Plots for a Sampling Design Based on a One- or Two-Sample t-Test, Assuming Lognormal Data
Create plots involving sample size, power, ratio of means, coefficient of variation, and significance level for a one- or two-sample t-test, 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 = 1e-07, 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 x-axis.
Possible values are |
y.var |
character string indicating what variable to use for the y-axis.
Possible values are |
range.x.var |
numeric vector of length 2 indicating the range of the x-variable 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 one-sample or
two-sample 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 non-central t-distribution. 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 two-sample t-test 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.
# Look at the relationship between power and sample size for a two-sample t-test,
# 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 two-sample t-test 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",
"Two-Sample t-Test, 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 pre-established 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 one-sample 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()Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.