data exploration using r - aucklandkxio001/workshop.pdf · data exploration using r statistics...

Data Exploration using R

Statistics Refresher Workshop

Kai Xiong

[email protected] Consulting ServiceThe Department of StatisticsThe University of Auckland

July 1, 2011

Kai Xiong Data Exploration using R 1/47

mailto:k,[email protected]

Exploring your data

Checking the data for patterns, relationships, structures, andother features.

Can be done through graphs and summary statistics.

We recommend R for generating graphs, much more flexiblethan Excel, SPSS, SAS.


Roles of Exploratory Graphics

1 Are there any errors or outliers?2 Are there any patterns in the data?

Symmetric, Skewed, Bimodal, Clusters?

3 Are there any relationships between the variables?

Linear (increasing, decreasing), polynomial, exponential...

4 What sort of model might be appropriate?


Types of variable

1 Quantitative

Continuous:e.g. gene expression, Body length of musselsDiscrete:e.g. number of photophores in lantern fish

2 Qualitative

Categoricale.g. SNPs, Location of marine reservesOrdinale.g. Position in a food chain


One Quantitative Variable

Dotplots

Five-number-summary statistics1 Minimum2 1st Quantile/Lower Quantile/25th percentile

25% of the sorted variable is smaller than the 1st quantile75% of the sorted variable is greater than the 1st quantile

3 2nd Quantile/Median/50th percentile

Divide the sorted variable in two equal halves

4 3rd Quantile/Upper Quantile/75th percentile

25% of the sorted variable is greater than the 3rd quantile75% of the sorted variable is smaller than the 3rd quantile

5 Maximum

Boxplot: visual display of 5-number-summary statistics.

Normal QQ plot

Histogram


010

2030

4050

Minimum

1st Quantile

Median

3rd Quantile

Maximum

Outlier?●

Figure: Boxplot with 5-number-summaryKai Xiong Data Exploration using R 6/47

●●●●●●●●●●●●●●●●●●●●●

050

100

150


●●●●●●●●●

0.0

0.5

1.0

1.5

2.0

2.5

3.0


Normal Quantile-Quantile (QQ) Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●●

●

●

●●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●●

●

●●

●

●●●●

●●

●●

●●●●●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

−2 −1 0 1 2

510

1520

Theoretical Quantiles

Sam

ple

Qua

ntile

s


Histogram showing Normal Distribution

Fre

quen

cy

−4 −2 0 2 4

020

040

060

080

010

00

Figure: Histogram Example OneKai Xiong Data Exploration using R 10/47

Histogram and boxplot showing Normal Distribution

Fre

quen

cy

−4 −2 0 2 4

020

040

060

080

010

00 ● ●●●● ●●● ●● ●● ●● ●●● ●● ●● ●●●● ●● ●●● ●●● ●● ●●● ● ●●●●●● ●●● ● ●●● ● ●● ● ●● ● ● ●● ●●

−4 −2 0 2 4

Figure: Histogram with boxplot example oneKai Xiong Data Exploration using R 11/47

Histogram showing left skewed distribution

Fre

quen

cy

2 4 6 8 10

010

020

030

040

050

060

0

Figure: Histogram Example TwoKai Xiong Data Exploration using R 12/47

Histogram and boxplot showing left skewed istribution

Fre

quen

cy

2 4 6 8 10

010

020

030

040

050

060

0

●●●● ●●● ● ●● ● ●●● ● ●● ● ●● ● ●● ●● ●● ●●● ●●● ●● ●●● ●●● ●● ●●● ● ●●● ● ●● ● ●●●● ● ● ●●● ●● ● ●● ● ●●● ●●● ● ●●●● ●● ●●● ●● ● ●●●● ●●●● ●●● ● ●●● ● ●● ●●● ●● ●● ●● ●● ●●●● ● ●● ●● ●● ●● ●●●● ●●●● ● ●●● ●●● ●● ●●●● ●● ● ●●●●● ●● ●●●● ●●● ●● ●●● ●● ●●●

2 4 6 8 10

Figure: Histogram with boxplot example twoKai Xiong Data Exploration using R 13/47

Histogram showing uniform distribution

Fre

quen

cy

0.0 0.2 0.4 0.6 0.8 1.0

020

4060

80

Figure: Histogram Example ThreeKai Xiong Data Exploration using R 14/47

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: Histogram with boxplot example threeKai Xiong Data Exploration using R 15/47

