How to interpret the H1(BF10) of Bayesian contingency table?
Thanks a lot for developing this great tool!
Recently, I am trying to use Bayesian contingency table to test whether the age/sex distribution of sample from different countries are different, the jasp files can be found at: https://osf.io/m86zx/;https://osf.io/m2bg4/.
When submitting the manuscript, the editor asked us to specify the meaning H1. I re-read Jamil et al (2017), it writes: "All Bayes factor tests are based on a comparison of two models: one model that represents the hypothesis of row-column independence (H0) and the other model that represents the hypothesis of row-column dependence (H1)." (page 641).
In our case, we used the column-fixed method and the alt hypothesis is "Group one not equal to group two". My original interpretation of H0 ("columns are independent") is that different columns are from different populations, so they should show different pattern of distribution. And H1 (columns are dependent) means that at least some column are from the same population (i.e., they have similar pattern of distributions).
However, after reading this post (https://forum.cogsci.nl/discussion/6795/bayesian-chi-square-test), I doubt my original understanding was wrong because E-J said "The test is similar to ANOVA in the sense that it compares the H0 of "the groups are equal" to the H1 of "the groups are different". This seems oppose to my original understanding.
My question is: how should I interpret the H1 in my case?
Thanks in advance
"Row-column independence" means that there is no association between the rows and the columns; so knowing the value of a column ("women" or "men") does not provide any hint as to the value of the row ("prefer dogs over cats" or "prefer cats over dogs"). So H0 does not mean "columns are independent **from other columns**"; rather, it means "the colums are statistically independent **from the rows**".