Graphs and graphical presentation

Peter Shaw

pH6

7

1 2 3 4 5 6 Pond #

121212N =

Collembola density in 3 habitats

in Colyford wood

SITE

coppiceconiferscleared

colle

mbo

la m

-2

14000

12000

10000

8000

6000

4000

2000

0121212N =

Species richness in 3 habitats

in Colyford wood

SITE

coppiceconiferscleared

Spec

ies

richn

ess

per s

ampl

e

14

12

10

8

6

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Your most important concept for the day:

A graph is the best way to communicate numerical information to people. Bar nothing.

Always graph data if you want to understand them or explain to others.

Shows maxima andminimapH

6

7

The distribution of pH valuesin ponds on Wimbledon Common

Rules for any graph:2: A title

1: Clearly labelled axes,units where appropriate

3: Explanations ofsymbols

1 2 3 4 5 6 Pond #

The most common fault:You use the PC stats package to plot the graph for you.Eh? Come on, are you seriously expecting me to draw them by hand when the PC does it for me?!

Well, actually, the number of times that an SPSS- or EXCEL-generated graph is acceptable as thesis-quality first time around is close to zero. Common errors are stupid axis ranges (weight or height starting at negative values), default variable names (VAR001 tells me nothing!), and glorious technicolor (that becomes illegible in the photocopied version).

Re-edit them to give big bold black symbols and sensible ranges. In several cases I don’t bother, but edit and past the graph into powerpoint and re-draw it by hand in powerpoint. All the diagrams in my book were redrawn in Powerpoint this way after I despaired of ever getting a useful graph out of SPSS!

888888N =

actual_distance

32.0016.008.004.002.00.00

Mea

n +

- 2

SE

litt

erde

pth

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SPSS gives you this…

actual_distance

32.0016.008.004.002.00.00

Mea

n lit

terd

epth

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40

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Or this…

Lit

ter

dept

h, m

m0

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00

0 2 4 8 16 32Distance, m

And the graph I really wanted…

Key1997-20011992-19961988-19901986-1987a species

cc

cc

Cc Co

C3

C5

Am

Ar

Lp Pi

Bs

Gr

Sv

Sl

Lh

-300

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00

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-100 0 100 200 300 400 500

2nd

DC

A a

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enva

lue

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1st DCA axis Eigenvalue = 0.375

Another hand-drawn in Powerpoint..This is an ordination diagram – more later on in the course

Types of graph:There are many types, and no laws stopping you from inventing a new format.

My aim for today is to show you the theory and practice of the commoner types of graph.

Then I will get you used to plotting them in your head to model the behaviour of different patterns within your data (rest assured that this s very quick and easy).

Then we head for the PCs to do them ourselves.

100 50 0

Number of individuals caught

1 2pond

These are useful for showing how properties differ between sites/classes, but work best when you have only one number (a total, average or other) per class.

Bar charts

Early successional Collembola

on PFA sites

Site age, years

40.0030.005.002.00

Mean C

ollem

bola

density m

-2

3000

2000

1000

0

Hypogastrura

vernalis m-2

Cryptopygus

thermophilus m-2

Late successional Collembola

of PFA sites

Site age, years

40.0030.005.002.00

Collem

bola

m-2

4000

3000

2000

1000

0

Tullbergia

macrochaeta m-2

Lepidocyrtus

lanuginosus m-2

Isotomodes

productus m-2

Friesea

mirabilis m-2

Hypogastrura denticulata

Cryptopygus thermophilus

Tullbergia sppLepidocyrtus lanuginosusIsotomodes productusFriesea mirabilis

Successional patterns in Collembola colonising an industrial waste.

Boxplots• These are under-

rated, but extremely helpful tools for examining the distribution of data.

• They have the big advantage over barcharts that they show the range of values in data.

0

50

100

median

25th centile

75th centile

Highest value

Lowest value

121212N =

Collembola density in 3 habitats

in Colyford wood

SITE

coppiceconiferscleared

colle

mbo

la m

-2

14000

12000

10000

8000

6000

4000

2000

0121212N =

Species richness in 3 habitats

in Colyford wood

SITE

coppiceconiferscleared

Spe

cies

rich

ness

per

sam

ple

14

12

10

8

6

4

2

0

Here we have an example of boxplots in action, describing soil insects in 3 areas of a wood in Devon (ancient oak, modern conifer, and newly cleared).

Scatterplots

pH

depth

These are very commonly used and powerful tools. The Y axis (going up) is always assumed to depend on the X variable.

Think hard before putting any marks on here! Generally you should fit a singe best fit line if the correlation is p<0.05, otherwise leave alone.

year

NEVER dot – dot!! Unless your areabsolutely sure that interpolation is valid

Lichen cover on tombstone

This is WRONG

year

Height of 1 child

This is OK

Species richness against %

fine fraction (2-0.5mm)

Rs = 0.61**, Spp = 1.2 + 0.09*%fine

% in fraction 2-0.5mm

3020100

Sp

eci

es

rich

ne

ss

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6

4

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A sample scattergraph with best-fit line.

A hybrid scatter-graph with error bars. You may want to consider the validity of joining the points up, but it can be justified.

Scatterplots, contd

Beware the false axis!

Why is this graph meaningless?

1 5 10Bag number

Weight of leaf

Pie charts

These are good for showing the proportional composition of communities, but not so good for comparing samples of different sizes.

CATSEAR

GRASS

ULEX

DFLEX

P-P graphsThese are used to decide about normality of data.

If the plotted points lie on the green line (the line of Y=X) the data distribution appears to be that of the Normal or Gaussian curve.

Here we see the same data before and after a logarithmic transformation.

Normal P-P Plot of LOI

Observed Cum Prob

1.00.75.50.250.00

Exp

ect

ed

Cu

m P

rob

1.00

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.50

.25

0.00

Normal P-P Plot of LOGLOI

Observed Cum Prob

1.00.75.50.250.00

Exp

ect

ed

Cu

m P

rob

1.00

.75

.50

.25

0.00

Kite diagramsThese are mainly used to show how communities of 3-10 entities vary along an axis (time, or a spatial gradient such as downstream from a pollution source). They are good for ecological studies, less so for physical data.

Age

, yea

rs0

5

10

Species A Species B Species CTotal counts for each species

I want to give you the secret to good results:

• The secret to a successful exercise in data collection is to plan (ie visualise) the final presentation BEFORE you start to collect the data!

• This does NOT mean you plot the graph then make up the data!! It means that you consider what patterns might arise in your data, how best to portray these on a graph, and thereby allows you to plan what data you will need to collect, and drives the whole project along.

Fieldwork PCs+

GRAPHS

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A student wants to measure the pH values of ponds on Wimbledon common, already planning the talk that they will give a week later. They want to show a graph like this:

Shows maxima andminima

pH6

7

1 2 3 4 5 6 Pond #

The distribution of pH valuesin ponds on Wimbledon Common

They know that there are 6 accessible ponds to visit and want to be able to talk about all of them. They work out how long they have for each pond, and collect 4 measurements from each.

A quick boxplot exercise

Imagine that you are to undertake research on the Common, measuring properties of two ponds.

Produce a boxplot chart comparing them between sites under TWO scenarios:

1: There is significant variation between the sites - at least one is different.2: There is a little variation between sites, but only due to random noise.

Now produce a scatter graph showing how two variables are related. Let’s plot yield of vegetation against dose of fertiliser added. Again plot 2 scenarios:

1: How you imagine the data would work out if the two variables are significantly related (correlated in the jargon)

2: What you might find if the fertiliser turned out to a waste of money.