Sample Size and Power For Lognormal Distribution

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Description

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

Usage

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

Arguments

n

sample size

power

power of the test = 1 - β

fstar

true percent of X's limit L

p

probability for Xp the 100pth percentile. Default is 0.95

gamma

one-sided confidence level γ. 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 ≥ 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 γ\% 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 ≥ Lp at the α = (1- γ ) significance level. See efraction.exact, percentile.exact and Section 2.3 of Frome and Wambach(2005) for further details.

Value

A vector with components:

n

sample size

power

power of the test = 1 -β

fstar

true percent of X's limit L

p

probability for Xp the 100pth percentile. Default is 0.95

gamma

one-sided confidence level γ. Default is 0.95

Note

The R function uniroot is used to find a parameter of the non-central t distribution. In some versions of R this may cause a warning message. See R bug report RP 9171 full precision was not achieved in 'pnt'. This warning message may occur in uniroot calls to pt and does not effect the precision of the final result

Author(s)

E.L. Frome

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

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#                              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")

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