Summary Statistics
The summary statistics include: sample size, number of missing values, mean, standard deviation, median, min, and max. Optional additional summary statistics include 1st quartile, 3rd quartile, and stadard error.
summaryStats(object, ...)
## S3 method for class 'formula'
summaryStats(object, data = NULL, subset,
na.action = na.pass, ...)
## Default S3 method:
summaryStats(object, group = NULL,
drop.unused.levels = TRUE, se = FALSE, quartiles = FALSE,
digits = max(3, getOption("digits") - 3),
digit.type = "round", drop0trailing = TRUE,
show.na = TRUE, show.0.na = FALSE, p.value = FALSE,
p.value.digits = 2, p.value.digit.type = "signif",
test = "parametric", paired = FALSE, test.arg.list = NULL,
combine.groups = p.value, rm.group.na = TRUE,
group.p.value.type = NULL, alternative = "two.sided",
ci = NULL, ci.between = NULL, conf.level = 0.95,
stats.in.rows = FALSE,
data.name = deparse(substitute(object)), ...)
## S3 method for class 'factor'
summaryStats(object, group = NULL,
drop.unused.levels = TRUE,
digits = max(3, getOption("digits") - 3),
digit.type = "round", drop0trailing = TRUE,
show.na = TRUE, show.0.na = FALSE, p.value = FALSE,
p.value.digits = 2, p.value.digit.type = "signif",
test = "chisq", test.arg.list = NULL, combine.levels = TRUE,
combine.groups = FALSE, rm.group.na = TRUE,
ci = p.value & test != "chisq", conf.level = 0.95,
stats.in.rows = FALSE, ...)
## S3 method for class 'character'
summaryStats(object, ...)
## S3 method for class 'logical'
summaryStats(object, ...)
## S3 method for class 'data.frame'
summaryStats(object, ...)
## S3 method for class 'matrix'
summaryStats(object, ...)
## S3 method for class 'list'
summaryStats(object, ...)object |
an object for which summary statistics are desired. In the default method,
the argument |
data |
when |
subset |
when |
na.action |
when |
group |
when |
drop.unused.levels |
when |
se |
for numeric data, logical scalar indicating whether to include
the standard error of the mean in the summary statistics.
The default value is |
quartiles |
for numeric data, logical scalar indicating whether to include
the estimated 25th and 75th percentiles in the summary statistics.
The default value is |
digits |
integer indicating the number of digits to use for the summary statistics.
When |
digit.type |
character string indicating whether the |
drop0trailing |
logical scalar indicating whether to drop trailing 0's when printing the summary statistics.
The value of this argument is added as an attribute to the returned list and is used by the
|
show.na |
logical scalar indicating whether to return the number of missing values.
The default value is |
show.0.na |
logical scalar indicating whether to diplay the number of missing values in the case when
there are no missing values. The default value is |
p.value |
logical scalar indicating whether to return the p-value associated with a test of hypothesis.
The default value is |
p.value.digits |
integer indicating the number of digits to use for the p-value. When |
p.value.digit.type |
character string indicating whether the |
test |
Numeric data: character string indicating whether to compute p-values and confidence
intervals based on parametric ( Factors: character string indicating which test to perform when |
paired |
applicable only to the case when there are two groups: |
test.arg.list |
a list with additional arguments to pass to the test used to compute p-values and confidence
intervals. For numeric data, when |
combine.groups |
logical scalar indicating whether to show summary statistics for all groups combined.
Numeric data: the default value is |
rm.group.na |
logical scalar indicating whether to remove missing values from the |
group.p.value.type |
for numeric data, character string indicating which p-value(s) to compute when
there is more than one group. When |
alternative |
for numeric data, character string indicating which alternative to assume
for p-values and confidence intervals. Possible values are |
ci |
Numeric data: logical scalar indicating whether to compute a confidence interval
for the mean or each group mean. The default value is Factors: logical scalar indicating whether to compute a confidence interval. A confidence
interval is computed only if the number of levels in |
ci.between |
for numeric data, logical scalar indicating whether to compute a confidence interval
for the difference between group means when there are two groups.
The default value is |
conf.level |
numeric scalar between 0 and 1 indicating the confidence level associated with the confidence intervals.
The default value is |
stats.in.rows |
logical scalar indicating whether to show the summary statistics in the rows or columns of the
output. The default is |
data.name |
character string indicating the name of the data used for the summary statistics. |
combine.levels |
for factors, a logical scalar indicating whether to compute summary statistics based on combining all levels of a factor. |
... |
additional arguments affecting the summary statistics produced. |
an object of class "summaryStats" (see summaryStats.object.
