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# Alternative hypothesis in Bayesian contigency tables

edited April 2021

Hi,

I'm a bit confused by the wording on the alternative hypothesis when conducting bayesian contigency tables in Jasp. For a non-directional test it reads "Note.  For all tests, the alternative hypothesis specifies that (row)group A not equal to (row) group B. ". For directional test it reads ”Group A is greater/is less than group B”.

To my understanding the test (which basically is the baysian counterpart to a chi-square test?) test if the distribution of Categorical variable one is independent of the distribution of categorical variable two. Or is this a missunderstanding?

Why then is the alternative hypothesis stated as if it only looked at one of the categorical variables? Why doesn't the alternative hypothesis focus on the relative frequencies? And additionally it almost sounds like the alternative hypothesis is that the distribution differs, although clearly when testing with some made up data the test seems to work as I understand it, i.e. very high bayes-factor (BF10) when the two categorical variables are related, but in such a situation the groups are of course clearly not equal (which seems to be the alternative hypothesis as it is worded?)

Or am I missing something?

• The directional tests make sense only when you have a 2x2 table and the interest is in comparing two proportions. The data for these two proportions can be collected in several different ways (poisson, multinomial).

Cheers,

E.J.

• Yes, I get that!

The main confusion and question here is the wording of the alternative hypothesis. Shoudnt it (for a non-directional test) rather read "The distribution of the row-variable is independent from the distribution of the column-variable"?

• I'm not sure that is more enlightening, but you can make a feature request on our GitHub page so the team can debate this!

Cheers,

E.J.