In a \(N(\mu,\sigma_0^2)\) population with known variance \(\sigma_0^2\), consider the two-sided one-sample \(z\)-test for testing the point null hypothesis \(H_0 : \mu = 0\) against \(H_1 : \mu \neq 0\). This function calculates the operating characteristics (OC) and average sample number (ASN) of the Sequential Bayes Factor design when a normal moment prior is assumed on the standardized effect size \(\mu/\sigma_0\) under the alternative.
SBFNAP_onez(es = c(0, 0.2, 0.3, 0.5), nmin = 1, nmax = 5000,
tau.NAP = 0.3/sqrt(2), sigma0 = 1,
RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
batch.size.increment, nReplicate = 50000, nCore)Numeric vector. Standardized effect sizes \(\mu/\sigma_0\) where OC and ASN are desired. Default: c(0, 0.2, 0.3, 0.5).
Positive integer. Minimum sample size in the sequential comparison. Default: 1.
Positive integer. Maximum sample size in the sequential comparison. Default: 1.
Positive numeric. Parameter in the moment prior. Default: \(0.3/\sqrt2\). This places the prior modes of the standardized effect size \(\mu/\sigma_0\) at \(0.3\) and \(-0.3\).
Positive numeric. Known standard deviation in the population. Default: 1.
Positive numeric. \(H_0\) is accepted if \(BF \le\)RejectH1.threshold. Default: exp(-3).
Positive numeric. \(H_0\) is rejected if \(BF \ge\)RejectH0.threshold. Default: exp(3).
function. Increment in sample size at each sequential step. Default: function(narg){20}. This means an increment of 20 samples at each step.
Positve integer. Number of replicated studies based on which the OC and ASN are calculated. Default: 50,000.
Positive integer. Default: One less than the total number of available cores.
A list with three components named summary, BF, and N.
$summary is a data frame with columns effect.size containing the values in es. At those values, acceptH0 contains the proportion of times H_0 is accepted, rejectH0 contains the proportion of times H_0 is rejected, inconclusive contains the proportion of times the test is inconclusive, ASN contains the ASN, and avg.logBF contains the expected weight of evidence values.
$BF is a matrix of dimension length(es) by nReplicate. Each row contains the Bayes factor values at the corresponding standardized effec size in nReplicate replicated studies.
$N is a matrix of the same dimension as $BF. Each row contains the sample size required to reach a decision at the corresponding standardized effec size in nReplicate replicated studies.
Pramanik, S. and Johnson, V. (2022). Efficient Alternatives for Bayesian Hypothesis Tests in Psychology. Psychological Methods. Just accepted.
Johnson, V. and Rossell, R. (2010). On the use of non-local prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B, 72:143-170. [Article]
# NOT RUN {
out = SBFNAP_onez(nmax = 100, es = c(0, 0.3), nCore = 1)
# }
Run the code above in your browser using DataLab