Bayesian t tests for accepting and rejecting the null hypothesis
Related Experiment Video
Updated: Jun 24, 2026

Defining the Role Of Language in Infants' Object Categorization with Eye-tracking Paradigms
Published on: February 8, 2019
Jeffrey N Rouder1, Paul L Speckman, Dongchu Sun
1University of Missouri, Columbia, MO 65211, USA. rouderj@missouri.edu
Abstract:
Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.
Related Concept Videos
Types of Hypothesis Testing
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.
Hypothesis: Accept or Fail to Reject?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null hypothesis and 'fail to...
Null and Alternative Hypotheses
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As a result if you cannot accept the null, it requires some action.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the population that is...
Comparing Experimental Results: Student's t-Test
Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with data...
Decision Making: Traditional Method
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...

