fixedNAP.twoz_es {NAP}

Fixed-design two-sample z-tests with NAP for varied sample sizes

Description

In two-sided fixed design two-sample z-tests with normal moment prior assumed on the difference between standardized effect sizes (\mu_2 - \mu_1)/\sigma_0 under the alternative, this function calculates the expected weights of evidence (that is, expected log(Bayes Factor)) of the test at a prefixed differences between standardized effect size for a varied range of sample sizes.

Usage

fixedNAP.twoz_es(es = 0, n1min = 20, n2min = 20, 
                 n1max = 5000, n2max = 5000, 
                 tau.NAP = 0.3/sqrt(2), sigma0 = 1, 
                 batch1.size.increment, batch2.size.increment, 
                 nReplicate = 50000)

Arguments

es

Numeric. Difference between standardized effect sizes where the expected weights of evidence is desired. Default: 0.

n1min

Positive integer. Minimum sample size from Grpup-1 to be considered. Default: 20.

n2min

Positive integer. Minimum sample size from Grpup-2 to be considered. Default: 20.

n1max

Positive integer. Maximum sample size from Grpup-1 to be considered. Default: 5000.

n2max

Positive integer. Maximum sample size from Grpup-2 to be considered. Default: 5000.

tau.NAP

Positive numeric. Parameter in the moment prior. Default: 0.3/\sqrt2. This places the prior modes of (\mu_2 - \mu_1)/\sigma_0 at 0.3 and -0.3.

sigma0

Positive numeric. Known common standard deviation of the populations. Default: 1.

batch1.size.increment

Positive numeric. Increment in sample size from Group-1. The sequence of sample size thus considered from Group-1 for the fixed design test is from n1min to n1max with an increment of batch1.size.increment. Default: function(narg){20}. This means an increment of 20 samples from Group-1 at each step.

batch2.size.increment

Positive numeric. Increment in sample size from Group-2. The sequence of sample size thus considered from Group-2 for the fixed design test is from n2min to n2max with an increment of batch2.size.increment. Default: function(narg){20}. This means an increment of 20 samples from Group-2 at each step.

nReplicate

Positve integer. Number of replicated studies based on which the expected weights of evidence is calculated. Default: 50,000.

Details

n1min, n1max, batch1.size.increment, and n2min, n2max, batch2.size.increment should be chosen such that the length of sample sizes considered from Group 1 and 2 are equal.

Value

A list with two components named summary and BF.

$summary is a data frame with columns n1 containing the sample sizes from Group-1, n2 containing the sample sizes from Group-2, and avg.logBF containing the expected weight of evidence values at those values.

$BF is a matrix of dimension number of sample sizes considered by nReplicate. Each row contains the Bayes factor values at the corresponding sample 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 = fixedNAP.twoz_es(n1max = 100, n2max = 100)