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 the prior assumed on the standardized effect size \(\mu/\sigma_0\) under the alternative places equal probability at \(+\delta\) and \(-\delta\) (\(\delta>0\) prefixed).
SBFHajnal_onez(es = c(0, 0.2, 0.3, 0.5), es1 = 0.3,
nmin = 1, nmax = 5000, 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 numeric. \(\delta\) as above. Default: \(0.3\). For this, the prior on the standardized effect size \(\mu/\sigma_0\) takes values \(0.3\) and \(-0.3\) each with equal probability 1/2.
Positive integer. Minimum sample size in the sequential comparison. Default: 1.
Positive integer. Maximum sample size in the sequential comparison. Default: 1.
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.
Hajnal, J. (1961). A two-sample sequential t-test.Biometrika, 48:65-75, [Article].
Schnuerch, M. and Erdfelder, E. (2020). A two-sample sequential t-test.Biometrika, 48:65-75, [Article].
# NOT RUN {
out = SBFHajnal_onez(nmax = 100, es = c(0, 0.3), nCore = 1)
# }
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