I am trying to compare large normal distributions (n > 1000) to mu = 0. Altough visually the distribution is relatively close to 0 (i.e., a large proportion of it overlaps 0 and the opposite side), frequentist and Bayesian t-tests are extremely supportive of the alternative hypothesis.
set.seed(123) p <- rnorm(4000, -0.3, 0.50) plot(density(p)) t.test(p) BayesFactor::ttestBF(p)
Are there any less sensitive alternatives? Methods that would require larger deviations to consider evidence for the alternative hypothesis?