Bayesian One-way Repeated Measures ANOVA Models

This feature requires Custom Tables and Advanced Statistics.

In Bayesian one-way analysis of variance (ANOVA) models, it is assumed that there is a single measurement per subject. However, this assumption is not always true. It is not uncommon that a study design aims to investigate mean responses over multiple time points or conditions. The Bayesian One-way Repeated Measures ANOVA procedure measures one factor from the same subject at each distinct time point or condition, and allows subjects to be crossed within the levels. It is assumed that each subject has a single observation for each time point or condition (as such, the subject-treatment interaction is not accounted for).

1. From the menus choose:

   Analyze > Bayesian Statistics > One-way Repeated Measures ANOVA

2. Select at least two Repeated measures variables from the Available Variables list.
3. Optionally, select a single variable to serve as the regression Weight from the Available Variables list. The Weight variable field can be empty.
   Note: The available variables list provides all variables except for String variables.
4. Select the desired Bayesian Analysis:
   • Characterize Posterior Distribution: When selected, the Bayesian inference is made from a perspective that is approached by characterizing posterior distributions. You can investigate the marginal posterior distribution of the parameter(s) of interest by integrating out the other nuisance parameters, and further construct credible intervals to draw direct inference. This is the default setting.
   • Estimate Bayes Factor: When selected, estimating Bayes factors (one of the notable methodologies in Bayesian inference) constitutes a natural ratio to compare the marginal likelihoods between a null and an alternative hypothesis.

     Table 1. Commonly used thresholds to define significance of evidence

     Bayes Factor	Evidence Category	Bayes Factor	Evidence Category	Bayes Factor	Evidence Category
     >100	Extreme Evidence for H1	1-3	Anecdotal Evidence for H1	1/30-1/10	Strong Evidence for H0
     30-100	Very Strong Evidence for H1	1	No Evidence	1/100-1/30	Very Strong Evidence for H0
     10-30	Strong Evidence for H1	1/3-1	Anecdotal Evidence for H0	1/100	Extreme Evidence for H0
     3-10	Moderate Evidence for H1	1/10-1/3	Moderate Evidence for H0

     H0: Null Hypothesis

     H1: Alternative Hypothesis

     ¹

     ²

   • Use Both Methods: When selected, both the Characterize Posterior Distribution and Estimate Bayes Factor inference methods as used.