ANOVA or what

Comments

• EJ

  January 2022

  Bayesian contingency tables or log-linear models. You can also entertain pairwise comparisons using the Bayesian A/B test.

  Cheers,

  E.J.
• dmalm

  January 2022

  Thanks, much appreciated.

  Would there be a way to use Bayesian Factor Design Analysis (Schönbrodt & Wagenmakers, 2017; Stefan et al., 2019) to calculate a needed sample size for an experiment with categorical data?
• EJ

  January 2022

  Absolutely. We haven't done it but it is perfectly possible.

  E.J.
• dmalm

  January 2022

  Thanks EJ,

  so, if I have one categorical variable with three levels, where the participant in each level will be able to give a yes or no answer, would a Bayesian analysis with contingency tables be a good fit for analysis.

  I have done a test in JASP but I am to new to this that it is hard for me to assess whether the analysis returns a reasonable result (see https://osf.io/f5wjz/?view_only=1d1448f40fbb457fa6e4ec6f9143e1a2).

  The hypothesis is that the effect will increase for from level 1, to level 2 and on to level 3 (highest effect).

  I would deeply appreciate any thoughts on this and help on using a suitable fit for analysis in the Bayesian framework.

  Also, who could help out with describing how to do a Bayesian Factor Design Analysis for such a design?

  Many thanks!

  Best,

  D
• EJ

  January 2022

  I would do the independent multinomial but "group" should be the fixed factor (yes/no is the dependent factor). It does look like the groups are very different. Currently there is no method implemented to enforce the order restriction; you could look at BFpack (R package). Alternatively you can do the pairwise comparisons using Bayesian AB tests.

  BFDA for the model including the order restriction requires that you consider reasonable effect sizes -- I think that the default AB priors are useful here. But obviously this takes some work to set up (in particular, to find the analysis that incorporates the order-restriction).

  Cheers,

  E.J.