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Abstract:
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To examine replication variation in p-value and confidence interval endpoints, we propose reporting the upper 95% confidence limit on the true p-value (?-value) and the lower 95% confidence limit on the true lower 95% confidence limit (c-value). When p=0.05, the 95% confidence interval for the true p-value is (0,0.38), demonstrating that p=0.05 provides high confidence of ducking only a much higher threshold (?=0.38). Achieving ?=0.05 requires p=0.001, a lower p-value than achieved by most studies. The ?-value depends only on the p-value. In contrast, for fixed p-value, the c-value is lower for larger odds-ratios (OR). For example, when p=0.05, and thus the lower limit of the 95%CI is 1 regardless of OR, for OR=1.5 (95%CI=1-2.25), the 95% lower confidence limit on the lower limit is c=0.76, while for OR=5 (95%CI=1-25), the c equals a much lower 0.34. The c-value is equivalent to the lower limit of the 99.95% confidence interval and thus achieving c=1 occurs when p=0.001 ?-value and c-value could help ensure properly cautious interpretation of barely significant findings.
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