Comparisons of means using exploratory and confirmatory approaches

Area of Science:

• Statistics
• Psychology
• Data Analysis

Background:

• Comparing means is fundamental in statistical analysis.
• Traditional methods often rely on hypothesis testing.
• Exploratory and confirmatory approaches offer different frameworks for analysis.

Purpose of the Study:

• To compare the efficacy of exploratory versus confirmatory approaches for comparing means.
• To evaluate three specific methods: hypothesis testing, information criteria-based model selection, and Bayesian model selection.
• To provide guidance on selecting appropriate methods based on research context.

Main Methods:

• Utilized both exploratory and confirmatory frameworks.
• Applied hypothesis testing, information criteria, and Bayesian model selection.
• Employed illustrative examples to demonstrate and evaluate methods.

Main Results:

• Confirmatory hypothesis testing demonstrated higher power in rejecting false null hypotheses.
• Confirmatory model selection showed a greater probability of identifying the correct hypothesis.
• Model selection proved superior to hypothesis testing when evaluating multiple hypotheses.

Conclusions:

• Confirmatory model selection is recommended when researchers can formulate clear hypotheses.
• Exploratory model selection is advised when hypotheses are not well-defined.
• The choice between approaches depends on the pre-specification of research expectations.