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#####
# File: Script - EPA09, Chapter 06 Examples.R
#
# Purpose: Reproduce Examples in Chapter 6 of the EPA Guidance Document
#
# USEPA. (2009). "Statistical Analysis of Ground Water
# Monitoring Data at RCRA Facilities, Unified Guidance."
# EPA 530-R-09-007.
# Office of Resource Conservation and Recovery,
# Program Information and Implementation Division.
# March 2009.
#
# Author: Steven P. Millard
#
# Last
# Updated: 2013/10/15
#####
#NOTE: Unless otherwise noted, differences between what is shown in the
# EPA Guidance Document and results shown here are due to the
# EPA Guidance Document rounding intermediate results prior to
# the final result.
#######################################################################################
library(EnvStats)
# Figure 6-2, p. 6-15
#--------------------
windows()
plotPredIntNormTestPowerCurve(n = 10, k = 1,
range.delta.over.sigma = c(0, 5),
pi.type = "upper", conf.level = 0.99,
ylim = c(0, 1),
xlab = expression(paste(Delta, " (SDs above Background)")),
ylab = "Power", cex.main = 1.1,
main = "Figure 6-2. Normal Power Curve (n = 10) for 99% Prediction Limit Test")
##############################################################################
# Figure 6-3, p. 6-17
#--------------------
windows()
plotPredIntNormTestPowerCurve(n = 10, k = 1,
range.delta.over.sigma = c(0, 5),
pi.type = "upper", conf.level = 0.99,
ylim = c(0, 1),
xlab = "SD Units Above BG",
ylab = "Power",
main = "Figure 6-3. EPA Reference Power Curves")
plotPredIntNormTestPowerCurve(n = 10, k = 2, conf.level = 0.99,
add = TRUE, plot.col = "red", plot.lty = 2)
plotPredIntNormTestPowerCurve(n = 10, k = 4, conf.level = 0.99,
add = TRUE, plot.col = "blue", plot.lty = 3)
legend("topleft", c("Quarterly", "Semi-Annual", "Annual"), lty = 3:1,
lwd = 3 * par("cex"), col = c("blue", "red", "black"))
##################################################################
# Example 6-1, p. 6-18
#---------------------
predIntNormTestPower(n = 10, k = 1,
delta.over.sigma = (15 - 6) / 2,
pi.type = "upper", conf.level = 0.99)
#[1] 0.9012473
# Example 6-3, pp. 6-20 to 6-21
#------------------------------
stats <- summaryStats(Sulfate.ppm ~ 1, data = EPA.09.Ex.6.3.sulfate.df,
data.name = "Sulfate", digits = 1)
stats
# N Mean SD Median Min Max
#Sulfate 10 545 29.7 546 490 590
n <- stats[, "N"]
SD <- stats[, "SD"]
delta <- c(0, 200)
windows()
plotPredIntNormTestPowerCurve(n = n, k = 1,
axes = F,
range.delta.over.sigma = range(delta / SD),
pi.type = "upper", conf.level = 0.99,
ylim = c(0, 1),
xlab = "Sulfate Conc. Increase (ppm)",
ylab = "Power",
main = "Figure 6-3. Approximate s-Based Power Curve for Sulfate")
axis(2)
x.axis.ticks <- seq(0, 200, by = 50)
axis(1, at = x.axis.ticks / SD, labels = x.axis.ticks)
box()
abline(v = 75 / SD, lty = 2, lwd = 2)
predIntNormTestPower(n = n, k = 1, delta.over.sigma = 75 / SD,
pi.type = "upper", conf.level = 0.99)
#[1] 0.3916402
rm(stats, n, SD, delta, x.axis.ticks)
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