SBFHajnal_onez: Sequential Bayes Factor using the Hajnal's ratio for...
In NAP: Non-Local Alternative Priors in Psychology

Description Usage Arguments Value Author(s) References Examples

In a N(μ,σ_0^2) population with known variance σ_0^2, consider the two-sided one-sample z-test for testing the point null hypothesis H_0 : μ = 0 against H_1 : μ \neq 0. This function calculates the operating characteristics (OC) and average sample number (ASN) of the Sequential Bayes Factor design when the prior assumed on the standardized effect size μ/σ_0 under the alternative places equal probability at +δ and -δ (δ>0 prefixed).

SBFHajnal_onez(es = c(0, 0.2, 0.3, 0.5), es1 = 0.3, 
               nmin = 1, nmax = 5000, sigma0 = 1, 
               RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3), 
               batch.size.increment, nReplicate = 50000, nCore)

`es`	Numeric vector. Standardized effect sizes μ/σ_0 where OC and ASN are desired. Default: `c(0, 0.2, 0.3, 0.5)`.
`es1`	Positive numeric. δ as above. Default: 0.3. For this, the prior on the standardized effect size μ/σ_0 takes values 0.3 and -0.3 each with equal probability 1/2.
`nmin`	Positive integer. Minimum sample size in the sequential comparison. Default: 1.
`nmax`	Positive integer. Maximum sample size in the sequential comparison. Default: 1.
`sigma0`	Positive numeric. Known standard deviation in the population. Default: 1.
`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.increment`	function. Increment in sample size at each sequential step. Default: `function(narg){20}`. This means an increment of 20 samples at each step.
`nReplicate`	Positve integer. Number of replicated studies based on which the OC and ASN are calculated. Default: 50,000.
`nCore`	Positive integer. Default: One less than the total number of available cores.

A list with three components named summary, BF, and N.

$summary is a data frame with columns effect.size containing the values in es. At those values, acceptH0 contains the proportion of times H_0 is accepted, rejectH0 contains the proportion of times H_0 is rejected, inconclusive contains the proportion of times the test is inconclusive, ASN contains the ASN, and avg.logBF contains the expected weight of evidence values.

$BF is a matrix of dimension length(es) by nReplicate. Each row contains the Bayes factor values at the corresponding standardized effec size in nReplicate replicated studies.

$N is a matrix of the same dimension as $BF. Each row contains the sample size required to reach a decision at the corresponding standardized effec size in nReplicate replicated studies.

Sandipan Pramanik and Valen E. Johnson

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].