implement.SBFNAP_onet: Implement Sequential Bayes Factor using the NAP for...
In NAP: Non-Local Alternative Priors in Psychology

Description Usage Arguments Value Author(s) References Examples

In a N(μ,σ^2) population with unknown variance σ^2, consider the two-sided one-sample t-test for testing the point null hypothesis H_0 : μ = 0 against H_1 : μ \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 μ/σ under the alternative.

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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)

`obs`	Numeric vector. The vector of sequentially observed data.
`tau.NAP`	Positive numeric. Parameter in the moment prior. Default: 0.3/√2. This places the prior modes of the standardized effect size μ/σ at 0.3 and -0.3.
`RejectH1.threshold`	Positive numeric. H_0 is accepted if BF ≤`RejectH1.threshold`. Default: `exp(-3)`.
`RejectH0.threshold`	Positive numeric. H_0 is rejected if BF ≥`RejectH0.threshold`. Default: `exp(3)`.
`batch.size`	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))`.
`return.plot`	Logical. Whether a sequential comparison plot to be returned. Default: `TRUE`.
`until.decision.reached`	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.

Sandipan Pramanik and Valen E. Johnson

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]