One Qualitative Variable

Frequency table

Table: One way frequency table

Phylum Frequency Percentage

Molluscs 250 61.4%Annelids 34 8.4%Arthropods 101 24.8%Echinoderms 22 5.4%Total 407 100%

Pie chart

Barplot


Molluscs

Arthropods

Annelids

Echinoderms

Figure: Piechart ExampleKai Xiong Data Exploration using R 17/47

Molluscs Arthropods Annelids Echinoderms

Phylum

Per

cent

age

010

2030

4050

60

Figure: Barplot ExampleKai Xiong Data Exploration using R 18/47

Two VariablesTwo Quantitative

Scatter Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

●

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

Figure: Scatterplot ExampleKai Xiong Data Exploration using R 19/47


Scatter Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

●

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

●

●



Scatter Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

●

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

●



Scatter Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

●

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

● Mistake?



Scatter Plot

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

●

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

● NOBEL PRIZE!!



Scatter Plot

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●



Scatter Plot

−20 0 20 40 60 80 100

140

160

180

200

220

240

260

Weight (g)

Foo

d C

onsu

mpt

ion

(mg/

day)

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●●

●

●

●

●

●

●

●●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

● ●

● ●

●

●● ●

●

●

●

● ●

●

●

●

●

●

●

●

y = 0.91x + 153.66


Two VariablesTwo Qualitative

Two way frequency table

Table: Two way frequency table

Phylum Hahei Leigh Total

Molluscs 130 120 250Annelids 29 5 34Arthropods 82 19 101Echinoderms 16 6 22Total 257 150 407

Side by side barplot: frequencies or percentages?



HaheiLeigh

Fre

quen

cy (

Abs

olut

e A

bund

ance

)

020

4060

8010

012

0

Figure: Two way frequency on a barplotKai Xiong Data Exploration using R 27/47


HaheiLeigh

Per

cent

age

(Rel

ativ

e A

bund

ance

)

0.0

0.2

0.4

0.6

0.8

Figure: Two way frequency on a barplotKai Xiong Data Exploration using R 28/47

Two VariablesOne Qualitative and One Quantitative

Side-by-side boxplot

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

Group One Group Two

0.0

0.5

1.0

1.5

2.0

Figure: Side by side boxplot



Side-by-side boxplot

●●

●

●●

●

●●●

●

●●●

●

●●

●

●●●●●●●●●●●●

Group One Group Two

02

46

810

Figure: Side by side boxplot



QQ Plot

●

● ●●

●●

●●●●●●

● ●●●●●●●●●●●●●●

●●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●

●●●●●●

●●●

●●

●●

● ●

0 2 4 6

01

23

45

67

Group One

Gro

up T

wo

Figure: Normal QQplot ExampleKai Xiong Data Exploration using R 31/47

Three VariablesThree Qualitative Variables

Table: Three way frequency table

Location

Hahei Leigh

Phylum Winter Summer Winter Summer

Molluscs 39 91 32 88Annelids 9 20 1 4Arthropods 25 57 6 13Echinoderms 6 10 2 4


Hahei Leigh

Mol

lusc

s

Art

hrop

ods

Ann

elid

s

Ech

inod

erm

s

Mol

lusc

s

Art

hrop

ods

Ann

elid

s

Ech

inod

erm

s

020

4060

80WinterSummer

Fre

quen

cy (

Abs

olut

e A

bund

ance

)

Figure: Three way frequency on a barplotKai Xiong Data Exploration using R 33/47

Three VariablesThree Quantitative Variables

Trellis Graphs: Display a variable or the relationship betweenvariables, conditioned on one or more other variables.

Three continuous variables -log(Concentration), Outcome andOxygen level.What is the relationship between -log(Concentration) andOutcome, conditioned on Oxygen level? In other words, howdoes the relationship between -log(Concentration) andOutcome change over different Oxygen level?

1 Plot -log(Concentration) against Outcome first.2 Break Oxygen level into ordinal groups. e.g. Divide Oxygen

level into 12 equally spaced interval.


