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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)

enter image description here

Are there any less sensitive alternatives? Methods that would require larger deviations to consider evidence for the alternative hypothesis?

Thanks

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  • $\begingroup$ Why would you want to use an inferior procedure? Perhaps the difficulty is that you're not addressing your underlying problem correctly. Could you edit this post to explain what that problem is? $\endgroup$ – whuber Apr 26 '18 at 15:25

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