Plotting and Tabulating Data and Results

Hal Whitehead

BIOL4062/5062

Plotting and Tabulating Data and Results

• Figures versus Tables– in presentations– in written work

• Formatting Tables

• Formatting Graphs

• Taxonomy of Graphs

Figures versus Tables??

Reduction in haplotype diversity:

Conditions: <50% 50-90% >90% Extinction

Control 756 4 0 0

=0.05 757 3 0 0

=0.10 745 14 1 0

=0.20 700 57 3 0

=0.40 473 130 65 92

=0.0125 544 29 21 166

=0.0250 285 46 18 411

=0.0500 132 35 13 580

=0.1000 71 38 29 622

0 0.01 0.1 10

1000

2000

K=

103 ;

=10

-3

Haplotype diversity

0 0.01 0.1 10

1000

2000Nucleotide diversity

0 0.01 0.1 10

500

1000

1500

K=

104 ;

=10

-3

0 0.01 0.1 10

500

1000

1500

0 0.01 0.1 10

1000

2000

K=

104 ;

=10

-4

0 0.01 0.1 10

1000

2000

0 0.01 0.1 10

200

400

K=

105 ;

=10

-4

0 0.01 0.1 10

200

400

0 0.01 0.1 10

200

400

GST

K=

105 ;

=10

-5

0 0.01 0.1 10

200

400

GST

>90% reduction50-90%<50%

In Presentations (Powerpoint, slides or overheads):

• Generally use figures

• Use tables when:– Numbers are important– Fewer than ~10 numbers (minimum digits)

Tables in Presentations:

Number of Limbs

Birds 4

Mammals 4

Spiders 8

Insects 6

Tables in Presentations:

Reduction in haplotype diversity:

Conditions: <50% 50-90% >90% Extinction

Control 756 4 0 0

=0.05 757 3 0 0

=0.10 745 14 1 0

=0.20 700 57 3 0

=0.40 473 130 65 92

=0.0125 544 29 21 166

=0.0250 285 46 18 411

=0.0500 132 35 13 580

=0.1000 71 38 29 622

Tables in Presentations:

Uncorrected estimate Estimate g(0) corrected Area Density: Town-send’s

Chlorophyll*

Area n CV n CV (1,000 km 2) (whales/1,000km 2)

plot (t in first m) whales/t Ref.

Northeast Atlantic SS 5,231 0.3 6,013 0.32 1,226 4.9 0 - - 1.

Iceland-Faeroes SS 1,542 0.2 1,772 0.18 2,309 0.77 0 1,079 1.64 2.

US east coast SS 4,702 0.4 5,405 0.37 317 17.04 210 212 25.49 3.

Northern Gulf of Mexico SS-AS 530 0.3 609 0.32 258 2.36 32 117 5.21 4.

Antarctic (S of 60°S) SS 10,500 0.2 12,069 0.17 18,548 0.65 0 4,258 2.83 5.

Eastern tropical Pacific SS 22,666 0.2 26,053 0.24 19,148 1.36 5,083 3,657 7.12 6.

Eastern temperate North Pacific SS 20,880 0.5 24,000 0.46 7,786 3.08 154 912 26.32 7.

Hawaii AS 66 0.6 76 0.57 81 0.94 30 6 12.64 8.

Western North Pacific SS 25,816 0.1 29,674 0.14 25,681 1.16 1,896 4,923 6.03 9.

All surveyed areas 105,671 0.13 75,354 1.40 7,405 14,085 7.50

Total globe 316,620 21,336 54,992

Uncorrected estimate Estimate g(0) corrected Area Density: Town-send’s

Chlorophyll*

Area n CV n CV (1,000 km 2) (whales/1,000km 2)

plot (t in first m) whales/t Ref.

Northeast Atlantic SS 5,231 0.3 6,013 0.32 1,226 4.9 0 - - 1.

Iceland-Faeroes SS 1,542 0.2 1,772 0.18 2,309 0.77 0 1,079 1.64 2.

US east coast SS 4,702 0.4 5,405 0.37 317 17.04 210 212 25.49 3.

Northern Gulf of Mexico SS-AS 530 0.3 609 0.32 258 2.36 32 117 5.21 4.

Antarctic (S of 60°S) SS 10,500 0.2 12,069 0.17 18,548 0.65 0 4,258 2.83 5.

Eastern tropical Pacific SS 22,666 0.2 26,053 0.24 19,148 1.36 5,083 3,657 7.12 6.

Eastern temperate North Pacific SS 20,880 0.5 24,000 0.46 7,786 3.08 154 912 26.32 7.

Hawaii AS 66 0.6 76 0.57 81 0.94 30 6 12.64 8.

