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Statistics Workshop
R graphics handout
Statistical Consulting ServiceThe Department of StatisticsThe University of Auckland
June 30, 2011
List of Figures
1 Boxplot with 5-number-summary . . . . . . . . . . . . . . . . . . 32 Boxplot showing right-skewed distribution . . . . . . . . . . . . . 43 Boxplot showing left-skewed distribution . . . . . . . . . . . . . . 54 Univariate Normal QQ plot . . . . . . . . . . . . . . . . . . . . . 65 Histogram showing normal distribution . . . . . . . . . . . . . . . 76 Histogram and boxplot showing normal distribution . . . . . . . 87 Histogram showing left skewed distribution . . . . . . . . . . . . 98 Histogram and boxplot showing left skewed distribution . . . . . 109 Histogram showing uniform distribution . . . . . . . . . . . . . . 1110 Histogram and boxplot showing uniform distribution . . . . . . . 1211 Piechart Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312 Barplot Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 1413 Scatterplot Example . . . . . . . . . . . . . . . . . . . . . . . . . 1514 Scatterplot pointing out the negative x values . . . . . . . . . . . 1615 Scatterplot with outlier . . . . . . . . . . . . . . . . . . . . . . . 1716 Scatterplot with mistake? . . . . . . . . . . . . . . . . . . . . . . 1817 Scatterplot with NOBEL PRIZE!! . . . . . . . . . . . . . . . . . 1918 Scatterplot without the outlier and the negative weights . . . . . 2019 Scatterplot with the fitted line . . . . . . . . . . . . . . . . . . . 2120 Two way frequency table of counts on a barplot . . . . . . . . . . 2221 Two way frequency table of percentage on a barplot . . . . . . . 2322 Boxplots with homogeneous variances . . . . . . . . . . . . . . . 2423 Boxplots with heterogeneous variances . . . . . . . . . . . . . . . 2524 Q-Q Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2625 Three way frequency on a barplot . . . . . . . . . . . . . . . . . . 2826 Polynomial relationship between two continuous variables . . . . 2927 Trellis graph with three continuous variables . . . . . . . . . . . . 30
1
28 Trellis graph with two qualitative variables and one quantitativevariable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
29 Iris scatterplot of Petal Length against Petal Width . . . . . . . 3230 Iris scatterplot with different species . . . . . . . . . . . . . . . . 3331 Iris trellis scatterplot graphs . . . . . . . . . . . . . . . . . . . . . 3432 Iris pairs plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3533 Iris trellis graphs with more than three variables . . . . . . . . . 3634 Iris trellis graphs with measurements from four different days . . 3735 PCA on iris data with the first two components . . . . . . . . . . 38
2
plot.new()
plot.window(xlim = c(1, 2), ylim = c(0, 55))
boxplot(1:45, add = T, at = 1.3, border = "red")
lines(x = c(0, 1.2), y = rep(1, 2), lty = 3, col = "grey")
lines(x = c(0, 1.1), y = rep(12, 2), lty = 3, col = "grey")
lines(x = c(0, 1.1), y = rep(23, 2), lty = 3, col = "grey")
lines(x = c(0, 1.1), y = rep(34, 2), lty = 3, col = "grey")
lines(x = c(0, 1.2), y = rep(45, 2), lty = 3, col = "grey")
text(1.9, 1, "Minimum", cex = 1.5)
text(1.9, 12, "1st Quantile", cex = 1.5)
text(1.9, 23, "Median", cex = 1.5)
text(1.9, 34, "3rd Quantile", cex = 1.5)
text(1.9, 45, "Maximum", cex = 1.5)
text(1.9, 50, "Outlier?", cex = 1.5)
arrows(rep(1.51, 6), c(1, 12, 23, 34, 45, 50), rep(1.7, 6), c(1,
12, 23, 34, 45, 50), length = 0.1, code = 3)
points(1.3, 50, col = "red")
010
2030
4050
Minimum
1st Quantile
Median
3rd Quantile
Maximum
Outlier?●
Figure 1: Boxplot with 5-number-summary
3
boxplot(exp(seq(1, 5, length.out = 500)))
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Figure 2: Boxplot showing right-skewed distribution
4
boxplot(log(seq(1, 20, length.out = 500)))
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Figure 3: Boxplot showing left-skewed distribution
5
x <- exp(seq(1, 3, length.out = 100)) + rnorm(100)
qqnorm(x, main = "")
qqline(x, col = "red", lwd = 2)
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−2 −1 0 1 2
510
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Theoretical Quantiles
Sam
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Qua
ntile
s
Figure 4: Univariate Normal QQ plot
6
hist1 <- rnorm(10000)
