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The behavior of the P-value when the alternative hypothesis is true
H M Hung1, R T O'Neill, P Bauer
1Division of Biometrics I, Food and Drug Administration, Rockville, Maryland 20852, USA.
Biometrics
|March 1, 1997
Summary
The P-value, a random variable, follows a uniform distribution under the null hypothesis. Its distribution under the alternative hypothesis depends on sample size and true parameter values, offering insights for clinical trial design.
Area of Science:
- Statistics
- Biostatistics
- Clinical Trial Design
Background:
- The P-value is a fundamental concept in statistical hypothesis testing.
- Its distribution under the null hypothesis is well-understood (uniform on [0, 1]).
- The behavior of the P-value under alternative hypotheses is less commonly explored but crucial for practical applications.
Purpose of the Study:
- To characterize the distribution of the P-value under the alternative hypothesis.
- To explore how this distribution is influenced by sample size and parameter values.
- To consider the implications of P-value distribution for clinical trial design, analysis, and interpretation.
Main Methods:
- Theoretical analysis of the P-value distribution.
- Examination of the P-value's behavior as a random variable.
- Consideration of statistical properties like mean and percentiles.
Main Results:
- The P-value's distribution under the alternative hypothesis is complex, depending on sample size and true parameter values.
- This contrasts with its uniform distribution under the null hypothesis, which is independent of sample size.
- Key characteristics of this distribution offer insights into P-value behavior.
Conclusions:
- Understanding the P-value distribution under the alternative hypothesis is vital for robust statistical inference.
- This knowledge can inform optimal clinical trial design and data interpretation.
- The study highlights the potential of P-value distribution analysis in biostatistics.
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