Objects of class "summaryStats" are numeric matrices that contain the
summary statisics produced by a call to summaryStats or summaryFull.
These objects have a special printing method that by default removes
trailing zeros for sample size entries and prints blanks for statistics that are
normally displayed as NA (see print.summaryStats).
Summary statistics for numeric data include sample size, mean, standard deviation, median,
min, and max. Options include the standard error of the mean (when se=TRUE),
the estimated quartiles (when quartiles=TRUE), p-values (when p.value=TRUE),
and/or confidence intervals (when ci=TRUE and/or ci.between=TRUE).
Summary statistics for factors include the sample size for each level of the factor and the
percent of the total for that level. Options include a p-value (when p.value=TRUE).
Note that unlike the R function summary and the EnvStats function
summaryFull, by default the digits argument for the EnvStats function
summaryStats refers to how many decimal places to round to, not how many
significant digits to use (see the explanation of the argument digit.type above).
Steven P. Millard (EnvStats@ProbStatInfo.com)
Berthouex, P.M., and L.C. Brown. (2002). Statistics for Environmental Engineers, Second Edition. Lewis Publishers, Boca Raton, FL.
Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-PLUS. CRC Press, Boca Raton, FL.
Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ, Chapter 24.
# The guidance document USEPA (1994b, pp. 6.22--6.25)
# contains measures of 1,2,3,4-Tetrachlorobenzene (TcCB)
# concentrations (in parts per billion) from soil samples
# at a Reference area and a Cleanup area. These data are strored
# in the data frame EPA.94b.tccb.df.
#----------
# First, create summary statistics by area based on the log-transformed data.
summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df)
# N Mean SD Median Min Max
#Cleanup 77 -0.2377 0.5908 -0.3665 -1.0458 2.2270
#Reference 47 -0.2691 0.2032 -0.2676 -0.6576 0.1239
#----------
# Now create summary statistics by area based on the log-transformed data
# and use the t-test to compare the areas.
summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df, p.value = TRUE)
summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df,
p.value = TRUE, stats.in.rows = TRUE)
# Cleanup Reference Combined
#N 77 47 124
#Mean -0.2377 -0.2691 -0.2496
#SD 0.5908 0.2032 0.481
#Median -0.3665 -0.2676 -0.3143
#Min -1.0458 -0.6576 -1.0458
#Max 2.227 0.1239 2.227
#Diff -0.0313
#p.value.between 0.73
#95%.LCL.between -0.2082
#95%.UCL.between 0.1456
#====================================================================
# Page 9-3 of USEPA (2009) lists trichloroethene
# concentrations (TCE; mg/L) collected from groundwater at two wells.
# Here, the seven non-detects have been set to their detection limit.
#----------
# First, compute summary statistics for all TCE observations.
summaryStats(TCE.mg.per.L ~ 1, data = EPA.09.Table.9.1.TCE.df,
digits = 3, data.name = "TCE")
# N Mean SD Median Min Max NA's N.Total
#TCE 27 0.09 0.064 0.1 0.004 0.25 3 30
summaryStats(TCE.mg.per.L ~ 1, data = EPA.09.Table.9.1.TCE.df,
se = TRUE, quartiles = TRUE, digits = 3, data.name = "TCE")
# N Mean SD SE Median Min Max 1st Qu. 3rd Qu. NA's N.Total
#TCE 27 0.09 0.064 0.012 0.1 0.004 0.25 0.031 0.12 3 30
#----------
# Now compute summary statistics by well.
summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df,
digits = 3)
# N Mean SD Median Min Max NA's N.Total
#Well.1 14 0.063 0.079 0.031 0.004 0.25 1 15
#Well.2 13 0.118 0.020 0.110 0.099 0.17 2 15
summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df,
digits = 3, stats.in.rows = TRUE)
# Well.1 Well.2
#N 14 13
#Mean 0.063 0.118
#SD 0.079 0.02
#Median 0.031 0.11
#Min 0.004 0.099
#Max 0.25 0.17
#NA's 1 2
#N.Total 15 15
# If you want to keep trailing 0's, use the drop0trailing argument:
summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df,
digits = 3, stats.in.rows = TRUE, drop0trailing = FALSE)
