# npower.lnorm: Sample Size and Power For Lognormal Distribution In STAND: Statistical Analysis of Non-Detects

## 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

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.

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") ```

### Example output

```Loading required package: survival
GSD = 2.03 GSD = 2.72 GSD = 3.4 GSD = 4.11 GSD = 4.86 GSD = 5.65
0.67         58        107       154        202        249        295
0.5          24         42        59         76         93        109
0.4          16         27        37         47         57         67
0.33         13         20        28         35         42         49
```

STAND documentation built on May 2, 2019, 3:39 p.m.