Optimising the trade-off between type I and II error rates in the Bayesian context

Area of Science:

• Decision Sciences
• Statistical Inference
• Bayesian Statistics

Background:

• Traditional hypothesis testing uses arbitrary Type I and Type II error rates (e.g., 5% and 10-20%).
• These standard rates often neglect the specific costs of errors and prior beliefs about the study outcome.
• Frequentist approaches have been challenged for not optimizing these error rates.

Purpose of the Study:

• To explore the optimization of Type I and Type II error trade-offs in studies with planned Bayesian statistical analysis.
• To provide a framework for stakeholders to determine appropriate error rates.
• To offer algebraic solutions for normally distributed data.

Main Methods:

• Utilized a Bayesian statistical framework for analysis.
• Investigated the trade-off between Type I and Type II error rates under resource constraints.
• Derived algebraic results for normally distributed data.

Main Results:

• Demonstrated a method to optimize the balance between Type I and Type II errors.
• Provided a scientific foundation for setting context-specific error rates.
• Derived specific results applicable to normally distributed data.

Conclusions:

• Bayesian analysis allows for optimizing the trade-off between Type I and Type II errors.
• This approach offers a more scientifically rigorous basis for error rate selection than traditional methods.
• The findings support informed discussions among stakeholders regarding appropriate error rates in research studies.