# Sample Size and Power For Lognormal Distribution

### 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 - |

`fstar` |
true percent of X's |

`p` |
probability for Xp the 100p |

`gamma` |
one-sided confidence level |

### 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 - |

`fstar` |
true percent of X's |

`p` |
probability for Xp the 100p |

`gamma` |
one-sided confidence level |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
# 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")
``` |