find.ab: Find beta parameters to approximate distribution of p-values.

In MChtest: Monte Carlo Hypothesis Tests with Sequential Stopping

Description

Find parameters of a beta distribution to approximate distribution of a p-value derived from a normal test statistic with one-sided significance level=ALPHA and power=1-BETA.

Usage

find.ab(n = 1e+05, ALPHA = 0.05, BETA = 0.2, higha = 100)

Arguments

n	the number of divisions for the numeric integration used to estimate the mean of p-value distribution, H (see details).
ALPHA	one-sided significance level of normal test statistic
BETA	type II error for normal test stastic
higha	an upper bound on the beta parameter (see details).

Details

The cumulative distribution function of the p-value from a normally distributed test statistic with one-sided significance level=ALPHA and power=1-BETA is H(p) = 1-pnorm( qnorm(1-p) - qnorm(1-ALPHA)+qnorm(BETA) ). We approximate this distribution with a beta distribution, B, which has the same mean as H and has B(ALPHA)=1-BETA. If two beta distributions meet both those criteria, we select the one closest to H in terms of integrated square error of the cumulative distribution function. That error is estimated by the sample variance of the differences in the two CDFs evaluated at (0:n)/n. Note that the two beta distributions come from the two roots of the following function: 1-BETA - B(ALPHA) We search for those two roots as the beta parameter within the range (1/higha, higha).

Value

A list with two elements:

a	numeric value of one of the shape parameters of the beta distribution
b	numeric value of the other shape parameter of the beta distribution

Author(s)

M.P. Fay

References

Fay, M.P., and Follmann, D.A. (2002). "Designing Monte Carlo implementations of permutation or bootstrap hypothesis tests" American Statistician, 56: 63-70.

Examples

## See first line of Table 1, Fay and Follmann, 2002 
find.ab(ALPHA=.05,BETA=.1)

MChtest documentation built on May 16, 2019, 5:06 p.m.