Western North Pacific SS 25,816 0.1 29,674 0.14 25,681 1.16 1,896 4,923 6.03 9.

All surveyed areas 105,671 0.13 75,354 1.40 7,405 14,085 7.50

Total globe 316,620 21,336 54,992

In Written Papers (Journal papers, Reports, Theses):

• Use tables when:– exact numbers are important– others may use results for meta-analysis– no trend or contrast to be emphasized (e.g. field sites

with sample sizes)– pre-analysis data set– multivariate data (figure would have 3 or more

dimensions)– very few numbers– several different data types

In Written Papers (Journal papers, Reports, Theses):

• Use figures when:– Trend (or lack of trend) to be emphasized

– Contrast (or lack of contrast) to be emphasized

– Many, many numbers

0 5 10 15 20 250

5

10

15

0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

-0.2 0 0.2 0.4 0.6 0.8 1 1.2-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Do not usually present the same data as both Tables and Figures

Tables

• Use minimum significant digits (especially for powerpoint/slides/overheads)

Group Size Estimates

Location n g gt

Chile 26 23.6 30.4

Galápagos Islands 97 18.8 24.8

Ecuador-Peru 15 26.2 28.8

Group Size Estimates

Location n g gt

Chile 26 23.6 30.4

Galápagos Islands 97 18.8 24.8

Ecuador-Peru 15 26.2 28.8

Group Size Estimates

Location n g gt

Chile 26 23.6456 30.4565

Galápagos Islands 97 18.8397 24.8345

Ecuador-Peru 15 26.2222 28.8667

Group Size Estimates

Location n g gt

Chile 26 23.6456 30.4565

Galápagos Islands 97 18.8397 24.8345

Ecuador-Peru 15 26.2222 28.8667

Tables

• Usually no vertical rules

Group Size Estimates

Location n g gt

Chile 26 23.6 30.4

Galápagos Islands 97 18.8 24.8

Ecuador-Peru 15 26.2 28.8

Group Size Estimates

Location n g gt

Chile 26 23.6 30.4

Galápagos Islands 97 18.8 24.8

Ecuador-Peru 15 26.2 28.8

Group Size Estimates

Location n g gt

Chile 26 23.6 30.4

Galápagos Islands 97 18.8 24.8

Ecuador-Peru 15 26.2 28.8

Tables:Eliminate large areas of empty space?

Group Number:

MaleID:

#3 #5 #18 #19 #20 #21 #22 #23 #24 #25 #26 #27 #28 #29 Total

5503 1 1

5504 1 1

5505 1 1

5507 1 1

5508 1 1

5509 2 2

5510 1 1

5511 1 1

5512 1 1

5513 1 1 3 1 6

5515 2 2

5516 1 1

5517 1 1 2 1 1 1 7

5518 1 1 2

5519 1 1

5520 1 1 1 1 1 5

5521 1 1

5522 1 1

5523 1 1

5525 1 1

5526 1 1

5527 1 1

5528 1 1

TablesDo not change column headings part way down

Location n g (SD) gt (SD)

Chile 26 23.6 (12.9) 30.4(16.7)

Galápagos 97 18.8 (10.0) 24.8 (11.0)

Ecuador-Peru 15 26.2 (7.4) 28.8 (6.4)

u (SD) ut (SD)

Chile 51 29.2 (26.8) 53.3 (49.1)

Galápagos 139 23.8 (15.5) 35.5 (19.6)

Ecuador-Peru 20 30.0 (13.5) 37.6 (18.3)

Tables

• Full explanation:– Written: Yes (in title, footnotes, etc.)– Presentation: No

Figures

independent variable, what was selected

dependent variable, what was measured

Figures

Count data

00 0

Or:

Figures:Space around pattern highlights its integrity

-0.2 0 0.2 0.4 0.6 0.8 1 1.2-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.2

-0.1

0

0.1

0.2

0.3

Figures:Pseudo 3-D

0

10

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1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

West

North

0

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1stQtr

2ndQtr

3rdQtr

4thQtr

EastWestNorth

(Real) 3-D displays

4 5 6 7 8SEPALLEN

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PA

LWID

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4 5 6 7 8SEPALLEN

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LWID

01234567

PETALLEN

Colour

4 5 6 7 8SEPALLEN

1

2

3

4

5

SE

PA

LWID

321

SPECIES

0 1 2 3 4 5 6 7 8 9LBEAKS

0

1

2

3

4

LGE

NE

RA

Z.c.P.m.M.l.M.c.H.pH.a.G.m.G.g

SPECIES

Colour

4 5 6 7 8SEPALLEN

1

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SE

PA

LWID

01234567

PETALLEN

2 4 6 8 10 12 14 16 18

2

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18

Beware: Rainbow~=Horsehoe

Logging axes can help

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

0

1000

2000

3000

4000

5000

6000

BE

AK

S

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

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SPECIES

1

10

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BE

AK

S

Other Figure Issues

• Graph needs indication of precision

• Not too complicated (< 5 lines plotted together)

