Empirical Proportion Test

Background: Statistical inference for binary outcomes often relies on parametric models, such as the Bernoulli or Binomial distributions, which assume identical and independent success probabilities. In many real-world applications, these assumptions are violated due to heterogeneous populations or time-varying mechanisms. Material and methods:We introduce the Empirical Proportion Test (EPT), a nonparametric procedure that evaluates the extremeness of an observed success proportion relative to a discrete uniform reference distribution defined on all attainable empirical proportions. Results:The test statistic is the observed proportion of successes, and p-values are computed exactly based on the rank of this proportion within its discrete support. A thresholded variant allows one-sided assessment relative to a meaningful benchmark. Applied to a clinical study of Leflunomide for preventing acute myocardial infarction (\(n=6138\), \(k=6132\) successes), the right-tailed p-value was \(p_{\text{right}} \approx 0.00114\), indicating strong evidence against a null of no structural preference. Conclusion:The EPT provides an exact, distribution-free, and transparent inference framework suitable for heterogeneous binary data without requiring parametric assumptions.