# Look at plots and summary statistics for the TcCB data given in
# USEPA (1994b), (the data are stored in EPA.94b.tccb.df).
# Arbitrarily set the one censored observation to the censoring level.
# Group by the variable Area.
EPA.94b.tccb.df
# TcCB.orig TcCB Censored Area
#1 0.22 0.22 FALSE Reference
#2 0.23 0.23 FALSE Reference
#...
#46 1.20 1.20 FALSE Reference
#47 1.33 1.33 FALSE Reference
#48 <0.09 0.09 TRUE Cleanup
#49 0.09 0.09 FALSE Cleanup
#...
#123 51.97 51.97 FALSE Cleanup
#124 168.64 168.64 FALSE Cleanup
# First plot the data
#--------------------
dev.new()
stripChart(TcCB ~ Area, data = EPA.94b.tccb.df,
xlab = "Area", ylab = "TcCB (ppb)")
mtext("TcCB Concentrations by Area", line = 3, cex = 1.25, font = 2)
dev.new()
stripChart(log10(TcCB) ~ Area, data = EPA.94b.tccb.df,
p.value = TRUE,
xlab = "Area", ylab = expression(paste(log[10], " [ TcCB (ppb) ]")))
mtext(expression(paste(log[10], "(TcCB) Concentrations by Area")),
line = 3, cex = 1.25, font = 2)
#--------------------------------------------------------------------
# Now compute summary statistics
#-------------------------------
sum(EPA.94b.tccb.df$Censored)
#[1] 1
with(EPA.94b.tccb.df, TcCB[Censored])
#0.09
# Summary statistics will treat the one censored value
# as assuming the detection limit.
summaryFull(TcCB ~ Area, data = EPA.94b.tccb.df)
# Cleanup Reference
#N 77 47
#Mean 3.915 0.5985
#Median 0.43 0.54
#10% Trimmed Mean 0.6846 0.5728
#Geometric Mean 0.5784 0.5382
#Skew 7.717 0.9019
#Kurtosis 62.67 0.132
#Min 0.09 0.22
#Max 168.6 1.33
#Range 168.5 1.11
#1st Quartile 0.23 0.39
#3rd Quartile 1.1 0.75
#Standard Deviation 20.02 0.2836
#Geometric Standard Deviation 3.898 1.597
#Interquartile Range 0.87 0.36
#Median Absolute Deviation 0.3558 0.2669
#Coefficient of Variation 5.112 0.4739
summaryStats(TcCB ~ Area, data = EPA.94b.tccb.df, digits = 1)
# N Mean SD Median Min Max
#Cleanup 77 3.9 20.0 0.4 0.1 168.6
#Reference 47 0.6 0.3 0.5 0.2 1.3
#----------------------------------------------------------------
# Compute Shapiro-Wilk Goodness-of-Fit statistic for the
# Reference Area TcCB data assuming a lognormal distribution
#-----------------------------------------------------------
sw.list <- gofTest(TcCB ~ 1, data = EPA.94b.tccb.df,
subset = Area == "Reference", dist = "lnorm")
sw.list
# Results of Goodness-of-Fit Test
# -------------------------------
#
# Test Method: Shapiro-Wilk GOF
#
# Hypothesized Distribution: Lognormal
#
# Estimated Parameter(s): meanlog = -0.6195712
# sdlog = 0.4679530
#
# Estimation Method: mvue
#
# Data: TcCB
#
# Subset With: Area == "Reference"
#
# Data Source: EPA.94b.tccb.df
#
# Sample Size: 47
#
# Test Statistic: W = 0.978638
#
# Test Statistic Parameter: n = 47
#
# P-value: 0.5371935
#
# Alternative Hypothesis: True cdf does not equal the
# Lognormal Distribution.
#----------
# Plot results of GOF test
dev.new()
plot(sw.list)
#----------------------------------------------------------------
# Based on the Reference Area data, estimate 90th percentile
# and compute a 95% confidence limit for the 90th percentile
# assuming a lognormal distribution.
#------------------------------------------------------------
with(EPA.94b.tccb.df,
eqlnorm(TcCB[Area == "Reference"], p = 0.9, ci = TRUE))
# Results of Distribution Parameter Estimation
# --------------------------------------------
#
# Assumed Distribution: Lognormal
#
# Estimated Parameter(s): meanlog = -0.6195712
# sdlog = 0.4679530
#
# Estimation Method: mvue
#
# Estimated Quantile(s): 90'th %ile = 0.9803307
#
# Quantile Estimation Method: qmle
#
# Data: TcCB[Area == "Reference"]
#
# Sample Size: 47
#
# Confidence Interval for: 90'th %ile
#
# Confidence Interval Method: Exact
#
# Confidence Interval Type: two-sided
#
# Confidence Level: 95%
#
# Confidence Interval: LCL = 0.8358791
UCL = 1.2154977
#----------
# Cleanup
rm(TcCB.ref, sw.list)
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