SBFNAP_twot {NAP}

Sequential Bayes Factor using the NAP for two-sample t-tests

Description

In case of two independent populations N(\mu_1,\sigma^2) and N(\mu_2,\sigma^2) with unknown common variance \sigma^2, consider the two-sample z-test for testing the point null hypothesis of difference in their means H_0 : \mu_2 - \mu_1 = 0 against H_1 : \mu_2 - \mu_1 \neq 0. This function calculates the operating characteristics (OC) and average sample number (ASN) of the Sequential Bayes Factor design when a normal moment prior is assumed on the difference between standardized effect sizes (\mu_2 - \mu_1)/\sigma under the alternative.

Usage

SBFNAP_twot(es = c(0, 0.2, 0.3, 0.5), n1min = 2, n2min = 2,
            n1max = 5000, n2max = 5000,
            tau.NAP = 0.3/sqrt(2), 
            RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
            batch1.size.increment, batch2.size.increment, 
            nReplicate = 50000, nCore)

Arguments

es

Numeric vector. Standardized effect size differences (\mu_2 - \mu_1)/\sigma where OC and ASN are desired. Default: c(0, 0.2, 0.3, 0.5).

n1min

Positive integer. Minimum sample size from Group-1 in the sequential comparison. Should be at least 2. Default: 1.

n2min

Positive integer. Minimum sample size from Group-2 in the sequential comparison. Should be at least 2. Default: 1.

n1max

Positive integer. Maximum sample size from Group-1 in the sequential comparison. Default: 1.

n2max

Positive integer. Maximum sample size from Group-2 in the sequential comparison. Default: 1.

tau.NAP

Positive numeric. Parameter in the moment prior. Default: 0.3/\sqrt{2}. This places the prior modes of (\mu_2 - \mu_1)/\sigma at 0.3 and -0.3.

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).

batch1.size.increment

function. Increment in sample size from Group-1 at each sequential step. Default: function(narg){20}. This means an increment of 20 samples at each step.

batch2.size.increment

function. Increment in sample size from Group-2 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

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]

Examples

out = SBFNAP_twot(n1max = 100, n2max = 100, es = c(0, 0.3), nCore = 1)