plotTTestLnormAltDesign {EnvStats}  R Documentation 
Create plots involving sample size, power, ratio of means, coefficient of variation, and significance level for a one or twosample ttest, assuming lognormal data.
plotTTestLnormAltDesign(x.var = "n", y.var = "power", range.x.var = NULL,
n.or.n1 = 25, n2 = n.or.n1,
ratio.of.means = switch(alternative, greater = 2, less = 0.5,
two.sided = ifelse(two.sided.direction == "greater", 2, 0.5)),
cv = 1, alpha = 0.05, power = 0.95,
sample.type = ifelse(!missing(n2), "two.sample", "one.sample"),
alternative = "two.sided", two.sided.direction = "greater", approx = FALSE,
round.up = FALSE, n.max = 5000, tol = 1e07, maxiter = 1000, plot.it = TRUE,
add = FALSE, n.points = 50, plot.col = "black", plot.lwd = 3 * par("cex"),
plot.lty = 1, digits = .Options$digits, cex.main = par("cex"), ...,
main = NULL, xlab = NULL, ylab = NULL, type = "l")
x.var 
character string indicating what variable to use for the xaxis.
Possible values are 
y.var 
character string indicating what variable to use for the yaxis.
Possible values are 
range.x.var 
numeric vector of length 2 indicating the range of the xvariable to use
for the plot. The default value depends on the value of

n.or.n1 
numeric scalar indicating the sample size. The default value is

n2 
numeric scalar indicating the sample size for group 2. The default value
is the value of 
ratio.of.means 
numeric scalar specifying the ratio of the first mean to the second mean. When
When 
cv 
numeric scalar: a positive value specifying the coefficient of
variation. When 
alpha 
numeric scalar between 0 and 1 indicating the Type I error level
associated with the hypothesis test. The default value is 
power 
numeric scalar between 0 and 1 indicating the power
associated with the hypothesis test. The default value is 
sample.type 
character string indicating whether to compute power based on a onesample or
twosample hypothesis test. When 
alternative 
character string indicating the kind of alternative hypothesis. The possible values
are 
two.sided.direction 
character string indicating the direction (greater than 1 or less than 1) for the
detectable ratio of means when 
approx 
logical scalar indicating whether to compute the power based on an approximation to
the noncentral tdistribution. The default value is 
round.up 
logical scalar indicating whether to round up the values of the computed
sample size(s) to the next smallest integer. The default value is

n.max 
for the case when 
tol 
numeric scalar indicating the toloerance to use in the

maxiter 
positive integer indicating the maximum number of iterations
argument to pass to the 
plot.it 
a logical scalar indicating whether to create a new plot or add to the existing plot
(see 
add 
a logical scalar indicating whether to add the design plot to the
existing plot ( 
n.points 
a numeric scalar specifying how many (x,y) pairs to use to produce the plot.
There are 
plot.col 
a numeric scalar or character string determining the color of the plotted
line or points. The default value is 
plot.lwd 
a numeric scalar determining the width of the plotted line. The default value is

plot.lty 
a numeric scalar determining the line type of the plotted line. The default value is

digits 
a scalar indicating how many significant digits to print out on the plot. The default
value is the current setting of 
cex.main , main , xlab , ylab , type , ... 
additional graphical parameters (see 
See the help files for tTestLnormAltPower
,
tTestLnormAltN
, and tTestLnormAltRatioOfMeans
for
information on how to compute the power, sample size, or ratio of means for a
one or twosample ttest assuming lognormal data.
plotTTestLnormAltDesign
invisibly returns a list with components
x.var
and y.var
, giving coordinates of the points that have
been or would have been plotted.
See the help files for tTestLnormAltPower
,
tTestLnormAltN
, and tTestLnormAltRatioOfMeans
.
Steven P. Millard (EnvStats@ProbStatInfo.com)
See the help files for tTestLnormAltPower
,
tTestLnormAltN
, and tTestLnormAltRatioOfMeans
.
tTestLnormAltPower
, tTestLnormAltN
,
tTestLnormAltRatioOfMeans
, t.test
.
# Look at the relationship between power and sample size for a twosample ttest,
# assuming lognormal data, a ratio of means of 2, a coefficient of variation
# of 1, and a 5% significance level:
dev.new()
plotTTestLnormAltDesign(sample.type = "two")
#
# For a twosample ttest based on lognormal data, plot sample size vs. the
# minimal detectable ratio for various levels of power, assuming a coefficient
# of variation of 1 and using a 5% significance level:
dev.new()
plotTTestLnormAltDesign(x.var = "ratio.of.means", y.var = "n",
range.x.var = c(1.5, 2), sample.type = "two", ylim = c(20, 120), main="")
plotTTestLnormAltDesign(x.var = "ratio.of.means", y.var = "n",
range.x.var = c(1.5, 2), sample.type="two", power = 0.9,
add = TRUE, plot.col = "red")
plotTTestLnormAltDesign(x.var = "ratio.of.means", y.var = "n",
range.x.var = c(1.5, 2), sample.type="two", power = 0.8,
add = TRUE, plot.col = "blue")
legend("topright", c("95%", "90%", "80%"), lty=1, lwd = 3*par("cex"),
col = c("black", "red", "blue"), bty = "n")
title(main = paste("Sample Size vs. Ratio of Lognormal Means for",
"TwoSample tTest, with CV=1, Alpha=0.05 and Various Powers",
sep="\n"))
#==========
# The guidance document Soil Screening Guidance: Technical Background Document
# (USEPA, 1996c, Part 4) discusses sampling design and sample size calculations
# for studies to determine whether the soil at a potentially contaminated site
# needs to be investigated for possible remedial action. Let 'theta' denote the
# average concentration of the chemical of concern. The guidance document
# establishes the following goals for the decision rule (USEPA, 1996c, p.87):
#
# Pr[Decide Don't Investigate  theta > 2 * SSL] = 0.05
#
# Pr[Decide to Investigate  theta <= (SSL/2)] = 0.2
#
# where SSL denotes the preestablished soil screening level.
#
# These goals translate into a Type I error of 0.2 for the null hypothesis
#
# H0: [theta / (SSL/2)] <= 1
#
# and a power of 95% for the specific alternative hypothesis
#
# Ha: [theta / (SSL/2)] = 4
#
# Assuming a lognormal distribution, a coefficient of variation of 2, and the above
# values for Type I error and power, create a performance goal diagram
# (USEPA, 1996c, p.89) showing the power of a onesample test versus the minimal
# detectable ratio of theta/(SSL/2) when the sample size is 6 and the exact power
# calculations are used.
dev.new()
plotTTestLnormAltDesign(x.var = "ratio.of.means", y.var = "power",
range.x.var = c(1, 5), n.or.n1 = 6, cv = 2, alpha = 0.2,
alternative = "greater", approx = FALSE, ylim = c(0.2, 1),
xlab = "theta / (SSL/2)")
#==========
# Clean up
#
graphics.off()