hist(hist1, breaks = 40, main = "Histogram showing Normal
Distribution", xlab = "", ylim = c(0, 1100))
box()
Histogram showing Normal Distribution
Fre
quen
cy
−4 −2 0 2 4
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060
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010
00
Figure 5: Histogram showing normal distribution
7
hist(hist1, breaks = 40, main = "Histogram and boxplot showing Normal
Distribution", xlab = "", ylim = c(0, 1100))
boxplot(hist1, horizontal = T, at = 1000, add = T, boxwex = 250)
Histogram and boxplot showing Normal Distribution
Fre
quen
cy
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Figure 6: Histogram and boxplot showing normal distribution
8
hist2 <- log(rnorm(10000)) + 10
hist(hist2, breaks = 60, main = "Histogram showing left skewed
distribution",
xlab = "", ylim = c(0, 600))
box()
Histogram showing left skewed distribution
Fre
quen
cy
2 4 6 8 10
010
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030
040
050
060
0
Figure 7: Histogram showing left skewed distribution
9
hist(hist2, breaks = 60, main = "Histogram and boxplot showing left
skewed istribution",
xlab = "", ylim = c(0, 600))
boxplot(hist2, horizontal = T, at = 550, add = T, boxwex = 120)
Histogram and boxplot showing left skewed istribution
Fre
quen
cy
2 4 6 8 10
010
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040
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060
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2 4 6 8 10
Figure 8: Histogram and boxplot showing left skewed distribution
10
hist3 <- runif(1000)
hist(hist3, breaks = 30, main = "Histogram showing uniform
distribution",
xlab = "", ylim = c(0, 80))
box()
Histogram showing uniform distribution
Fre
quen
cy
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020
4060
80
Figure 9: Histogram showing uniform distribution
11
hist(hist3, breaks = 30, main = "Histogram and boxplot showing uniform
distribution",
xlab = "", ylim = c(0, 80))
boxplot(hist3, horizontal = T, at = 75, add = T, boxwex = 10)
Histogram and boxplot showing uniform distribution
Fre
quen
cy
0.0 0.2 0.4 0.6 0.8 1.0
020
4060
80
0.0 0.2 0.4 0.6 0.8 1.0
Figure 10: Histogram and boxplot showing uniform distribution
12
count <- c(250,34,101,22)
order.count <- order(count, decreasing = T)
phylum <- c("Molluscs", "Annelids", "Arthropods", "Echinoderms")
pie(count[order.count], labels = phylum[order.count], col = 2:5)
Molluscs
Arthropods
Annelids
Echinoderms
Figure 11: Piechart Example
13
barplot(count[order.count]/sum(count) * 100, names.arg =
phylum[order.count], ylab = "Percentage", xlab = "Phylum")
Molluscs Arthropods Annelids Echinoderms
Phylum
Per
cent
age
010
2030
4050
60
Figure 12: Barplot Example
14
set.seed(07012011)
x <- c(rnorm(99, 0, 10) + 1:99, 2)
y <- c(rnorm(99, 0, 10) + 150:248, 260)
plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)")
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Weight (g)
Foo
d C
onsu
mpt
ion
(mg/
day)
Figure 13: Scatterplot Example
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plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)")
points(x[which(x<0)], y[which(x<0)], pch = 20, col = "black", bg = "black")
abline(v = 0, lty = 2)
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Weight (g)
Foo
d C
onsu
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(mg/
day)
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Figure 14: Scatterplot pointing out the negative x values
16
plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)")
points(2, 260, pch = 20, col = "black", bg = "black")
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Weight (g)
Foo
d C
onsu
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(mg/
day)
●
Figure 15: Scatterplot with outlier
17
plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)")
points(2, 260, pch = 20, col = "black", bg = "black")
text(20, 261, labels = "Mistake??", cex = 1.5)
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onsu
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(mg/
day)
● Mistake?
Figure 16: Scatterplot with mistake?
18
plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)")
points(2, 260, pch = 20, col = "black", bg = "black")
text(28, 261, labels = "NOBEL PRIZE!!", cex = 1.5)
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● NOBEL PRIZE!!
Figure 17: Scatterplot with NOBEL PRIZE!!
