SBFHajnal_onez {NAP}

Sequential Bayes Factor using the Hajnal's ratio for one-sample z-tests

Description

In a N(\mu,\sigma_0^2) population with known variance \sigma_0^2, consider the two-sided one-sample z-test for testing the point null hypothesis H_0 : \mu = 0 against H_1 : \mu \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 \mu/\sigma_0 under the alternative places equal probability at +\delta and -\delta (\delta>0 prefixed).

Usage

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)

Arguments

es

Numeric vector. Standardized effect sizes \mu/\sigma_0 where OC and ASN are desired. Default: c(0, 0.2, 0.3, 0.5).

es1

Positive numeric. \delta as above. Default: 0.3. For this, the prior on the standardized effect size \mu/\sigma_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 \leRejectH1.threshold. Default: exp(-3).

RejectH0.threshold

Positive numeric. H_0 is rejected if BF \geRejectH0.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.

Value

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.

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 = SBFHajnal_onez(nmax = 100, es = c(0, 0.3), nCore = 1)