Strategy and tactics for
graphic multiples in Stata
Nicholas J. Cox
Department of Geography
Durham University, UK
1
Comparison
Many useful graphs compare two or more sets of
values, and so can be thought as of multiples.
Often there can be a fine line between richly
detailed graphics and busy, unintelligible
graphics that lead nowhere.
In this presentation I survey strategy and tactics
for developing good graphic multiples in Stata.
2
Strategies: what to do
superimpose (on top) or juxtapose (alongside)?
plot different versions or reductions of the data
transform scales for easier comparison
linear reference patterns
backdrops of context
3
Tactics: details of what to do
over() and by() options and graph combine
kill the key or lose the legend if you can
annotations and self-explanatory markers
4
Datasets visited
James Short’s collation from the transit of Venus
Florence Nightingale’s data on deaths in the
Crimean War
deaths from the Titanic sinking
Grunfeld panel data
admissions to Berkeley
hostility in response to insult or apology
fluctuations in Arctic sea ice
5
Original programs discussed
catplot (SSC)
devnplot (SSC)
qplot (Stata Journal)
sparkline (SSC)
spineplot (SJ)
stripplot (SSC)
tabplot (SSC)
6
Categorical comparisons
7
Berkeley admissions data
A classic dataset covers admissions to six graduate
majors by gender at UC Berkeley.
At first sight, females were discriminated against.
But there is an underlying interaction: major by
major, females generally do well, yet their
acceptance rates are worse on more popular
majors.
This is an example of an amalgamation paradox
named for E.H. Simpson (1922–) but known to
K. Pearson (1857–1936) and G.U. Yule (1871–
1951).
8
Berkeley data references
The original reference was Bickel, P.J., E.A.
Hammel and J.W. O’Connell. 1975. Sex bias in
graduate admissions: Data from Berkeley.
Science 187: 398–404.
The Berkeley data were discussed as an example
for Stata in Cox, N.J. 2008. Spineplots and
their kin. Stata Journal 8: 105–121.
9
A simple problem?
The structure of the data is already well known.
The challenge is how best to present it.
There are three categorical variables
major (anonymously A, B, C, D, E, F)
gender (male, female)
decision (accept, reject)
so the data are just 24 frequencies.
10
Bar chart
Many researchers would reach first for a bar chart.
Here is a slightly non-standard example, produced
by tabplot (SSC), which is for one-way, twoway or three-way bar charts.
One feature here is showing numbers too in a
hybrid of graph and table.
A cosmetic detail is toning down the use of colour.
Large blocks with strong colours are unsubtle.
11
admitted
30.4%
55.5%
male
69.6%
female
decision
44.5%
rejected
12
Mosaic plot or spineplot
The previous bar chart omitted the frequencies. We
can show them using a mosaic plot or spineplot.
The proportions of both variables are shown,
giving marginal and conditional distributions.
Areas of tiles are proportional to raw frequencies.
Departures from independence are easily seen.
The program here is spineplot.
13
0
25
percent by gender
50
75
100
100
75
55.5%
69.6%
rejected
30.4%
admitted
50
25
0
44.5%
male
female
14
Drilling down
The bar chart and spineplot do a fair job of
showing the gross breakdown with four percents.
(Two are redundant.)
Predictably, both would be rejected as trivial by
many journal reviewers, but both could be useful
for presentations.
But clearly we need to drill down to see the
patterns for different majors.
15
More detailed bar chart
Stacking bars is a standard strategy, but the result
is immediately much more complicated.
Showing all the detail does not always help.
Focusing more sharply on the response of
interest is a way forward.
In general there is no need for alphabetical order.
Here majors A to F are already ordered by
admission rate.
16
A
male
female
B
male
female
C
male
female
D
male
female
E
male
female
F
male
female
0
200
400
frequency
admitted
600
800
rejected
17
Dot chart
Dot charts as advocated by W.S. Cleveland remain
under-used by comparison with bar charts.
In Stata that usually means graph dot.
By using marker position alone, rather than bar
length, they are less busy and thus ease more
detailed comparison.
Here it is easier to identify that female admission
rates are higher for four majors and lower for the
other two.
18
A
B
C
D
E
F
0
25
50
admission rate (%)
male
75
100
female
19
Details for dot charts
Open symbols (e.g. ○ not ●) tolerate overlap much
better than closed symbols. ○ can even be
combined with + whenever nearly equal values
are possible.
Legends (keys) are at best a necessary evil. Selfexplanatory or at least memorable symbolisation
is to be prized wherever it is possible. Using blue
for males and pink for females is a simple
example.
