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plotPredIntNormDesign(x.var = "n", y.var = "half.width", range.x.var = NULL, n = 25, k = 1, n.mean = 1, half.width = 4 * sigma.hat, sigma.hat = 1, method = "Bonferroni", conf.level = 0.95, round.up = FALSE, n.max = 5000, tol = 1e-07, maxiter = 1000, plot.it = TRUE, add = FALSE, n.points = 100, 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")"n" (sample size; the default),
"half.width" (the half-width of the confidence interval),
"k" (number of future observations or averages),
"sigma.hat" (the estimated standard deviation), and
"conf.level" (the confidence level).
"half.width" (the half-width of the confidence interval;
the default), and "n" (sample size).
x.var.
When x.var="n" the default value is c(2,50).
When x.var="half.width" the default value is c(2.5 * sigma.hat, 4 * sigma.hat).
When x.var="k" the default value is c(1, 20).
When x.var="sigma.hat", the default value is c(0.1, 2).
When x.var="conf.level", the default value is c(0.5, 0.99).
n=25.
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.
conf.level. The default value is k=1. This argument is
ignored if x.var="k".
n.mean=1 (i.e., individual observations).
Note that all future averages must be based on the same sample size.
half.width=4*sigma.hat. This argument is ignored
if either x.var="half.width" or y.var="half.width".
sigma.hat=1. This argument is ignored if
x.var="sigma.hat".
k) is greater than 1. The possible values are method="Bonferroni"
(approximate method based on Bonferonni inequality; the default), and
method="exact" (exact method due to Dunnett, 1955).
This argument is ignored if k=1.
conf.level=0.95.
y.var="n", logical scalar indicating whether to round
up the values of the computed sample
sizes to the next smallest integer. The default value is round.up=TRUE.
y.var="n", the maximum possible sample size. The default
value is n.max=5000.
uniroot
search algorithm. The default value is tol=1e-7.
uniroot search algorithm. The default value is
maxiter=1000.
add below) on the current graphics device.
If plot.it=FALSE, no plot is produced, but a list of (x,y) values is returned
(see the section VALUE). The default value is plot.it=TRUE.
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.
n.points x-values evenly spaced between range.x.var[1] and
range.x.var[2]. The default value is n.points=100.
plot.col="black". See the entry for col in the help file for par
for more information.
3*par("cex"). See the entry for lwd in the help file for par
for more information.
plot.lty=1. See the entry for lty in the help file for par
for more information.
options("digits").
par).
plotPredIntNormDesign invisibly returns a list with components:predIntNorm, predIntNormK,
predIntNormHalfWidth, and predIntNormN for
information on how to compute a prediction interval for the next $k$
observations or averages from a normal distribution, how the half-width is
computed when other quantities are fixed, and how the
sample size is computed when other quantities are fixed.
predIntNorm.
predIntNorm, predIntNormK,
predIntNormHalfWidth, predIntNormN,
Normal.
# Look at the relationship between half-width and sample size for a
# prediction interval for k=1 future observation, assuming an estimated
# standard deviation of 1 and a confidence level of 95%:
dev.new()
plotPredIntNormDesign()
#==========
# Plot sample size vs. the estimated standard deviation for various levels
# of confidence, using a half-width of 4:
dev.new()
plotPredIntNormDesign(x.var = "sigma.hat", y.var = "n", range.x.var = c(1, 2),
ylim = c(0, 90), main = "")
plotPredIntNormDesign(x.var = "sigma.hat", y.var = "n", range.x.var = c(1, 2),
conf.level = 0.9, add = TRUE, plot.col = "red")
plotPredIntNormDesign(x.var = "sigma.hat", y.var = "n", range.x.var = c(1, 2),
conf.level = 0.8, add = TRUE, plot.col = "blue")
legend("topleft", c("95%", "90%", "80%"), lty = 1, lwd = 3 * par("cex"),
col = c("black", "red", "blue"), bty = "n")
title(main = paste("Sample Size vs. Sigma Hat for Prediction Interval for",
"k=1 Future Obs, Half-Width=4, and Various Confidence Levels",
sep = "\n"))
#==========
# The data frame EPA.92c.arsenic3.df contains arsenic concentrations (ppb)
# collected quarterly for 3 years at a background well and quarterly for
# 2 years at a compliance well. Using the data from the background well,
# plot the relationship between half-width and sample size for a two-sided
# 90% prediction interval for k=4 future observations.
EPA.92c.arsenic3.df
# Arsenic Year Well.type
#1 12.6 1 Background
#2 30.8 1 Background
#3 52.0 1 Background
#...
#18 3.8 5 Compliance
#19 2.6 5 Compliance
#20 51.9 5 Compliance
mu.hat <- with(EPA.92c.arsenic3.df,
mean(Arsenic[Well.type=="Background"]))
mu.hat
#[1] 27.51667
sigma.hat <- with(EPA.92c.arsenic3.df,
sd(Arsenic[Well.type=="Background"]))
sigma.hat
#[1] 17.10119
dev.new()
plotPredIntNormDesign(x.var = "n", y.var = "half.width", range.x.var = c(4, 50),
k = 4, sigma.hat = sigma.hat, conf.level = 0.9)
#==========
# Clean up
#---------
rm(mu.hat, sigma.hat)
graphics.off()
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