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[Sample size determination given data of preliminary experiment for student's t-test, ANOVA and Tukey's multiple
1Department of Cognitive and Behavioral Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902.
Shinrigaku Kenkyu : the Japanese Journal of Psychology
|March 5, 2005
Summary
This study introduces a method to calculate the probability of rejecting a null hypothesis using preliminary data. This allows researchers to determine optimal sample sizes for robust experimental design.
Area of Science:
- Statistics
- Experimental Design
Context:
- Preliminary experiments provide initial data that can inform future study design.
- Traditional methods for determining sample size may not fully leverage preliminary experimental data.
Purpose:
- To develop a procedure for calculating the probability of rejecting a null hypothesis based on preliminary experimental data.
- To determine appropriate sample sizes by linking this probability to desired statistical power.
Summary:
- The proposed method involves generating parameters from the posterior distribution, then test statistics from a conditional distribution, and finally counting exceedances over a critical value.
- This simulation-based approach estimates the probability of null hypothesis rejection.
- The procedure is demonstrated using Student's t-test and compared against conventional sample size determination techniques.
Impact:
- Enables researchers to make more informed decisions about sample size, potentially leading to more efficient and powerful studies.
- Provides a statistically rigorous framework for sample size determination informed by early experimental results.
- Facilitates better resource allocation in research by optimizing the number of subjects or observations needed.