19
plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)", type = "n")
points(x[-c(100, which(x<0))],y[-c(100,which(x<0))])
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Weight (g)
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d C
onsu
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day)
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Figure 18: Scatterplot without the outlier and the negative weights
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plot(x, y, xlab = "Weight (g)", ylab = "Food Consumption (mg/day)", type = "n")
points(x[-c(100, which(x<0))],y[-c(100,which(x<0))])
abline(coef(lm(y[-c(100, which(x<0))]~x[-c(100, which(x<0))])),
col = "red", lwd = 2)
text(10, 260, labels =
paste("y = ", round(coef(lm(y[-c(100, which(x<0))]~x[-c(100,
which(x<0))]))[2], 2), "x + ",
round(coef(lm(y[-c(100, which(x<0))]~x[-c(100, which(x<0))]))[1], 2),
sep = ""), cex = 1.5)
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Weight (g)
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d C
onsu
mpt
ion
(mg/
day)
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y = 0.91x + 153.66
Figure 19: Scatterplot with the fitted line
21
count <- matrix(c(130,29,82,16,120,5,19,6), nrow = 2, ncol = 4, byrow = T)
colnames(count) <- c("Molluscs", "Annelids", "Arthropods", "Echinoderms")
rownames(count) <- c("Hahei","Leigh")
order.count = order(colSums(count), decreasing = T)
barplot(count[, order.count], beside = T, legend.text = T,
ylab = "Frequency (Absolute Abundance)")
Molluscs Arthropods Annelids Echinoderms
HaheiLeigh
Fre
quen
cy (
Abs
olut
e A
bund
ance
)
020
4060
8010
012
0
Figure 20: Two way frequency table of counts on a barplot
22
proportion <- round(count / rowSums(count), 3)
barplot(proportion[,order.count], beside = T, legend.text = T,
ylab = "Percentage (Relative Abundance)")
Molluscs Arthropods Annelids Echinoderms
HaheiLeigh
Per
cent
age
(Rel
ativ
e A
bund
ance
)
0.0
0.2
0.4
0.6
0.8
Figure 21: Two way frequency table of percentage on a barplot
23
group1 <- rgamma(1000, 2, 5)
group2 <- rgamma(1000, 3, 6)
groupname <- rep(c("Group One","Group Two"),c(1000,1000))
boxplot(c(group1,group2)~groupname)
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Group One Group Two
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2.0
Figure 22: Boxplots with homogeneous variances
24
group1 <- rgamma(1000, 2, 5)
group2 <- seq(1, 10, length.out = 1000)
groupname <- rep(c("Group One","Group Two"),c(1000,1000))
boxplot(c(group1,group2)~groupname)
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02
46
810
Figure 23: Boxplots with heterogeneous variances
25
x1 <- rnorm(100, 3, 1)
y1 <- rnorm(100, 3.5, 1)
qqplot(x1, y1, asp = 1, xlim = c(0, 7), ylim = c(0, 7), xlab = "Group One",
ylab = "Group Two")
abline(0, 1, col = "red", lwd = 2)
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Group One
Gro
up T
wo
Figure 24: Q-Q Plot
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count <- matrix(c(39,9,25,6,91,20,57,10,32,1,6,2,88,4,13,4), nrow = 4, ncol = 4)
order.count <- order(rowSums(count), decreasing = T)
par(las = 3, cex.axis = 0.8 )
plot.new()
plot.window(xlim = c(0,20), ylim = c(0, max(count) + 2))
rect(seq(0, 7.5, by= 2.5),0,seq(0, 7.5, by=2.5)+1,count[order.count,1],
col = "grey")
rect(seq(0, 7.5, by= 2.5)+1,0,seq(0, 7.5, by=2.5)+2,count[order.count,2],
col = "green")
rect(seq(0, 7.5, by= 2.5)+11,0,seq(0, 7.5, by=2.5)+12,count[order.count,3],
col = "grey")
rect(seq(0, 7.5, by= 2.5)+12,0,seq(0, 7.5, by=2.5)+13,count[order.count,4],
col = "green")
text(c(5, 15), max(count)+1, c("Hahei", "Leigh"), cex = 2)
axis(1, at = c(seq(1,8.5, 2.5), seq(12, 19.5, by = 2.5)),
labels = rep(c("Molluscs", "Arthropods", "Annelids","Echinoderms"),2), cex.lab = 0.5)
axis(2)
abline(v = 10, lty = 2)
box()
legend(15, 80, fill = c("grey", "green"), legend = c("Winter", "Summer"), cex = 1.2)
title(ylab = "Frequency (Absolute Abundance)")
27
Hahei Leigh
Mol
lusc
s
Art
hrop
ods
Ann
elid
s
Ech
inod
erm
s
Mol
lusc
s
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hrop
ods
Ann
elid
s
Ech
inod
erm
s
020
4060
80
WinterSummer
Fre
quen
cy (
Abs
olut
e A
bund
ance
)
Figure 25: Three way frequency on a barplot
28
x1 <- seq(-2, 4, length.out = 1200)
x2 <- -2*x1^2 + 5*x1 + 2 + rnorm(1200, 0, 2)
