NAP (version 1.1)

fixedHajnal.onez_es: Fixed-design one-sample \(z\)-tests using Hajnal's ratio for varied sample sizes

Description

In two-sided fixed design one-sample \(z\)-tests with composite alternative prior assumed on the standardized effect size \(\mu/\sigma_0\) 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.onez_es(es = 0, es1 = 0.3, nmin = 20, nmax = 5000, 
                    sigma0 = 1, batch.size.increment, nReplicate = 50000)

Arguments

es

Numeric. Standardized effect size where the expected weights of evidence is desired. Default: 0.

es1

Positive numeric. Default: \(0.3\). For this, the composite alternative 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 to be considered. Default: 20.

nmax

Positive integer. Maximum sample size to be considered. Default: 5000.

sigma0

Positive numeric. Known standard deviation in the population. Default: 1.

batch.size.increment

function. Increment in sample size. The sequence of sample size thus considered for the fixed design test is from nmin to nmax with an increment of batch.size.increment. 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 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.onez_es(nmax = 100)
# }