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Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing
Clemens Draxler1,2, Rainer W Alexandrowicz3,4
1The Health and Life Sciences University, EWZ 1, 6060 , Hall, Austria. clemens.draxler@umit.at.
Psychometrika
|July 10, 2015
Summary
This study determines sample sizes for hypothesis tests, including Wald, score, and likelihood ratio tests, within the exponential family and conditional maximum likelihood (CML) framework. It provides a formal method for sample size calculations, particularly for Rasch models.
Area of Science:
- Statistical Theory
- Probability Distributions
- Hypothesis Testing
Background:
- Discusses the exponential family of probability distributions.
- Introduces conditional maximum likelihood (CML) theory.
- Highlights the importance of sample size determination in statistical testing.
Purpose of the Study:
- To determine the sample size for three fundamental hypothesis tests: Wald, score, and likelihood ratio tests.
- To provide a formal framework for sample size calculations.
- To address the specific application of Rasch models.
Main Methods:
- Applies conditional maximum likelihood (CML) theory.
- Develops a theoretical background for sample size determination.
- Establishes a formal framework for calculations based on desired error probabilities and effect size.
Main Results:
- Provides a method for calculating sample sizes for hypothesis tests.
- Offers a framework applicable to the Rasch model class.
- Considers predetermined deviations from the model and error probabilities (Type I and Type II errors).
Conclusions:
- The study offers a robust theoretical and practical framework for sample size calculations in hypothesis testing.
- The methods are particularly relevant for researchers working with Rasch models.
- Accurate sample size determination is crucial for the validity of statistical inferences.
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