implement.SBFHajnal_onet: Implement Sequential Bayes Factor using the Hajnal's ratio...

In NAP: Non-Local Alternative Priors in Psychology

Description

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 the prior assumed on the standardized effect size μ/σ under the alternative places equal probability at +δ and -δ (δ>0 prefixed).

Usage

implement.SBFHajnal_onet(obs, es1 = 0.3, 
                         RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
                         batch.size, return.plot = TRUE, until.decision.reached = TRUE)

Arguments

obs	Numeric vector. The vector of sequentially observed data.
es1	Positive numeric. δ as above. Default: 0.3. For this, the prior on the standardized effect size μ/σ takes values 0.3 and -0.3 each with equal probability 1/2.
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. 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.

Value

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.

Author(s)

Sandipan Pramanik and Valen E. Johnson

References

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].

Examples

out = implement.SBFHajnal_onet(obs = rnorm(100))

NAP documentation built on Jan. 6, 2022, 5:07 p.m.