# NOT RUN {
# Look at the relationship between power and sample size
# for a one-way ANOVA, assuming k=2 groups, group means of
# 0 and 1, a population standard deviation of 1, and a
# 5% significance level:
dev.new()
plotAovDesign()
#--------------------------------------------------------------------
# Plot power vs. sample size for various levels of significance:
dev.new()
plotAovDesign(mu.vec = c(0, 0.5, 1), ylim=c(0, 1), main="")
plotAovDesign(mu.vec = c(0, 0.5, 1), alpha=0.1, add=TRUE, plot.col=2)
plotAovDesign(mu.vec = c(0, 0.5, 1), alpha=0.2, add=TRUE, plot.col=3)
legend(35, 0.6, c("20%", "10%", " 5%"), lty=1, lwd = 3, col=3:1,
bty = "n")
mtext("Power vs. Sample Size for One-Way ANOVA", line = 3, cex = 1.25)
mtext(expression(paste("with ", mu, "=(0, 0.5, 1), ", sigma,
"=1, and Various Significance Levels", sep="")),
line = 1.5, cex = 1.25)
#--------------------------------------------------------------------
# The example on pages 5-11 to 5-14 of USEPA (1989b) shows
# log-transformed concentrations of lead (mg/L) at two
# background wells and four compliance wells, where
# observations were taken once per month over four months
# (the data are stored in EPA.89b.loglead.df).
# Assume the true mean levels at each well are
# 3.9, 3.9, 4.5, 4.5, 4.5, and 5, respectively. Plot the
# power vs. sample size of a one-way ANOVA to test for mean
# differences between wells. Use alpha=0.05, and assume the
# true standard deviation is equal to the one estimated
# from the data in this example.
names(EPA.89b.loglead.df)
#[1] "LogLead" "Month" "Well" "Well.type"
# Perform the ANOVA and get the estimated sd
aov.list <- aov(LogLead ~ Well, data=EPA.89b.loglead.df)
summary(aov.list)
# Df Sum Sq Mean Sq F value Pr(>F)
#Well 5 5.7447 1.14895 3.3469 0.02599 *
#Residuals 18 6.1791 0.34328
#---
#Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 '' 1
# Now create the plot
dev.new()
plotAovDesign(range.x.var = c(2, 20),
mu.vec = c(3.9,3.9,4.5,4.5,4.5,5),
sigma=sqrt(0.34),
ylim = c(0, 1), digits=2)
# Clean up
#---------
rm(aov.list)
graphics.off()
# }
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