How to quantify support for and against the null hypothesis: a flexible WinBUGS implementation of a default Bayesian...

Area of Science:

• Statistics
• Bayesian inference
• Hypothesis testing

Background:

• Traditional t tests primarily focus on rejecting the null hypothesis.
• Quantifying evidence in favor of the null hypothesis is statistically challenging.
• Existing Bayesian t tests, like the Jeffreys-Zellner-Siow (JZS) test, have limitations in applicability.

Purpose of the Study:

• To introduce a novel sampling-based Bayesian t test, the Savage-Dickey (SD) t test.
• To enable researchers to quantify statistical evidence supporting the null hypothesis.
• To extend the capabilities of Bayesian hypothesis testing to a wider range of problems.

Main Methods:

• Development of a sampling-based Bayesian t test.
• Adaptation of concepts from the Jeffreys-Zellner-Siow (JZS) t test.
• Implementation for testing order restrictions and unequal variance two-sample situations.

Main Results:

• The Savage-Dickey (SD) t test provides a method to quantify evidence for the null hypothesis.
• The SD test is applicable to a broader set of statistical scenarios than prior methods.
• The test successfully handles order restrictions and two-sample comparisons with heterogeneous variances.

Conclusions:

• The Savage-Dickey (SD) t test offers a valuable tool for Bayesian hypothesis testing.
• Researchers can now more effectively evaluate evidence for the null hypothesis.
• The SD test enhances statistical analysis capabilities in various research fields.