# Greatly overlapping density distributions; however, the difference is statistically significant

I am looking for the statistical significance of a difference between two groups (red and blue). Group sizes are equal (n = 4500). The distributions of these distributions overlap in a great deal as you can see on the plot, indicating no statistically significant difference.

However, the difference distribution is significant, 2.3 [95% CI: 0.4; 4.3], therefore it's statistically significant. Is used posterior_summary() function to calculate credible intervals. https://rdrr.io/cran/brms/man/posterior_summary.html

  ggplot(data, aes())+
geom_density(aes(red), color = "red")+
geom_density(aes(blue), color = "blue")+
geom_density(aes(red-blue), color = "black") #difference between two groups


Could you please confirm that my approach is correct? (I am not doing anything wrong)

• What test are you using to test this? How many units do you have in the samples? Commented Sep 29, 2020 at 9:48
• Without knowing the details at least nothing of this looks wrong. If you have enough data points, these two distributions will indeed show up as significantly different. Commented Sep 29, 2020 at 9:50
• I edited the initial post. N = 4500 for both groups (I use Bayesian regression posterior data). Commented Sep 29, 2020 at 9:53
• Without disagreeing with any other comment, I note that there is a spike around zero for one group and not for the other group. That surely needs some thought and discussion. Also, I can't follow what you did at all clearly, as you seem to be mixing some unstated significance test, some unstated confidence interval procedure and a Bayesian approach, Commented Sep 29, 2020 at 11:04
• @NickCox the spike around 0 is the difference between the groups that has been plotted Commented Sep 29, 2020 at 11:15