The density of the \(p\)-value generated by a test of the hypothesis
$$H_0 : Y \sim N(0, \sigma^2) \ \ vs. \ \ H_1 : Y \sim N(\theta, \eta^2)$$
has the form
$$f(p; \theta, \sigma, \eta) = \frac{\sigma}{2 \eta} \frac{\phi\Bigl((-\sigma \Phi^{-1}(p / 2) - \theta) / \eta\Bigr) + \phi\Bigl((\sigma \Phi^{-1}(p / 2) - \theta) / \eta\Bigr)}{\phi(\Phi^{-1}(p / 2))}$$
where \(\eta^2 = u^2 + \sigma^2\). We refer to Rufibach (2011) for details.
dPval(p, u, theta, sigma2)
pPval(q, u, theta, sigma2)
qPval(prob, u, theta, sigma2)
rPval(n, u, theta, sigma2, seed = 1)dPval gives the density, pPval gives the distribution function, qPval gives the quantile function, and rPval generates
random deviates for the density \(f(p; \theta, \sigma, \eta)\).
Quantile.
Probability.
Standard error of the effect size.
Effect size.
Random effect variance component.
Number of random numbers to be generated.
Seed to set.
Kaspar Rufibach (maintainer), kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Dear, K.B.G. and Begg, C.B. (1992). An Approach for Assessing Publication Bias Prior to Performing a Meta-Analysis. Statist. Sci., 7(2), 237--245.
Rufibach, K. (2011). Selection Models with Monotone Weight Functions in Meta-Analysis. Biom. J., 53(4), 689--704.