In a \(N(\mu,\sigma^2)\) population with unknown variance \(\sigma^2\), consider the two-sided one-sample \(t\)-test for testing the point null hypothesis \(H_0 : \mu = 0\) against \(H_1 : \mu \neq 0\). For a sequentially observed data, this function implements the Sequential Bayes Factor design when the prior assumed on the standardized effect size \(\mu/\sigma\) under the alternative places equal probability at \(+\delta\) and \(-\delta\) (\(\delta>0\) prefixed).
implement.SBFHajnal_onet(obs, es1 = 0.3,
RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
batch.size, return.plot = TRUE, until.decision.reached = TRUE)
Numeric vector. The vector of sequentially observed data.
Positive numeric. \(\delta\) as above. Default: \(0.3\). For this, the prior on the standardized effect size \(\mu/\sigma\) takes values \(0.3\) and \(-0.3\) each with equal probability 1/2.
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)
.
Integer vector. The vector of batch sizes at each sequential comparison. Default: c(2, rep(1, length(obs)-2))
.
Logical. Whether a sequential comparison plot to be returned. Default: TRUE
.
Logical. Whether the sequential comparison is performed until a decision is reached or until the data is observed. Default: TRUE
. This means the comparison is performed until a decision is reached.
A list with three components named N
, BF
, and decision
.
$N
contains the number of sample size used.
$BF
contains the Bayes factor values at each sequential comparison.
$decision
contains the decision reached. 'A'
indicates acceptance of \(H_0\), 'R'
indicates rejection of \(H_0\), and 'I'
indicates inconclusive.
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 = implement.SBFHajnal_onet(obs = rnorm(100))
# }
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