# Well.1 Well.2
#N 14.000 13.000
#Mean 0.063 0.118
#SD 0.079 0.020
#Median 0.031 0.110
#Min 0.004 0.099
#Max 0.250 0.170
#NA's 1.000 2.000
#N.Total 15.000 15.000
#====================================================================
# Page 13-3 of USEPA (2009) lists iron concentrations (ppm) in
# groundwater collected from 6 wells.
#----------
# First, compute summary statistics for each well.
summaryStats(Iron.ppm ~ Well, data = EPA.09.Ex.13.1.iron.df,
combine.groups = FALSE, digits = 2, stats.in.rows = TRUE)
# Well.1 Well.2 Well.3 Well.4 Well.5 Well.6
#N 4 4 4 4 4 4
#Mean 47.01 55.73 90.86 70.43 145.24 156.32
#SD 12.4 20.34 59.35 25.95 92.16 51.2
#Median 50.05 57.05 76.73 76.95 137.66 171.93
#Min 29.96 32.14 39.25 34.12 60.95 83.1
#Max 57.97 76.71 170.72 93.69 244.69 198.34
#----------
# Note the large differences in standard deviations between wells.
# Compute summary statistics for log(Iron), by Well.
summaryStats(log(Iron.ppm) ~ Well, data = EPA.09.Ex.13.1.iron.df,
combine.groups = FALSE, digits = 2, stats.in.rows = TRUE)
# Well.1 Well.2 Well.3 Well.4 Well.5 Well.6
#N 4 4 4 4 4 4
#Mean 3.82 3.97 4.35 4.19 4.8 5
#SD 0.3 0.4 0.66 0.45 0.7 0.4
#Median 3.91 4.02 4.29 4.34 4.8 5.14
#Min 3.4 3.47 3.67 3.53 4.11 4.42
#Max 4.06 4.34 5.14 4.54 5.5 5.29
#----------
# Include confidence intervals for the mean log(Fe) concentration
# at each well, and also the p-value from the one-way
# analysis of variance to test for a difference in well means.
summaryStats(log(Iron.ppm) ~ Well, data = EPA.09.Ex.13.1.iron.df,
digits = 1, ci = TRUE, p.value = TRUE, stats.in.rows = TRUE)
# Well.1 Well.2 Well.3 Well.4 Well.5 Well.6 Combined
#N 4 4 4 4 4 4 24
#Mean 3.8 4 4.3 4.2 4.8 5 4.4
#SD 0.3 0.4 0.7 0.5 0.7 0.4 0.6
#Median 3.9 4 4.3 4.3 4.8 5.1 4.3
#Min 3.4 3.5 3.7 3.5 4.1 4.4 3.4
#Max 4.1 4.3 5.1 4.5 5.5 5.3 5.5
#95%.LCL 3.3 3.3 3.3 3.5 3.7 4.4 4.1
#95%.UCL 4.3 4.6 5.4 4.9 5.9 5.6 4.6
#p.value.between 0.025
#====================================================================
# Using the built-in dataset HairEyeColor, summarize the frequencies
# of hair color and test whether there is a difference in proportions.
# NOTE: The data that was originally factor data has already been
# collapsed into frequency counts by catetory in the object
# HairEyeColor. In the examples in this section, we recreate
# the factor objects in order to show how summaryStats works
# for factor objects.
Hair <- apply(HairEyeColor, 1, sum)
Hair
#Black Brown Red Blond
# 108 286 71 127
Hair.color <- names(Hair)
Hair.fac <- factor(rep(Hair.color, times = Hair),
levels = Hair.color)
#----------
# Compute summary statistics and perform the chi-square test
# for equal proportions of hair color
summaryStats(Hair.fac, digits = 1, p.value = TRUE)
# N Pct ChiSq_p
#Black 108 18.2
#Brown 286 48.3
#Red 71 12.0
#Blond 127 21.5
#Combined 592 100.0 2.5e-39
#----------
# Now test the hypothesis that 10% of the population from which
# this sample was drawn has Red hair, and compute a 95% confidence
# interval for the percent of subjects with red hair.
Red.Hair.fac <- factor(Hair.fac == "Red", levels = c(TRUE, FALSE),
labels = c("Red", "Not Red"))
summaryStats(Red.Hair.fac, digits = 1, p.value = TRUE,
ci = TRUE, test = "binom", test.arg.list = list(p = 0.1))
