NAP (version 1.1)

fixedHajnal.twoz_es: 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.

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

# NOT RUN {
out = fixedHajnal.twoz_es(n1max = 100, n2max = 100)
# }