●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●●●

●

●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●●●

●●●

●

●

●

●

●●

●●

●

●●

●

●

●●

●

●

●

●●●●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●●

●

●●

●

●●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●●

●

●●●●●●●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●●●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●●

●●●●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●●●

●

●

●●

●

●●

●●

●

●

●●

●●

−2 −1 0 1 2 3 4

05

1015

2025

30

−log (Concentration)

Out

com

e


−log (Concentration)

Out

com

e

0

5

10

15

20

25

30

−2 −1 0 1 2 3 4

●

●

●

●●●●●

●●●

●

●●●●●

●

●

●

●

●●●

●

●●

●●●●●●

●

●●

●

●●

●●●

●●●●●●●●●●●●●

●

●●●

●●

●

●●

●

●●

●●●●●

●

●

●

●●●

●●●●●

●●●●●

●

●

●●●

●●

●

●●●●

Oxygen

●

●●●

●●●●

●●●●

●

●●●

●

●●●

●●

●●●

●

●●●

●

●●●●●●

●

●●●●●●●●●

●

●●

●

●●●

●●

●

●●●

●

●

●●

●●●●●●●●●

●●●●●

●●●●●

●●

●●●●

●

●●●●

●

●●●

●

●●

Oxygen

−2 −1 0 1 2 3 4

●

●●

●

●●

●●

●●●●●

●●●

●●

●

●

●

●

●

●●

●●●●●●●

●●●

●

●

●●

●●●●●●●

●●●●●

●●●●●

●●

●

●●

●●●●●●●●

●

●●●●

●●

●

●●●●●●●

●●●●

●

●●

●●●●●●●

●

●

Oxygen

●●●●●●●●●●●

●

●●

●

●

●●

●●

●●

●

●●●

●●●

●

●

●●●

●

●

●●

●●

●

●●

●●●●

●●●

●

●

●●●●●

●●●●

●●

●

●●●●

●

●●●

●●●●●

●●

●●●●

●●●

●

●●●●●●●●

●

●

●

●●

Oxygen

●●●

●

●

●●

●

●

●●

●

●●

●

●

●●

●●●●●●●●●●●

●●

●

●●●●●

●

●

●●●●

●

●

●●

●

●

●

●●●●●

●

●●●●●

●●

●

●

●

●●●

●

●●

●

●

●

●●●●

●●●●●

●

●●●

●

●●●●●●

●

●

●

●

●

Oxygen

●

●

●

●●●●

●●●●●●●●

●●

●

●●●

●

●●●●●

●●●

●

●

●

●●

●

●

●

●●●●●

●

●●

●●●

●●

●

●●

●●

●●

●

●

●●●

●●

●●●●●

●

●●●

●

●

●●

●

●●●●●●●●

●

●

●●●

●●●

●

●

●

●

●

Oxygen

●

●●●●●●●●

●●

●●

●

●●●●

●

●●●

●

●

●●●

●●●●

●●

●●●●●

●

●

●

●

●●●

●●●●●

●●

●

●

●●●●

●●●

●●●

●

●

●●

●

●●●●●●●

●●

●●●

●●●●●●●●

●

●●●

●

●

●

●

●●●

Oxygen

0

5

10

15

20

25

30

●●●

●

●●●●

●

●

●●●

●●

●●

●

●

●

●●●●●●●

●●●

●

●●●●●

●●●

●

●●●

●

●

●●

●

●

●

●●●●

●

●●

●

●●●

●

●

●●●

●●

●●●●●●

●●●●

●●●●

●

●●●

●

●●

●●●●

●

●●●

●

●●

Oxygen0

5

10

15

20

25

30

●

●●

●●●●●●●●

●●●

●

●●●

●●●●

●●

●

●●

●●

●

●●

●●

●●

●

●

●●●

●●●●●●

●●●●

●●

●●●●●

●

●●

●

●●●●

●

●●●●●●

●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●●

●

●●●●●

Oxygen

−2 −1 0 1 2 3 4

●●●●●

●

●

●

●

●●

●

●

●●●

●

●

●

●●●●

●

●●●●

●●●

●●●

●●●●●●

●●●●●●●●

●●●●

●

●

●

●●●●

●

●●

●●

●●

●●●●●●

●

●●

●

●●●●

●●

●●●●●●●

●●

●●●●

●●●●●

Oxygen

●

●

●

●●●

●●●

●●

●

●●

●●●●●

●●

●

●●●

●

●

●●●

●●●●●●

●

●●●●●●●●

●●

●●

●●

●●●●●●●

●●●●

●

●●

●●●●

●●

●●●

●

●

●●●●●●●

●

●

●●●●

●

●●

●●

●●

●

●

●●

Oxygen

−2 −1 0 1 2 3 4

●●●●

●

●

●

●

●

●●●

●●●●●●●

●

●●

●●

●

●●

●

●

●●

●●

●●●●

●

●

●●●

●●●●●

●

●

●●●●●●●●

●●●

●●●●

●●

●

●

●●●●●●

●

●●

●●●

●

●●

●

●

●

●●

●

●●

●

●●●●●●

●●

Oxygen

Figure: Trellis graph with three continuous variablesKai Xiong Data Exploration using R 36/47

