Impact of Sample Size and Its Estimation in Medical Research

In medical research, study samples are used to estimate and compare characteristics of target populations. However, because samples inevitably differ from their target populations, statistical inferences are subject to inherent uncertainty. Among various contributing factors, sample size plays a critical role in determining the reliability and precision of research findings. This study used data simulations to examine how sample size affects statistical outcomes and its relationships with key metrics of statistical inference.

Two normal distributions, representing the null and alternative hypotheses, were generated to illustrate the relationships between type I error, type II error, statistical power, and sample size. Statistical power and theoretical p-values were calculated using a two-sample t-test for equal sample sizes ranging from 10 to 300 per group and Cohen's standardized effect sizes (d) of 0.2, 0.5, and 0.8 to demonstrate the interactions between these factors. Additionally, five representative scenarios were constructed to compare p-values and 95% confidence intervals in relation to statistical significance, clinical importance, and precision of effect estimates.

Required sample size is determined by expected effect size, variability, significance level, and desired statistical power. As sample size increases, statistical power increases and p-values decrease when a true effect is present; both metrics gradually level off as they approach their theoretical limits. In contrast, effect estimates remain relatively stable, while their 95% confidence intervals become narrower, reflecting improved precision. Compared with p-values, confidence intervals provide more comprehensive information, including direction, magnitude, precision, statistical significance, and clinical importance of effect estimates. Therefore, reporting effect estimates and 95% confidence intervals alongside p-values is essential for transparent and meaningful interpretation of research findings.

Sample size estimation is a critical component of rigorous study design. It ensures adequate statistical power, improves precision, and facilitates meaningful interpretation of research findings.