fixedHajnal.twoz_n {NAP}

Fixed-design two-sample z-tests using Hajnal's ratio and a pre-fixed sample size

Description

In two-sided fixed design two-sample z-tests with composite alternative prior assumed on the standardized effect size (\mu_2 - \mu_1)/\sigma_0 under the alternative and a prefixed sample size, this function calculates the expected log(Hajnal's ratio) at a varied range of differences between standardized effect sizes.

Usage

fixedHajnal.twoz_n(es1 = 0.3, es = c(0, 0.2, 0.3, 0.5), 
                   n1.fixed = 20, n2.fixed = 20, sigma0 = 1,
                   nReplicate = 50000, nCore)

Arguments

es1

Positive numeric. 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.

es

Numeric vector. Standardized effect size differences (\mu_2 - \mu_1)/\sigma_0 where the expected weights of evidence is desired. Default: c(0, 0.2, 0.3, 0.5).

n1.fixed

Positive integer. Prefixed sample size from Group-1. Default: 20.

n2.fixed

Positive integer. Prefixed sample size from Group-2. Default: 20.

sigma0

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

nReplicate

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

nCore

Positive integer. Default: One less than the total number of available cores.

Value

A list with two components named summary and BF.

$summary is a data frame with columns effect.size containing the values in es and avg.logBF containing the expected log(Hajnal's ratios) at those values.

$BF is a matrix of dimension length(es) by nReplicate. Each row contains the Hajnal's ratios at the corresponding standardized effec 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_n(n1.fixed = 20, n2.fixed = 20, es = c(0, 0.3), nCore = 1)