# N Pct Exact_p 95%.LCL 95%.UCL
#Red 71 12 9.5 14.9
#Not Red 521 88
#Combined 592 100 0.11
#----------
# Now test whether the percent of people with Green eyes is the
# same for people with and without Red hair.
HairEye <- apply(HairEyeColor, 1:2, sum)
Hair.color <- rownames(HairEye)
Eye.color <- colnames(HairEye)
n11 <- HairEye[Hair.color == "Red", Eye.color == "Green"]
n12 <- sum(HairEye[Hair.color == "Red", Eye.color != "Green"])
n21 <- sum(HairEye[Hair.color != "Red", Eye.color == "Green"])
n22 <- sum(HairEye[Hair.color != "Red", Eye.color != "Green"])
Hair.fac <- factor(rep(c("Red", "Not Red"), c(n11+n12, n21+n22)),
levels = c("Red", "Not Red"))
Eye.fac <- factor(c(rep("Green", n11), rep("Not Green", n12),
rep("Green", n21), rep("Not Green", n22)),
levels = c("Green", "Not Green"))
#----------
# Here are the results using the chi-square test and computing
# confidence limits for the difference between the two percentages
summaryStats(Eye.fac, group = Hair.fac, digits = 1,
p.value = TRUE, ci = TRUE, test = "prop",
stats.in.rows = TRUE, test.arg.list = list(correct = FALSE))
# Green Not Green Combined
#Red(N) 14 57 71
#Red(Pct) 19.7 80.3 100
#Not Red(N) 50 471 521
#Not Red(Pct) 9.6 90.4 100
#ChiSq_p 0.01
#95%.LCL.between 0.5
#95%.UCL.between 19.7
#----------
# Here are the results using Fisher's exact test and computing
# confidence limits for the odds ratio
summaryStats(Eye.fac, group = Hair.fac, digits = 1,
p.value = TRUE, ci = TRUE, test = "fisher",
stats.in.rows = TRUE)
# Green Not Green Combined
#Red(N) 14 57 71
#Red(Pct) 19.7 80.3 100
#Not Red(N) 50 471 521
#Not Red(Pct) 9.6 90.4 100
#Fisher_p 0.015
#95%.LCL.OR 1.1
#95%.UCL.OR 4.6
rm(Hair, Hair.color, Hair.fac, Red.Hair.fac, HairEye, Eye.color,
n11, n12, n21, n22, Eye.fac)
#====================================================================
# The data set EPA.89b.cadmium.df contains information on
# cadmium concentrations in groundwater collected from a
# background and compliance well. Compare detection frequencies
# between the well types and test for a difference using
# Fisher's exact test.
summaryStats(factor(Censored) ~ Well.type, data = EPA.89b.cadmium.df,
digits = 1, p.value = TRUE, test = "fisher")
summaryStats(factor(Censored) ~ Well.type, data = EPA.89b.cadmium.df,
digits = 1, p.value = TRUE, test = "fisher", stats.in.rows = TRUE)
# FALSE TRUE Combined
#Background(N) 8 16 24
#Background(Pct) 33.3 66.7 100
#Compliance(N) 24 40 64
#Compliance(Pct) 37.5 62.5 100
#Fisher_p 0.81
#95%.LCL.OR 0.3
#95%.UCL.OR 2.5
#====================================================================
#--------------------
# Paired Observations
#--------------------
# The data frame ACE.13.TCE.df contians paired observations of
# trichloroethylene (TCE; mg/L) at 10 groundwater monitoring wells
# before and after remediation.
#
# Compare TCE concentrations before and after remediation and
# use a paired t-test to test for a difference between periods.
summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df,
p.value = TRUE, paired = TRUE)
summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df,
p.value = TRUE, paired = TRUE, stats.in.rows = TRUE)
# Before After Combined
#N 10 10 20
#Mean 21.624 3.6329 12.6284
#SD 13.5113 3.5544 13.3281
#Median 20.3 2.48 8.475
#Min 5.96 0.272 0.272
#Max 41.5 10.7 41.5
#Diff -17.9911
#paired.p.value.between 0.0027
#95%.LCL.between -27.9097
#95%.UCL.between -8.0725
#==========
# Repeat the last example, but use a one-sided alternative since
# remediation should decrease TCE concentration.
summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df,
p.value = TRUE, paired = TRUE, alternative = "less")
summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df,
p.value = TRUE, paired = TRUE, alternative = "less",
stats.in.rows = TRUE)
# Before After Combined
#N 10 10 20
#Mean 21.624 3.6329 12.6284
#SD 13.5113 3.5544 13.3281
#Median 20.3 2.48 8.475
#Min 5.96 0.272 0.272
#Max 41.5 10.7 41.5
#Diff -17.9911
#paired.p.value.between.less 0.0013
#95%.LCL.between -Inf
#95%.UCL.between -9.9537Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.