plotTTestLnormAltDesign.RdCreate 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$digits, cex.main = par("cex"), ...,
main = NULL, xlab = NULL, ylab = NULL, type = "l")character string indicating what variable to use for the x-axis.
Possible values are "n" (sample size; the default),
"ratio.of.means" (minimal or maximal detectable ratio of means),
"cv" (coefficient of variaiton), "power" (power of the test), and
"alpha" (significance level of the test).
character string indicating what variable to use for the y-axis.
Possible values are "power" (power of the test; the default),
"ratio.of.means" (minimal or maximal detectable ratio of means), and
"n" (sample size).
numeric vector of length 2 indicating the range of the x-variable to use
for the plot. The default value depends on the value of x.var:
When x.var="n" the default value is c(2,50).
When x.var="ratio.of.means" and alternative="greater" or alternative="two.sided" and two.sided.direction="greater",
the default value is c(1, 2).
When x.var="delta" and alternative="less" or alternative="two.sided" and two.sided.direction="less",
the default value is c(0.5, 1).
When x.var="cv" the default value is c(0.5, 2).
When x.var="power" the default value is c(alpha + .Machine$double.eps, 0.95).
When x.var="alpha", the default value is c(0.01, 0.2).
numeric scalar indicating the sample size. The default value is
n.or.n1=25. When sample.type="one.sample", n.or.n1
denotes the number of observations in the single sample. When
sample.type="two.sample", n.or.n1 denotes the number of
observations from group 1. Missing (NA), undefined (NaN),
and infinite (Inf, -Inf) values are not allowed. This
argument is ignored if either x.var="n" or y.var="n".
numeric scalar indicating the sample size for group 2. The default value
is the value of n.or.n1. Missing (NA), undefined (NaN),
and infinite (Inf, -Inf) values are not allowed. This
argument is ignored when sample.type="one.sample".
numeric scalar specifying the ratio of the first mean to the second mean. When
sample.type="one.sample", this is the ratio of the population mean to the
hypothesized mean. When sample.type="two.sample", this is the ratio of the
mean of the first population to the mean of the second population.
When alternative="greater" or alternative="two.sided" and two.sided.direction="greater", the default value is ratio.of.means=2.
When alternative="less" or alternative="two.sided" and
two.sided.direction="less", the default value is ratio.of.means=0.5.
This argument is ignored when x.var="ratio.of.means" or y.var="ratio.of.means".
numeric scalar: a positive value specifying the coefficient of
variation. When sample.type="one.sample", this is the population coefficient
of variation. When sample.type="two.sample", this is the coefficient of
variation for both the first and second population. The default value is cv=1.
numeric scalar between 0 and 1 indicating the Type I error level
associated with the hypothesis test. The default value is alpha=0.05.
numeric scalar between 0 and 1 indicating the power
associated with the hypothesis test. The default value is power=0.95.
character string indicating whether to compute power based on a one-sample or
two-sample hypothesis test. When sample.type="one.sample", the computed
power is based on a hypothesis test for a single mean. When sample.type="two.sample", the computed power is based on a hypothesis test
for the difference between two means. The default value is sample.type="one.sample" unless the argument n2 is supplied.
character string indicating the kind of alternative hypothesis. The possible values
are "two.sided" (the default), "greater", and "less".
character string indicating the direction (greater than 1 or less than 1) for the
detectable ratio of means when alternative="two.sided". When two.sided.direction="greater" (the default), the detectable ratio of means
is greater than 1. When two.sided.direction="less", the detectable ratio of
means is less than 1 (but greater than 0). This argument is ignored if
alternative="less" or alternative="greater".
logical scalar indicating whether to compute the power based on an approximation to
the non-central t-distribution. The default value is approx=FALSE.
logical scalar indicating whether to round up the values of the computed
sample size(s) to the next smallest integer. The default value is
TRUE.
for the case when y.var="n", a positive integer greater than 1 indicating
the maximum sample size when sample.type="one.sample" or the maximum sample
size for group 1 when sample.type="two.sample". The default value is
n.max=5000.
numeric scalar indicating the toloerance to use in the
uniroot search algorithm.
The default value is tol=1e-7.
positive integer indicating the maximum number of iterations
argument to pass to the uniroot function. The default
value is maxiter=1000.
a logical scalar indicating whether to create a new plot or add to the existing plot
(see add) on the current graphics device. If plot.it=FALSE, no plot
is produced, but a list of (x,y) values is returned (see VALUE). The default value
is plot.it=TRUE.
a logical scalar indicating whether to add the design plot to the
existing plot (add=TRUE), or to create a plot from scratch
(add=FALSE). The default value is add=FALSE.
This argument is ignored if plot.it=FALSE.
a numeric scalar specifying how many (x,y) pairs to use to produce the plot.
There are n.points x-values evenly spaced between range.x.var[1] and range.x.var[2]. The default value is n.points=100.
a numeric scalar or character string determining the color of the plotted
line or points. The default value is plot.col="black". See the
entry for col in the help file for par
for more information.
a numeric scalar determining the width of the plotted line. The default value is
3*par("cex"). See the entry for lwd in the help file for par
for more information.
a numeric scalar determining the line type of the plotted line. The default value is
plot.lty=1. See the entry for lty in the help file for par
for more information.
a scalar indicating how many significant digits to print out on the plot. The default
value is the current setting of options("digits").
additional graphical parameters (see par).
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.
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()