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 \ (pₑ₈₆₇ₓ 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.
Ilija Barukčić (Mon,) studied this question.