implement.SBFNAP_twot: 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 case of two independent populations N(μ_1,σ^2) and N(μ_2,σ^2) with unknown common variance σ^2, consider the two-sample t-test for testing the point null hypothesis of difference in their means H_0 : μ_2 - μ_1 = 0 against H_1 : μ_2 - μ_1 \neq 0. For a sequentially observed data, this function implements the Sequential Bayes Factor design when a normal moment prior is assumed on the difference between standardized effect sizes (μ_2 - μ_1)/σ under the alternative.

implement.SBFNAP_twot(obs1, obs2, tau.NAP = 0.3/sqrt(2), 
                      RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
                      batch1.size, batch2.size, return.plot = TRUE,
                      until.decision.reached = TRUE)

`obs1`	Numeric vector. The vector of sequentially observed data from Group-1.
`obs2`	Numeric vector. The vector of sequentially observed data from Group-2.
`tau.NAP`	Positive numeric. Parameter in the moment prior. Default: 0.3/√2. This places the prior modes of the difference between standardized effect sizes (μ_2 - μ_1)/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)`.
`batch1.size`	Integer vector. The vector of batch sizes from Group-1 at each sequential comparison. The first element (the first batch size) needs to be at least 2. Default: `c(2, rep(1, length(obs1)-2))`.
`batch2.size`	Integer vector. The vector of batch sizes from Group-2 at each sequential comparison. The first element (the first batch size) needs to be at least 2. Default: `c(2, rep(1, length(obs2)-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 N1, N2, BF, and decision.

$N1 and $N2 contains the number of sample size used from Group-1 and 2.

$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]