Three VariablesTwo Qualitative Variables and One Quantitative Variable

IQ (

in 1

0s)

5

10

15

Female Male

●

●

●

●

●

●

●●

●

●

Biology

Female Male

●

●

●

●●●

●

●●

●

●●

●

●

Statistics

Figure: Trellis graph with two continuous variables and one qualitativevariable


Three VariablesTwo Quantitative Variables and One Qualitative Variable

Iris flower data set

Four continuous measure on Petal Length, Petal Width, SepalLength and Sepal Width.

One nominal variable, Species.

Suppose we are interested in the relationship between PetalLength and Petal Width, and how such relationship changesfor different species.

1 Plot Petal Length against Petal Width.2 Use different plotting character/color to represent different

species.



●●● ●●

●

●

●●

●

●●

●●

●

●●

● ●●

●

●

●

●

●●

●

●● ●●

●

●

●●●●

●

● ●

●●

●

●

●

●

●●●●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

1 2 3 4 5 6 7

0.5

1.0

1.5

2.0

2.5

Petal.Length

Pet

al.W

idth

Figure: Iris scatter plot



1 2 3 4 5 6 7

0.5

1.0

1.5

2.0

2.5

Petal.Length

Pet

al.W

idth

●●● ●●

●

●

●●

●

●●

●●

●

●●

● ●●

●

●

●

●

●●

●

●● ●●

●

●

●●●●

●

● ●

●●

●

●

●

●

●●●●

● setosaversicolorvirginica

Figure: Iris scatter plot with different species



Petal.Length

Pet

al.W

idth

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7

●●● ●●

●●

●●●●●

●●●

●●● ●●

●

●

●

●

●●

●

●● ●●

●

●●●●●●

● ●●●●

●

●●

●●●●

setosa0.0

0.5

1.0

1.5

2.0

2.5versicolor

0.0

0.5

1.0

1.5

2.0

2.5virginica

setosaversicolorvirginica

●

Figure: Iris trellis scatter graphs


More Than Three VariablesPairs Plot

Sepal.Length

2.0 3.0 4.0

●●

●●

●

●

●

●

●

●

●

●●

●

● ●●

●

●

●●

●

●

●●

● ●●●

●●

●●

●

●●

●

●

●

●●

● ●

● ●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●● ●

●

●

●●

●

●●

●●

●●

●● ●

●●

●●●●

●

●

●

●

●●●

●●

●

● ●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

● ●

●●

●●

●

●

●

●

●

●

●

● ●●

●●

●

●●●

●

●●

●

●●●

●

●●●

●●

●●

●●●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●

●

●

●●

●●●●

●●

●●●

●●

●

●

●

●●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●● ●

●

●

●●

●

●●

●●

●●●

●●

●●

●●●

●

●

●

●

●

●● ●

●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●●

●

●●●

●

●●

●

●●

●

●

●●●

●●●

●

0.5 1.5 2.5

●●●●

●

●

●

●

●

●

●

●●

●

● ●●

●

●

●●

●

●

●●● ●●●

●●

●●

●

●●

●

●

●

●●

●●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●● ●

●

●

●●

●

●●

●●

●●

●● ●

●●

●●●

●

●

●

●

●

●●●

●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

● ●

●●

●●

●

●

●

●

●

●

●

●●●

●●

●

●●●

●

●●

●

●●

●

●

● ●●

●●

●●

4.5

5.5

6.5

7.5

●●●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●●

●

●●●●●●

●●

●●●

●●

●

●

●

●●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●●

●

●●●●●●●●●

●●●●●●

●

●

●

●

●●●

●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●●

●

●●●

●

●●

●

●●●

●

●●●

●●●●

2.0

3.0

4.0

●

●●

●

●

●

● ●

●●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●● ●

●

●

●

●

●●

● ●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

● ●●

●●

●●

●●

●

●

●●●

●

●

●●

●●●

●

●●

●

●

●

●

●Sepal.Width

●

●●●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●●●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●●●

●●

●

●●●

● ●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●●● ●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

● ●●

●●

●●

●●

●

●

●●●

●

●

●●

●●●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●●●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●●

● ●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●●

●●

●

●

●●●

●

●

●●

● ●●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●●●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●●●●●●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●●●●●

