Statistics Workshop R graphics handoutkxio001/handouts.pdf · Statistics Workshop R graphics...

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")





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")

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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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050

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150

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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Theoretical Quantiles

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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

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cy

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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

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−4 −2 0 2 4

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

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quen

cy

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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))


Histogram and boxplot showing left skewed istribution

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quen

cy

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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

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quen

cy

0.0 0.2 0.4 0.6 0.8 1.0

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))


Histogram and boxplot showing uniform distribution

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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

15


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)

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onsu

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(mg/

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Figure 14: Scatterplot pointing out the negative x values

16


points(2, 260, pch = 20, col = "black", bg = "black")

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Weight (g)

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(mg/

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Figure 15: Scatterplot with outlier

17



text(20, 261, labels = "Mistake??", cex = 1.5)

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(mg/

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● Mistake?

Figure 16: Scatterplot with mistake?

18



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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d C

onsu

mpt

ion

(mg/

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Figure 18: Scatterplot without the outlier and the negative weights

20

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)

Foo

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)")


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)")


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

0.0

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1.5

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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Group One Group Two

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

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Figure 24: Q-Q Plot

26

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")


col = "grey")


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

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s

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Art

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elid

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inod

erm

s

020

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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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−2 −1 0 1 2 3 4

05

1015

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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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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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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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1 2 3 4 5 6 7

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Petal.Length

Pet

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)

}

)

1 2 3 4 5 6 7

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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))

Petal.Length

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al.W

idth

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2.5virginica

setosaversicolorvirginica

●

Figure 31: Iris trellis scatterplot graphs

34

pairs(iris)

Sepal.Length

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Figure 32: Iris pairs plot

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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)))

Petal.Length + Petal.Width

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idth

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Figure 33: Iris trellis graphs with more than three variables

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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

idth

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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

38

Statistics Workshop R graphics handoutkxio001/handouts.pdf · Statistics Workshop R graphics...

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