# NOT RUN {
# 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()
# }
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