x2 = x2 - min(x2)
plot(x1,x2, xlab = "-log (Concentration)", ylab = "Outcome")
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05
1015
2025
30
−log (Concentration)
Out
com
e
Figure 26: Polynomial relationship between two continuous variables
29
• May need to install lattice package in R
• In R, click Packages ⇒ InstallPackage(s) ⇒ NewZealand ⇒ lattice
library(lattice)
Oxygen <- equal.count(runif(1200), number = 12, overlap = 0)
xyplot(x2~x1|Oxygen, xlab = "-log (Concentration)", ylab = "Outcome")
−log (Concentration)
Out
com
e
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30
−2 −1 0 1 2 3 4
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Figure 27: Trellis graph with three continuous variables
30
IQ <- c(rnorm(500, 10, 2), rnorm(500, 12, 2), rnorm(500, 12, 2), rnorm(500, 10, 2))
Group1 <- rep(c("Male", "Female"), rep(1000, 2))
Group2 <- rep(rep(c("Biology", "Statistics"), rep(500, 2)), 2)
bwplot(IQ~Group1|Group2, ylab = "IQ (in 10s)")IQ
(in
10s
)
5
10
15
Female Male
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Figure 28: Trellis graph with two qualitative variables and one quantitativevariable
31
with(iris, plot(Petal.Length, Petal.Width))
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al.W
idth
Figure 29: Iris scatterplot of Petal Length against Petal Width
32
with(iris, plot(Petal.Length, Petal.Width, type = "n"))
with(iris, for (i in 1:length(unique(Species))){
points(Petal.Length[Species == unique(Species)[i]],
Petal.Width[Species == unique(Species)[i]],
pch = 20+i, col = i, bg = i)
}
)
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Figure 30: Iris scatterplot with different species
33
key.variety <- list(columns = 1, space = "right", text = list(levels(iris$Species)),
points = list(pch = 21:23, fill = 1:3, col = 1:3))
with(iris, xyplot(Petal.Width~Petal.Length|Species,layout = c(1,3),
groups = Species, pch = 21:23,
fill =1:3, col = 1:3, key = key.variety))
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Figure 31: Iris trellis scatterplot graphs
34
pairs(iris)
Sepal.Length
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Figure 32: Iris pairs plot
35
xyplot(Sepal.Length + Sepal.Width ~ Petal.Length + Petal.Width | Species,
data = iris, scales = "free", layout = c(2, 2),
auto.key = list(x = .6, y = .7, corner = c(0, 0)))
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h +
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idth
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Figure 33: Iris trellis graphs with more than three variables
36
key.day <- list(columns = 3, space = "top", text = list(levels(iris$Species)),
points = list(pch = 21:23, fill = 1:3, col = 1:3))
day <- rep(rep(c("Day 1", "Day 2", "Day 3", "Day 4"), c(12, 12, 12, 14)), 3)
with(iris, xyplot(Petal.Width~Petal.Length|day, groups = Species,
pch = 21:23, fill = 1:3, col = 1:3, key = key.day))
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al.W
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setosa versicolor virginica●
Figure 34: Iris trellis graphs with measurements from four different days
37
pca <- princomp(iris[, 1:4])
plot.pch <- with(iris, ifelse(Species == levels(Species)[1], 21,
ifelse(Species == levels(Species)[2], 22, 23)))
plot.col <- with(iris, ifelse(Species == levels(Species)[1], 1,
ifelse(Species == levels(Species)[2], 2, 3)))
plot(pca$scores[, 1:2], type = "n", asp = 1,
xlab = paste("Component One (",
round(pca$sdev[1]^2/sum(pca$sdev^2), 3)*100, "%)",sep = ""),
ylab = paste("Component Two (",
round(pca$sdev[2]^2/sum(pca$sdev^2), 3)*100, "%)",sep = ""),
main = paste(round(sum(pca$sdev[1:2]^2)/sum(pca$sdev^2), 3)*100,
"% of the total variance is explained",
"\n", "in this two dimensional graph", sep = ""))
points(pca$scores[, 1:2], pch = plot.pch, col = plot.col, bg = plot.col)
legend(2, 3, pch = 21:23, col = 1:3, legend = levels(iris$Species), pt.bg = 1:3)
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01
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97.8% of the total variance is explainedin this two dimensional graph
Component One (92.5%)
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● setosaversicolorvirginica
Figure 35: PCA on iris data with the first two components
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