• Brief

descriptions

(written)

• Thick lines

1988 1990 1992 1994 1996 1998 2000 2002 20040

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Rel

iabl

y-m

arke

d in

divi

dual

s

PetersenTrend

Simplified taxonomy of graphs:

# Variables: 1 2 Many

Continuous BoxDensity

ProbabilityQuantile

GraphScatter plot

Multiple graphMultiple graphs

Scatter plots3-D graph, etc.

Categorical BarPie

[Use tables]

Mixed - BarBox

Category plot

BarCategory plot,etc

[Table?]

One continuous variable

0 5 10 15 20 25GENERA

0 5 10 15 20 25GENERA

0 5 10 15 20 25GENERA

-3

-2

-1

0

1

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3

Exp

ecte

d V

alue

for

Nor

ma l

Dis

trib

utio

n

0 5 10 15 20 25GENERA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fra

ctio

n o

f D

ata

Box Density

ProbabilityQuantile

Two continuous variables

Graph Scatter plot

1 10 100 1000Beaks

5

10

15

2025

Ge

ne

ra

1988 1990 1992 1994 1996 1998 2000 2002 20040

20

40

60

80

100

120

140

Rel

iabl

y-m

arke

d in

divi

dual

s

Many continuous variables (1)

1988 1990 1992 1994 1996 1998 2000 2002 20040

10

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Po

pula

tion

siz

e

Left-sideRight-side

Multiple graph

1988 1990 1992 1994 1996 1998 2000 2002 20040

20

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60

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120

140

Re

lia

bly

-m

ark

ed

in

div

idu

als

1988 1990 1992 1994 1996 1998 2000 2002 20040

20

40

60

80

100

120

140

Reliably

-m

arked in

div

iduals

Multiple graphs

SEPALLEN

SE

PA

LL E

N

SEPALWID PETALLEN PETALWID

SE

PA

LLE

N

SE

PA

LWID

SE

PA

LWID

PE

TALL

EN

PE

TALL

EN

SEPALLEN

PE

TALW

ID

SEPALWID PETALLEN PETALWID

PE

TALW

ID

Multiple scatter plots 3-D graph

Many continuous variables (2)

ColourContour

4 5 6 7 8SEPALLEN

1

2

3

4

5

SE

PA

LWID

01234567

PETALLEN

4 5 6 7 8SEPALLEN

1

2

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5

SE

PA

LWID

1

2

3

4

5

6

7

One categorical variable

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

0

10

20

30

40

50

Co

un

t

G.g

G.m.

H.a.

H.pM.c.

M.l.

P.m.

Z.c.

Bar Pie

Two or more categorical variables:

Tables N Atlantic Pacific S Ocean TotalG.g 1 0 0 1G.m. 0 0 4 4H.a. 9 0 0 9H.p 0 0 2 2M.c. 0 5 1 6M.l. 0 0 45 45P.m. 7 6 7 20Z.c. 12 3 1 16Total 29 14 60 103

BostonAge 50 60 70Alive 39 89 43Dead 19 33 30 GlamorganAge 50 60 70Alive 45 80 28Dead 26 29 13 TokyoAge 50 60 70Alive 128 89 13Dead 23 31 6

+ multiple pies, ...

One categorical and one continuous

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

1

10

100

1000

BE

AK

S

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

1

10

100

1000

BE

AK

S

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

1

10

100

1000

BE

AK

S

Bar Box Category

Multiple categorical and continuous

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

1

10

100

1000

BE

AK

S

MF?F

SEX

0 1 2 3 4 5 6 7 8 9LBEAKS

0

1

2

3

4

LGE

NE

RA

Z.c.P.m.M.l.M.c.H.pH.a.G.m.G.g

SPECIES

G.gG.m

.H.a.

H.pM.c. M.l.

P.m.

Z.c.

SPECIES

1

10

100

1000

BE

AK

S

MF?F

SEX

Summary• Presentations

– Usually use Figure rather than Table

– Keep it very simple

• Papers– Decide whether to use Table or Figure

– Experiment with different displays

– Explain clearly

– Measure of confidence or precision

• Posters– Complexity: intermediate between papers/presentations

• General– No pseudo 3-D!

– Use 3-D and colour sparingly and carefully