fixedHajnal.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 composite alternative prior assumed on the difference between standardized effect sizes (\mu_2 - \mu_1)/\sigma_0 under the alternative, this function calculates the expected log(Hajnal's ratio) at a prefixed standardized effect size for a varied range of sample sizes.

Usage

fixedHajnal.twoz_es(es = 0, es1 = 0.3, n1min = 20, n2min = 20, 
                    n1max = 5000, n2max = 5000, 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.

es1

Positive numeric. \delta as above. Default: 0.3. For this, the prior on (\mu_2 - \mu_1)/\sigma_0 takes values 0.3 and -0.3 each with equal probability 1/2.

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.

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.

Value

A list with two components named summary and BF.

$summary is a data frame with columns n containing the values of sample sizes and avg.logBF containing the expected log(Hajnal's ratios) at those values.

$BF is a matrix of dimension number of sample sizes considered by nReplicate. Each row contains the Hajnal's ratios at the corresponding sample 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 = fixedHajnal.twoz_es(n1max = 100, n2max = 100)