20
A scatter plot?
Many statistically-minded people find the idea of
bar charts trivial, but their practice not very
helpful. Where is the scatter plot, they cry?
Plotting admission rate against number of
applicants re-introduces a crucial aspect, size of
major. This allows identification of positive
correlation for males and negative correlation
for females, hence the paradox.
This is currently my favourite plot for these data.
21
females
males
A
80
B
B
60
40
C
D D
E
A
C
E
20
F F
0
0
200
400
number of applicants
600
800
22
Previously…
In an earlier version of this plot I had admissions
versus applications, both raw frequencies.
Reference lines here are lines through the origin
such as y = x and y = 0.5x for 100% and 50%
admission rates.
But it is simpler to plot admission rates. Then the
reference lines are horizontal.
23
Slogans: the banal in search of the profound
Focus as far as possible on the response or
outcome, the variable you most want to explain.
Linear reference patterns are good and horizontal
patterns better.
Omit what is unimportant and keep what is
important.
Even for a very simple problem, it is rare that a
single graph meets all needs.
24
Continuous comparisons
25
Hostility change
Results of an experiment reported by Atkinson, C.
and J. Polivy. 1976. Effects of delay, attack, and
retaliation on state depression and hostility.
Journal of Abnormal Psychology 85: 570–576.
Male and female subjects were made to wait and
then either were insulted or received an apology.
Half were given a chance to retaliate by negatively
evaluating the experimenter.
Hostility was measured before and after the
experiment.
26
Variables in hostility study
Response:
Change in hostility, a difference of scores and so
approximately continuous
Predictors all binary:
Treatment: insult, apology
Gender: male, female
Retaliation allowed: yes, no
27
ANOVA-type problems: What to plot?
Change in hostility is adequately modelled by a
simple linear model, using analysis of variance.
What to plot for similar analyses is key here.
Box plots (with medians etc.) are surprisingly
common even when comparison of means is the
central question.
Plotting means with standard errors or confidence
intervals is also common, but what about the
detail omitted?
28
devnplot (SSC)
devnplot (SSC) is named for its emphasis on
plotting deviations. Deviations are measured
from any level you care to specify, but deviations
from means are the default.
“devplot” was too ugly and “deviationplot”
too long.
Quantile enthusiasts will see it as a way to plot
ordered quantiles side by side. Compare
quantile or qplot (SJ).
29
devnplot syntax
The syntax resembles standard modelling syntax,
response named first and any predictors
following.
With one variable named we get in essence a
quantile plot for that variable, a plot of the
ordered values versus an implicit cumulative
probability scale.
The scaffolding emphasising that each value can be
represented by a deviation from a level might
seem redundant, but bear with me.
30
60
change
40
20
0
-20
31
Adding predictors to the syntax
You can specify either one or two predictors.
The result is a quantile plot for each subset, namely
a category or combination of categories.
An undocumented upper limit arising from a limit
in graph is 20 subsets, but more than 20 would
likely be too busy any way.
A third binary predictor can be shown indirectly by
a separate() option.
32
60
change
40
20
0
-20
insult
apology
treatment
33
treatment
insult
apology
60
change
40
20
0
-20
male
female
male
female
gender
34
treatment
apology
insult
60
change
40
20
0
-20
male
male
female
female
gender
no retaliation
retaliation
35
devnplot virtues
The display serves well in showing variation within
subsets as well as variation between.
Interactions can be seen.
The scaffolding (in subtle gray) helps to tie the
values of a group together visually.
The separate() option is best used to highlight a
few unusual or interesting cases.
36
Waterfall plots
Similar plots have been called waterfall plots,
especially in clinical oncology.
But watch out: waterfall plots (or charts) have at
least two quite different meanings elsewhere, in
business and physical science contexts.
Sometimes the jungle of plot names is just a
confounded nuisance.
37
James Short and
the transit of Venus (1763)
Short collated and corrected observations made by
various astronomers during the transit of Venus
in 1761.
The parallax here is the angle subtended by the
earth’s radius, as if viewed and measured from
the surface of the sun.
The data will be published and discussed in Stata
Journal 13(3).
38
Deviation plot
A deviation plot adjusts to the differing sample
sizes.
Here deviations are relative to 25% trimmed
means (otherwise known as midmeans or
interquartile means). Boxplot fans can think that
they average values within the box.
The context here of careful precise measurement
does not rule out the occasional mild or even
strong outlier.
