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<p>This technical note investigates a <i>p</i>-value paradox that emerges in the conventional proportion test. The paradox is defined as the phenomenon where “decisions made on the same effect size from data of different sample sizes may be inconsistent.” It is illustrated with two examples from clinical trial research. We argue that this <i>p</i>-value paradox stems from the use (or misuse) of <i>p</i>-values to compare two proportions and make decisions. We propose replacing the conventional proportion test and its <i>p</i>-value with estimation statistics that include both the observed effect size and a reliability measure known as the signal content index (SCI).</p>

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A p-Value Paradox in Proportion Tests and its Resolution

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Hening Huang

摘要

This technical note investigates a p-value paradox that emerges in the conventional proportion test. The paradox is defined as the phenomenon where “decisions made on the same effect size from data of different sample sizes may be inconsistent.” It is illustrated with two examples from clinical trial research. We argue that this p-value paradox stems from the use (or misuse) of p-values to compare two proportions and make decisions. We propose replacing the conventional proportion test and its p-value with estimation statistics that include both the observed effect size and a reliability measure known as the signal content index (SCI).