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 a normal moment prior is assumed on the standardized effect size \(\mu/\sigma\) under the alternative.
implement.SBFNAP_onet(obs, tau.NAP = 0.3/sqrt(2),
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. Parameter in the moment prior. Default: \(0.3/\sqrt2\). This places the prior modes of the standardized effect size \(\mu/\sigma\) at \(0.3\) and \(-0.3\).
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. The first element (the first batch size) needs to be at least 2. 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.
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 = implement.SBFNAP_onet(obs = rnorm(100))
# }
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