NAP (version 1.1)

HajnalBF_onez: Hajnal's ratio in one-sample \(z\) tests

Description

In a \(N(\mu,\sigma_0^2)\) population with known variance \(\sigma_0^2\), consider the two-sided one-sample \(z\)-test for testing the point null hypothesis \(H_0 : \mu = 0\) against \(H_1 : \mu \neq 0\). Based on an observed data, this function calculates the Hajnal's ratio in favor of \(H_1\) when the prior assumed on the standardized effect size \(\mu/\sigma_0\) under the alternative places equal probability at \(+\delta\) and \(-\delta\) (\(\delta>0\) prefixed).

Usage

HajnalBF_onez(obs, nObs, mean.obs, test.statistic, 
              es1 = 0.3, sigma0 = 1)

Arguments

obs

Numeric vector. Observed vector of data.

nObs

Numeric or numeric vector. Sample size(s). Same as length(obs) when numeric.

mean.obs

Numeric or numeric vector. Sample mean(s). Same as mean(obs) when numeric.

test.statistic

Numeric or numeric vector. Test-statistic value(s).

es1

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

sigma0

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

Value

Positive numeric or numeric vector. The Hajnal's ratio(s).

Details

• Users can either specify obs, or nObs and mean.obs, or nObs and test.statistic.

• If obs is provided, it returns the corresponding Bayes factor value.

• If nObs and mean.obs are provided, the function is vectorized over both arguments. Bayes factor values corresponding to the values therein are returned.

• If nObs and test.statistic are provided, the function is vectorized over both arguments. Bayes factor values corresponding to the values therein are returned.

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 {
HajnalBF_onez(obs = rnorm(100))
# }