Bayesian Methodology for Assessing Invariance in Behavioral Data

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This project will focus on developing Bayes factors, a methodology that is an alternative to traditional statistical testing. Bayes factors have a natural advantage over classical frequentist hypothesis testing methods in that they can assess the evidence both for and against a null hypothesis. Bayesian analysis, however, relies on a degree of prior information supplied by the investigator. This prior specification can be viewed as representation of the investigator's belief in the state of nature before collecting data, and this degree of subjectivity has been a major criticism of Bayesian analysis. The project will develop so-called "default" methods that both minimize the reliance on this subjectivity and also provide optimal statistical properties in testing both for and against the null hypothesis. The theoretical study of Bayes factors will guide the choice of default prior.The physical sciences have made gains by demonstrating that certain relationships hold across all conditions. These kinds of relationships can be termed invariant. Some social and behavioral sciences, in contrast, traditionally discover new theories by demonstrating that experimental manipulations produce altered responses rather than by proving that the response is unchanged. Conventional statistical methodology has been developed to prove that responses are not invariant to stimuli, but these tools are ill-suited to proving invariance. In addition to the development of a Bayesian alternative to classical statistical testing, the project will develop software and make it available through web applets so that researchers can easily use the new statistical tools. It is anticipated that these new developments will make Bayes factors useful and common in a number of fields, including epidemiology, economics, psychology, wildlife, and biology.