●

●●●

●

●

●●●●●

●

●●

●

●

●

●

●

●●●● ●

●● ●● ● ●●

●● ●

●●●

●●

●●

●

●●

●●●●●● ●● ●●

● ●●●●

●●●●●

●●

● ●●

●●

●

●

●●●

●

●

●●

●●

●

●

●●●

●

●

●

●

●●

●●●

●

●

●●●

●

●

● ●●

●●●

●●

●

●

●●● ●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●●●

●●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●●

●●

●●

●●

●●

●

●● ●● ●

●●●● ● ●●

●● ●

●●●

●●

●●

●

●●

● ●●●●● ● ●●●● ●●●

●●● ●●

●

●●

● ●●

●●

●

●

●●●

●

●

●●

●●

●

●

●●●

●

●

●

●

●●

●●●

●

●

●●●

●

●

● ●●

●●●

●●

●

●

● ●●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

● ●●

●

●●

●

●

●

●

●

●●

● ●

●●

●●

●

●

●

●

●●

●

●●

●●

●●

●●

●●

●

Petal.Length

●●●●●

●●●●●●●●

●●●●●

●●

●●

●

●●● ●●●●● ●●●●●●

●●●

●●●●

●

●●●●●

●●●

●

●●●

●

●

●●

●●

●

●

●●●

●

●

●

●

●●

●●●

●

●

●●●

●

●

●●●

●●●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

● ●●

●

●●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●●

●●

●●

●●

●●

●

12

34

56

7

●●●●●●●●●●●●●●●●●●●●●●

●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●

●●●

●

●●●

●

●

●●

●●

●

●

●●●●

●

●

●

●●●●●●

●

●●●●

●

●●●●●●●●

●

●

●●●●

●

●

●

●

●●●

●

●

●

●●

●●●

●●●●

●●

●

●

●

●

●

●●

●●

●●●●

●

●

●

●

●●

●

●●

●●

●●

●●●●●

0.5

1.5

2.5

●●●● ●●

●●●

●●●

●●●

●●● ●●

●●

●

●

●●●

●●●●●

●●●● ●

●● ●

●●●

●●

●●● ●●

●● ●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●●

●●

●●

●●●

●

●●

●●

●●●●

●●

●

●●● ●

●●

●

●●

●

●●

●●●

●

●●

●●

●●

●

●●

●

●

● ●●

●

●●●

●

●

●●

●

●●

●●

●●

●

●●

●

●●●

●●

●

●

●● ●● ●●

●●●

●●●

●●●

●●● ●●

●●

●

●

●●●

●●●●●

●●●● ●

●● ●

●●●

●●

●●● ●●

●●●

●●●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●●

●●

●●

●●●

●

●●

●●

● ●●●

●●

●

●●

●●●

●

●

●●

●

●●

●●●

●

●●

●●

●●

●

●●

●

●

●●●

●

●● ●

●

●

●●

●

●●

●●

●●

●

●●

●

●●

●

●●

●

●

●●●●●●

●●●●●●●●

●●●●●●

●●

●

●

●●●●●●●●

●●●●●●●●●●●

●●

●●●●●

●● ●

●●●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●●● ●

●●

●●●●

●●●●

●●●●●

●●

●●●●

●●

●

●●

●

●●

●●●

●

●●●

●

●●

●

●●

●

●

● ●●

●

●●●

●

●

●●

●

●●

●●

●●

●

●●

●

●●

●

●●

●

●

Petal.Width

●●●●●●●●●●●●●●●●●●●●●●●

●

●●●●●●●●

●●●●●●●●●●●

●●●●●●●

●●●●●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●●

●●●●

●●

●●●●

●●●●●●●●●●●

●●●●●●

●

●●

●

●●

●●●

●

●●●●

●●

●

●●

●

●

●●●

●

●●●

●

●

●●●

●●

●●

●●

●

●●

●

●●●

●●

●

●

4.5 5.5 6.5 7.5

●●●● ● ●● ●● ● ●●●● ●●●● ●● ●●● ●●●●●●●● ●● ●●● ●●● ●●●● ●●● ●● ●●

●● ●● ●● ●● ●●● ●●●● ●●● ●● ●●●● ●●●●●●●● ●●● ● ●●●●● ●●● ●●● ●● ●

●● ●●● ●● ●● ●●● ●●● ●● ●●● ●● ●● ● ●●● ● ●● ●●●● ●●●● ●●●● ●●●●●●●

●● ●● ● ●●●● ● ●●●● ● ●●● ●●● ●●●●● ●●●●● ● ●●●● ●●● ●●● ● ● ●● ●● ●●

●●●● ●● ●● ●●● ●● ●● ●●●● ● ●●● ●●●● ●●●●● ●● ● ●●● ●●● ●●● ● ●●●● ●

●● ●●●●● ●● ●●● ●● ● ●● ●●● ●●●● ●●● ●● ●● ●●●● ● ●●●●●●● ●●●● ● ●●

1 2 3 4 5 6 7

●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●

●● ●● ●●●● ●●● ●● ●● ●●● ●● ●● ●●●● ●●●●●●● ●●●●●●● ●●●● ●●●●● ●

●● ●●● ●● ●●●●●●●●●● ●●● ●● ●● ●●●● ●●●●●● ● ●●●● ●●●● ●●●●●●●

●●●●● ●●●●●●●●●● ●●●●●● ●● ●●● ●●●●● ●●●●●●●●●●●● ●●●●●●●

●●●● ●● ●● ●●● ●● ●●●●● ●● ●● ●●●●● ●●●●● ● ●●●●●●●● ●●● ●●●●● ●

