# andrewheiss/diff-means-half-dozen-ways

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 // Stan implementation of John Kruschke's Bayesian Estimation Supersedes the // t-test (BEST), in John K. Kruschke, "Bayesian Estimation Supersedes the t // test," *Journal of Experimental Psychology* 142, no. 2 (May 2013): 573–603, // doi:10.1037/a0029146. // Adapted from code by Michael Clark // https://github.com/m-clark/Miscellaneous-R-Code/blob/master/ModelFitting/Bayesian/rstant_testBEST.R // Stuff coming in from R data { int N; // Sample size int n_groups; // Number of groups vector[N] y; // Outcome variable int group_id[N]; // Group variable } // Stuff to transform in Stan transformed data { real mean_y; mean_y = mean(y); } // Stuff to estimate parameters { vector[2] mu; // Estimated group means vector[2] sigma; // Estimated group sd real nu; // df for t distribution } // Models and distributions model { // Priors // curve(expr = dnorm(mean_y, 2), from = -5, to = 5) mu ~ normal(mean_y, 2); // curve(expr = dcauchy(x, location = 0, scale = 1), from = 0, to = 40) sigma ~ cauchy(0, 1); // Kruschke uses a nu of exponential(1/29) // curve(expr = dexp(x, 1/29), from = 0, to = 200) nu ~ exponential(1.0/29); // Likelihood for (n in 1:N){ y[n] ~ student_t(nu, mu[group_id[n]], sigma[group_id[n]]); } } // Stuff to calculate with Stan generated quantities { // Mean difference real mu_diff; // Effect size; see footnote 1 in Kruschke:2013 // Standardized difference between two means // See https://en.wikipedia.org/wiki/Effect_size#Cohen's_d real cohen_d; // Common language effect size // The probability that a score sampled at random from one distribution will // be greater than a score sampled from some other distribution // See https://janhove.github.io/reporting/2016/11/16/common-language-effect-sizes real cles; mu_diff = mu[1] - mu[2]; cohen_d = mu_diff / sqrt(sum(sigma)/2); cles = normal_cdf(mu_diff / sqrt(sum(sigma)), 0, 1); }