Super large Bayes factor, problem or solution?
Kruskal-Wallis H Test, with a H statistic of 39.0917 and p-value of 0.00000002. There is no Bayesian version of this statistical test type that I could find. But there is for the one-way ANOVA test, which assumes normality, which is breached in this case (Shapiro-Wilk test on the residuals returns a p-value of 0.001004), and so the BF10 value for this data, extremely high at 9.092*10^16, is presented here with that caveat (test conducted in JASP version 0.19.1.0, all settings as default except "compare to null model" selected). Although one-way ANOVA can be robust to some non-normality, and a good sign here is that the Q-Q plot of residuals is quite linear, along the diagonal reference line, just deviating thereform at both ends. Furthermore, homogeneity of variances, another assumption of one-way ANOVA, is suggested by Levene's test (p-value = 0.196), allbeit with the caveat that its power is somewhat low in this case (0.27). Trying an alternative methodology: there is a published equation to get a BF10 value from a Kruskal-Wallis H statistic value [REFERENCE] which I used with (aforementioned) H = 39.0917 to get BF10 = 1,461,396.7.
[REFERENCE] Yuan Y, Johnson VE (2008) Bayesian hypothesis tests using nonparametric statistics. Statistica Sinica. 1185-200.
MY QUESTION TO JASPERS - these BF10 values are huge. Do they strike you as unfeasably large? Such that something might have gone wrong? To get the context you can see the p-value in the first sentence there.
Comments
This does not strike me as unreasonably large
EJ
I've published papers with multinomial tests and contingency table tests where the Bayes Factor was infinity, so no, this is pretty reasonable. Considering the practically perfect linear relationship between Bayes Factors and p-values, you can rest assured that this is a reasonable number.