●● ●● ●●●●● ●●● ●● ●●● ●●● ●●●● ●●●● ●● ●● ●●● ●●●● ● ●●● ● ●●●● ●●

1.0 2.0 3.0

1.0

2.0

3.0

Species

Figure: Pairs Plot


More Than Three Variables

Petal.Length + Petal.Width

Sep

al.L

engt

h +

Sep

al.W

idth

34

5

0.5 1.0 1.5

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

● ●

●●

●●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

● ●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●

●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●●●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

setosa

23

45

67

1 2 3 4 5

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●●

●●

●●

●●

●

●●●

●●

●

●

●

●

●● ●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●●

●●

●●●

●

●

●●●

●●

●

●

●

●

●●●

●

●

●

●●●

●

●

●

●●●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●●

● ●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●●

● ●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

versicolor

23

45

67

8

2 3 4 5 6 7

●

●

●

●●

●

●

●

●

●

● ●

●

●●

● ●

● ●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

● ●

●●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●●

●

●●

●

●

● ●●

●●

●

●

●

●

●● ● ●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

● ●●

● ●

●●

●●

●

●

●●●

●

●

●● ● ●●

●

●●

●

●

●

●

●

●

●

●● ●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●●

●●

●

●

●●●

●

●

●● ● ●●

●

● ●

●

●

●

●

●

virginica

Sepal.Length * Petal.LengthSepal.Length * Petal.WidthSepal.Width * Petal.LengthSepal.Width * Petal.Width

●

●

●

●

Figure: Iris trellis graphs with more than three variablesKai Xiong Data Exploration using R 43/47

More Than Three Variables

Petal.Length

Pet

al.W

idth

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7

●●●●●

●●●●●●●

Day 1

●●●

●●● ●●

●

●

●

●

Day 2

●●

●

●●●●

●

●●●●

Day 3

1 2 3 4 5 6 7

0.0

0.5

1.0

1.5

2.0

2.5

●●

●●●●●

●

●●

●●●●

Day 4

setosa versicolor virginica●

Figure: Iris trellis graphs with measurements from four different daysKai Xiong Data Exploration using R 44/47

Multivariate

Suppose a dataset has n observations (rows) and p variables(columns).

The n observations lie in a p dimensional space.

To visualise the data, we apply some mathematical proceduresto reduce the dimensionality of the data cloud, optimally intotwo dimensions.

1 Throw away some/lots of variances/information, TANSTAAFL.2 Plot the reduced data into a two/three dimensional graphs,

and visualise the MAIN components of variance.


MultivariatePrincipal Component Analysis (PCA)

−3 −2 −1 0 1 2 3 4

−3

−2

−1

01

23

97.8% of the total variance is explainedin this two dimensional graph

Component One (92.5%)

Com

pone

nt T

wo

(5.3

%)

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

● ●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

● setosaversicolorvirginica

Figure: PCA on iris data with the first two components


Recommended Reading

Kai.http://www.stat.auckland.ac.nz/~kxio001.

Paul Murrell.R Graphics.Chapman & Hall/CRC, Boca Raton, FL, 2005.


http://www.stat.auckland.ac.nz/~kxio001

data exploration using r - aucklandkxio001/workshop.pdf · data exploration using r statistics...

Documents