Obtaining a sample size that is significantly higher than the target or feasible range as a result of power analysis is a frequently encountered methodological challenge in academic studies. The statistical power of a study is fundamentally determined by the interplay of four main variables: the Type I error rate (alpha), statistical power (1-beta), effect size (What is the Concept of Effect Size?), and sample size. Due to the mathematical relationship between these variables, optimizing other parameters is necessary to reduce the sample size on a rational and scientific basis.
The most effective way to reduce sample size is to re-evaluate the expected effect size. The distinction between statistical significance and clinical or scientific importance is critical here. If the target effect size in the study (e.g., Cohen’s d or Pearson r) is set too small, the number of subjects required to detect this small difference will increase logarithmically. By examining meta-analysis results of similar studies in the literature or pilot study data and defining a higher effect size based on the “minimum clinically important difference” (MCID) criterion, the sample requirement will be directly reduced. However, this increase must be based on scientific evidence rather than speculation.
A second strategy is to increase precision in the study’s statistical design and variable management. Improving the reliability of measurement tools and reducing the standard deviation helps to achieve the same power with fewer subjects by reducing noise in the data. For instance, opting for repeated measures designs where subjects act as their own controls instead of independent samples designs minimizes variance, leading to significant savings in sample size. Similarly, controlling for confounding variables using methods like analysis of covariance (ANCOVA) reduces the error term, thereby lowering the required sample size.
While relaxing statistical parameters (alpha and beta) is an option, it should be managed carefully as it increases the error margin of the study. The standard accepted power values of 80% or 90% should be maintained within a reasonable limit (e.g., not falling below 80%) depending on the nature of the study. Increasing the Type I error rate (alpha) above 0.05 is generally not recommended in terms of academic ethics and acceptability; however, the use of one-tailed hypotheses, if supported by the theoretical framework, can reduce the required number of subjects.
Finally, changes in data collection methodology can increase sample efficiency. Balancing the allocation ratio between groups maximizes statistical power. If there is a deviation from the 1:1 ratio between groups, the total number of subjects must be increased to achieve the same power. Therefore, keeping the allocation ratio as close to equal as possible will help maintain the sample size at the lowest possible level. While making these adjustments, it is essential for the academic integrity of the final report that the scientific validity of the study and the risk of Type II error are not compromised for the sake of reducing the sample size.
Technical Interventions at the Calculation Stage
Optimizing sample size during the power analysis calculation stage is possible not only by changing statistical parameters but also by improving the technical construction of the data analytic model. The mathematical depth of statistical modeling provides the researcher with various technical maneuvers to bring the sample requirement to a rational level.
One of the most fundamental ways to reduce sample size technically is to optimize the scale type and measurement precision of the dependent variable. Categorical or dichotomous variables require much larger samples than continuous variables. For example, instead of categorizing a patient as “recovered/not recovered,” measuring the level of recovery with a numerical scale increases the ability of the statistical test to explain variance. The use of continuous variables prevents information loss in the data, allowing for higher test power to be achieved with a smaller group.
Including covariates in the analysis model—that is, constructing ANCOVA or multiple regression models—is another key technical strategy. Adding control variables that can explain a portion of the total variance in the dependent variable and are not the main focus reduces the “error variance” term. The shrinking of the error term makes the main effect under investigation statistically more prominent, thereby mathematically lowering the number of subjects needed to reach the targeted power.
In multi-center or stratified studies, considering the clustering effect is a critical technical detail. If data are collected within specific groups (e.g., different hospitals or classrooms), the dependency between subjects increases the sample size due to the “design effect.” In this case, correctly estimating the intraclass correlation using random effects modeling or mixed-effects models at the analysis stage prevents unnecessary sample inflation.
Transitioning from a “frequentist” approach to a “Bayesian” approach in the calculation method can also provide a technical alternative. Bayesian power analysis uses existing knowledge by incorporating prior distributions from the existing literature into the analysis, rather than constructing a dataset from scratch. This method, especially in studies involving rare cases or high-cost research, provides a foundation for making meaningful inferences with smaller sample sizes thanks to the information power provided by prior data. By calculating the statistical details and the effect size of a study, the relevant study is cited, and the power analysis is conducted in light of these data. This stage is one that requires expertise in statistical interpretation and power analysis.
Finally, the management of multiple comparison corrections (Bonferroni, Tukey, etc.) used during analysis requires technical optimization. As the number of hypotheses increases, these corrections made to control the risk of Type I error dramatically reduce the power of the test and increase the sample requirement. Therefore, avoiding unnecessary subgroup analyses and focusing only on the primary endpoint is one of the most technical approaches to ensure the calculated sample size remains within operational limits.
Focus on the Main Hypothesis, Don’t Get Bogged Down in Side Hypotheses
Focusing on secondary or side hypotheses instead of the primary endpoint when conducting power analysis is one of the biggest technical problems of power analysis. Statistical power brings a separate mathematical burden for each independent variable tested and each additional hypothesis. Especially in multivariate analysis models like logistic regression, each predictor included in the model increases the sample size in a non-linear fashion to keep the error margin under control. The “events per variable (EPV)” rule, widely accepted in the literature as “at least 10-20 events for each variable,” explains why the total sample requirement reaches enormous proportions as the model becomes more complex.
Since the assumptions of some of my analyses and their applicability to your data structure will only become clear after the dataset is collected, one must avoid the misconception that all analyses will be conducted definitively in ethics committee applications. The feasibility of some analyses depends on the distribution and structure of the data and may not be suitable for every dataset. As a general rule, it is the most appropriate method to conduct power analysis only with the main hypothesis in ethics committee applications.
Pursuing side hypotheses in multivariate models not only increases the number of subjects but can also weaken the stability and predictive power of the model. When power is calculated for a large number of interaction terms or secondary outcomes instead of focusing on the main hypothesis, the “multiple comparisons problem” arises. When this is combined with corrections like Bonferroni, which are made to maintain the alpha error margin, it necessitates collecting thousands of additional subjects to maintain the statistical power of the study. This represents an operationally and financially unsustainable research design.
For a researcher who wants to keep the sample size at a rational level, the most scientific approach is to build the entire design and power calculation of the study solely on the primary hypothesis. Side hypotheses and sub-breakdowns within logistic regression models should be defined as “exploratory” analyses rather than the “powered” primary objectives of the study. When this distinction is made, the sample size remains at the optimized limit required to capture the main effect, while secondary findings can be presented in the discussion section with academic integrity. Thus, both academic validity is preserved and unnecessary sample inflation is avoided.
