Pval

dPval

pPval

qPval

rPval

p, q

prob

theta

sigma2

Number of random numbers to be generated.

seed

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.

distribution

htest

nonparametric

Publication bias, the fact that studies identified for inclusion in a meta analysis do not represent all studies on the topic of interest, is commonly recognized as a threat to the validity of the results of a meta analysis. One way to explicitly model publication bias is via selection models or weighted probability distributions. In this package we provide implementations of several parametric and nonparametric weight functions. The novelty in Rufibach (2011) is the proposal of a non-increasing variant of the nonparametric weight function of Dear & Begg (1992). The new approach potentially offers more insight in the selection process than other methods, but is more flexible than parametric approaches. To maximize the log-likelihood function proposed by Dear & Begg (1992) under a monotonicity constraint we use a differential evolution algorithm proposed by Ardia et al (2010a, b) and implemented in Mullen et al (2009). In addition, we offer a method to compute a confidence interval for the overall effect size theta, adjusted for selection bias as well as a function that computes the simulation-based p-value to assess the null hypothesis of no selection as described in Rufibach (2011, Section 6).

Pval: Functions for the distribution of p-values

Description

Usage

Arguments

Value

References