rrisk {MChtest}

Calculate resampling risk and expected resampling size

Description

Calculates for a particular stopping boundary the resampling risk of making the wrong accept/reject decision. Can be calculated for different distributions of the p-value. If type="p" then assume point mass at pparms. If type="b" then assume a beta distribution with two shape parameters given by pparms.

Usage

rrisk(bound, pparms, sig.level = 0.05, type = "b")

Arguments

bound

an object of class MCbound, i.e., a stopping boundary. See MCbound to create

pparms

either a vector of possible point mass p-value distributions (type="p"), or a vector (or matrix with two columns) representing two beta shape parameters (type="b")

sig.level

significance level for defining resampling risk

type

either "p" for point mass p-value distributions, or "b" for a beta distribution

Details

The resampling risk (RR) is defined as the probability of making an accept/reject decision different from complete enumeration. In other words, for any Monte Carlo test the true p-value for any data is either below the sig.level (reject the null) or above the sig.level (accept the null), and the RR is the probability of either deciding p<=sig.level when p>sig.level or vise versa. We also calculate the expected resampling size for the assumed distributions on the p-values. As a check of the MCbound, we sum the probability of stopping at any point in the boundary over the entire stopping boundary for each assumed distribution on the p-values; the ouput value check should give a vector of all ones if the MCbound is calculated correctly.

Value

A list with the following elements:

check

Sum of the probabilities of the stopping boundary corresponding to the p-value distribution(s). Should be a vector with all values equal to 1.

rr

resampling risk corresponding to the p-value distribution(s)

EN

expected resampling size corresponding to the p-value distribution(s)

Author(s)

Michael P. Fay

References

Fay, M.P., Kim, H-J. and Hachey, M. (2007). Using truncated sequential probability ratio test boundaries for Monte Carlo implementation of hypothesis tests. Journal of Computational and Graphical Statistics. 16(4):946-967.

Examples

### caculate resampling risk and E(N) under null, i.e., uniform distribution on p-values 
rrisk(MCbound.precalc1,c(1,1))