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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
20
30
40
50
60
70
80
90
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East
West
North
0
20
40
60
80
100
1stQtr
2ndQtr
3rdQtr
4thQtr
EastWestNorth
(Real) 3-D displays
4 5 6 7 8SEPALLEN
1
2
3
4
5
SE
PA
LWID
1
2
3
4
5
6
7
4 5 6 7 8SEPALLEN
1
2
3
4
5
SE
PA
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
2
3
4
5
SE
PA
LWID
01234567
PETALLEN
2 4 6 8 10 12 14 16 18
2
4
6
8
10
12
14
16
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.
Z.c.
SPECIES
1
10
100
1000
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
20
40
60
80
100
120
140
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
2
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
20
30
40
50
60
70
80
90
100
110
Po
pula
tion
siz
e
Left-sideRight-side
Multiple graph
1988 1990 1992 1994 1996 1998 2000 2002 20040
20
40
60
80
100
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
3
4
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
Recommended