Bayesian One-way ANOVA

This feature requires SPSS® Statistics Standard Edition or the Advanced Statistics option.

The One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent variable by a single factor (independent) variable. Analysis of variance is used to test the hypothesis that several means are equal. SPSS Statistics supports Bayes-factors, conjugate priors and noninformative priors.

  1. From the menus choose:

    Analyze > Bayesian Statistics > One-way ANOVA

  2. Select a single, numeric Dependent variable from the Variables list. You must select at least one variable.
  3. Select a single Factor variable for the model from the Variables list. You must select at least one Factor variable.
  4. Select a single, non-string, variable to serve as the regression Weight from the Variables list. The Weight variable field can be empty.
  5. 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 Bayesian confidence 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 H0 1-3 Anecdotal Evidence for H0 1/30-1/10 Strong Evidence for H1
      30-100 Very Strong Evidence for H0 1 No Evidence 1/100-1/30 Very Strong Evidence for H1
      10-30 Strong Evidence for H0 1/3-1 Anecdotal Evidence for H1 1/100 Extreme Evidence for H1
      3-10 Moderate Evidence for H0 1/10-1/3 Moderate Evidence for H1    

      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.
Optionally, you can:
  • Click Criteria to specify the credible interval percentage and numerical method settings.
  • Click Priors to define reference and conjugate prior distribution settings.
  • Click Bayes Factor to specify Bayes factor settings.
  • Click Plots to control the plots that are output.
Parent topic: Bayesian statistics
1 Lee, M.D., and Wagenmakers, E.-J. 2013. Bayesian Modeling for Cognitive Science: A Practical Course. Cambridge University Press.
2 Jeffreys, H. 1961. Theory of probability. Oxford University Press.