Pval {selectMeta}

Functions for the distribution of p-values

Description

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.

Usage

dPval(p, u, theta, sigma2)
pPval(q, u, theta, sigma2)
qPval(prob, u, theta, sigma2)
rPval(n, u, theta, sigma2, seed = 1)

Arguments

p, q

Quantile.

prob

Probability.

u

Standard error of the effect size.

theta

Effect size.

sigma2

Random effect variance component.

n

Number of random numbers to be generated.

seed

Seed to set.

Value

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).

Author(s)

Kaspar Rufibach (maintainer), [e-mail],
http://www.kasparrufibach.ch

References

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.