STAND (version 2.0)

npower.lnorm: Sample Size and Power For Lognormal Distribution

Description

Find either the sample size or power for complete sample from lognormal distribution

Usage

npower.lnorm(n=NA,power=NA,fstar=1,p=0.95,gamma=0.95)

Arguments

n

sample size

power

power of the test = 1 - $\beta$

fstar

true percent of X's $\ge$ limit L

p

probability for Xp the 100pth percentile. Default is 0.95

gamma

one-sided confidence level $\gamma$. Default is 0.95

Value

A vector with components:

n

sample size

power

power of the test = 1 -$\beta$

fstar

true percent of X's $\ge$ limit L

p

probability for Xp the 100pth percentile. Default is 0.95

gamma

one-sided confidence level $\gamma$. Default is 0.95

Details

Find either the sample size n or the power of the test for specified values of fstar, p, and gamma. Either n is missing or power is missing.

The null hypothesis of interest is $Ho: F \ge Fo = 1-p$; i.e., Fo is the maximum proportion of the population that can exceed the limit Lp. The null hypothesis is rejected if the $100 \gamma\%$ UCL for F is less than Fo , indicating that the exposure profile is acceptable. For the complete data case this is equivalent to testing the null hypothesis $Ho: Xp \ge Lp$ at the $\alpha = (1- \gamma )$ significance level. See efraction.exact, percentile.exact and Section 2.3 of Frome and Wambach(2005) for further details.

References

Johnson, N. L. and B. L. Welch (1940), "Application of the Non-Central t-Distribution," Biometrika, 31(3/4), 362-389.

Lyles R. H. and L. L. Kupper (1996), "On strategies for comparing occupational exposure data to limits," American Industrial Hygiene Association Journal, 57:6-15.

Frome, E. L. and Wambach, P. F. (2005), "Statistical Methods and Software for the Analysis of Occupational Exposure Data with Non-Detectable Values," ORNL/TM-2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf

Ignacio, J. S. and W. H. Bullock (2006), A Strategy for Assesing and Managing Occupational Exposures, Third Edition, AIHA Press, Fairfax, VA.

Mulhausen, J. R. and J. Damiano (1998), A Strategy for Assessing and Managing Occupational Exposures, Second Edition, AIHA Press, Fairfax, VA.

See Also

Help files for efraction.ml,percentile.ml, efclnp,aihand

Examples

#                              EXAMPLE 1
#    Table VII.1 Mulhausen and Damiano (1998) adapted from
#    Table II in Lyles and Kupper (1996) JAIHA vol 57 6-15 Table II
#    Sample Size Needed When Using UTL(95,95) to Show 95% Confidence
#    that the 95th Percentile is below the OEL (Power = 0.8)
rx<-c(1.5,2,2.5,3)
sdx<- sqrt(c(0.5,1,1.5,2,2.5,3))
tabn<-matrix(0,4,6)
for ( i in 1:4) {
  for (j in 1:6) {
fstar<- 100*(1 -pnorm( log(rx[i])/sdx[j] + qnorm(0.95) ))
tabn[i,j]<- npower.lnorm(NA,0.8,fstar,p=0.95,gamma=0.95)[1] 
}
}
cn<- paste("GSD = ",round(exp(sdx),2),sep="" )
dimnames(tabn)<-list( round(1/rx,2),cn)
rm(cn,rx,sdx)
tabn
#                              EXAMPLE 2
top<-"Power For Sample Size n = 20 for p=0.95 gamma=0.95"
fstar <- seq(0.2,4.8,0.1)
pow <- rep(1,length(fstar))
for (i in 1 : length(fstar)) {
pow[i]<-npower.lnorm(20,NA,fstar[i],p=0.95,gamma=0.95)[2]
}
plot(fstar,pow,xlim=c(0,5),ylim=c(0,1),main=top,
xlab="fstar = True Percent of Xs > L(Specified Limit )",ylab="Power")