95% (confidence level you chose) chance that you're within 4% (the margin of error you chose) of the correct answer.

    The second approach for determining sample size is power calculations (G*Power is a great free tool). A power analysis helps us avoid Type I and Type II errors. It is the calculation used to estimate the smallest sample size needed for an experiment, given a required significance level, statistical power, the analysis or statistical test used, and effect size. It helps to determine if a result from an experiment or survey is due to chance, or if it is a correct result and significant. This is important because testing, experiments, and surveys are expensive to conduct, and we do not want to run an experiment and realize afterward that the sample size was too small to determine if the outcome was genuine or not.

    Rene Paulson, PhD
    Rene Paulson, PhDPresident, Elite Research, LLC

    Follow Established Sample Size Guidelines

    To establish a sample size, follow standard guidelines set forth by governmental bodies or industry organizations. These guidelines have been developed based on extensive research and general consensus within the field. They often provide ranges for sample sizes suitable for different types of studies, taking into account common research scenarios.

    Adhering to these recommendations can lend credibility to a study and ensure its acceptance in professional circles. Explore the relevant guidelines for your area of research to ensure your study's sample size meets established standards.

    Account for Project Resource Limitations

    The reality of resources available for a project can significantly affect the determination of sample size. Statisticians must consider how much time, workforce, and money they have at their disposal. These practical limitations ensure that the study can be completed within its means without compromising its integrity excessively.

    A careful balance has to be struck between ideal statistical conditions and what is feasible, which often requires compromises and ingenuity from the research team. When planning your study, take a hard look at your resources and plan your sample size accordingly.

    Anticipate Effect Size Variability

    In planning a study, one needs to consider the variability of the effect size they expect to find in their research. If the effect size is predicted to be large, then a smaller sample size may suffice for detecting this effect. However, if minor differences are being investigated, then a larger sample may be necessary to observe such subtle changes.

    Understanding and anticipating the variability and magnitude of the phenomenon under study is crucial for determining an adequate sample. Before conducting a study, carefully consider your expectations regarding the effect size to decide on a suitable sample size.