0

I would like to use an Bayesian approach to compare a continuous non-normally distributed variable taking values between -1 to 1 between two populations. The measurements are not paired.

Overall my data is comparable to the example shown in fitting a distribution to skewed data with negative values (in the sense that it is not a symmetrical normal-distribution around a mean, but less extreme values are more commonly observed than extreme ones) just that I have observations for the variable/score for two groups and my variable/score takes values between -1 and 1 (and not -2 and 2 like in the graph below):

enter image description here

I already performed a Mann-Whitney-Wilcoxon test as a classical standard approach and would now like to use Bayesian inference in addition.

I just began to apply Bayesian analysis and don't know which model I could use in this case to answer the question how much more likely the subjects in one group than in the other have a score exceeding a threshold of 0.75.

NicolasBourbaki
  • 101
  • 1
    A key part of any Bayesian approach concerns adopting a suitable model and a suitable prior distribution. We might be able to help you with those if you provide appropriate details as well as a statement of how (on what basis) you wish to compare the populations. – whuber Oct 10 '23 at 14:46
  • 3
    The model generalization of the Wilcoxon test is the proportional odds semiparametric model. The Bayesian version of that is the Bayesian PO semiparametric model. See here for a full example, and then see Section 7.11 below that. More resources are here. – Frank Harrell Oct 10 '23 at 14:49
  • Your text says "a continuous non-normally distributed variable taking values between -1 to 1 between two populations" ... but the histogram you show does not stay between -1 and 1. Please clarify why your histogram is not like your description (what quantity did you display there? Are those pair differences?) – Glen_b Oct 11 '23 at 00:26
  • You say "not like the graph below" ... but then what information is the graph providing about the actual situation? What are we looking at if not the altruism scores you're discussing? Your edit is insufficient to resolve the issue. – Glen_b Oct 11 '23 at 23:17

0 Answers0