39
11
10
9
8
7
6
310
316
page in Short (1763)
325_1
325_2
25% trimmed means shown
40
Quantile plots
Deviation plots (waterfall plots, if you prefer) are
in essence quantile plots.
qplot from SJ can
superimpose through its over() option
or juxtapose through its by() option.
How well does that compare?
41
11
10
9
8
7
310
316
325_1
325_2
6
0
.2
.4
.6
fraction of the data
.8
1
42
310
316
325_1
325_2
12
10
8
6
0
.5
1
0
.5
1
0
.5
1
0
.5
1
fraction of the data
Graphs by page in Short (1763)
43
devnplot or qplot?
I prefer devnplot here, although qplot has
useful options too, including flexibility over axis
scales.
For example, if we plot against standard normal
quantiles, normal (Gaussian) distributions will
follow straight lines.
44
325_2
325_1
316
310
12
10
8
6
-2 -1 0
1
2
-2 -1 0
1
2
-2 -1 0
1
2
-2 -1 0
1
2
standard normal quantile
Graphs by page in Short (1763)
45
Strip plot
An alternative display is a strip plot or dot plot.
(Many other names exist.)
Here it takes on the flavour of a histogram but with
markers or point symbols for each value. Some
binning allows stacking.
stripplot from SSC offers an alternative to
official Stata’s dotplot.
46
325_2
325_1
316
310
6
7
8
9
parallax (seconds)
10
11
25% trimmed means shown
47
Histograms or box plots?
Many statistical people would start almost
automatically with histograms or box plots for
such data. How do they compare?
You can judge for yourself.
A specific problem with histograms is keeping the
amount of scaffolding down. It is easy to lose
valuable real estate in axis and title information.
48
10
5
0
0
5
10
316
0
5
10
325_1
5
10
325_2
0
Frequency
310
6
8
10
12
parallax (seconds)
Graphs by page in Short (1763)
49
frequency
10
310
5
0
10
316
5
0
10
325_1
5
0
10
325_2
5
0
6
8
10
12
parallax (seconds)
Graphs by page in Short (1763)
50
How did we do that?
The main trick here is moving the subtitles to the
left. It only works here because they are so short,
but accept good fortune, however it comes.
The incantation is
subtitle(, ring(1) pos(9) nobox
nobexpand)
51
Box plots
Box plots do work fairly well, but they just leave
out too much detail for my taste.
If the details are accessible, you can decide for
yourself whether they are trivial.
52
310
316
325_1
325_2
6
7
9
8
parallax (seconds)
10
11
53
Timed comparisons
54
Time series
Comparisons of time series are an especially rich,
and especially challenging, area of statistical
graphics.
The widespread term spaghetti plot hints
immediately at the difficulties.
As always, we want to combine a grasp of general
patterns with access to individual details.
55
sparkline
The Grunfeld data (webuse grunfeld) are a
classic dataset in panel-based economics.
Ten companies were monitored for 1935–54.
This can be an example for sparkline (SSC).
The name sparkline was suggested by Edward
Tufte for intense text-like graphics. Time series
are the most obvious example.
56
Vertical and horizontal
By default sparkline stacks small graphs
vertically.
If several graphs are combined, it is typical to cut
down on axis labels and rely on differences in
shape to convey information.
Horizontal stacking is also supported, which can be
useful for archaeological or environmental
problems focused on variations with depth or
height.
57
2226.3
kstock
2.8
6241.7
mvalue
2792.2
1486.7
invest
257.7
1935
1940
1945
year
1950
1955
58
1
2
3
4
5
6
7
8
kstock
mvalue
invest
kstock
mvalue
invest
1935 1940 1945 1950 1955 1935 1940 1945 1950 1955
9
10
kstock
mvalue
invest
1935 1940 1945 1950 1955 1935 1940 1945 1950 1955
Graphs by company
59
1
2
3
2226.3
669.7
4
888.9
414.9
kstock
6241.7
2.8
2676.3 50.5
2803.3
97.8
1001.5
10.2
mvalue
1486.7
2792.2
645.5
1362.4
189.6
1170.6
410.9
174.93
invest
257.7
209.9
5
33.1
6
40.29
7
804.9
238.7
8
511.3
213.5
kstock
183.2
398.4
6.5
927.3
91.9
197
135.72
210.1
100.2
.8
1193.5
191.5
90.08
mvalue
151.2
98.1
89.51
invest
39.67
20.36
23.21
12.93
1935 1940 1945 1950 1955 1935 1940 1945 1950 1955
9
10
468
14.33
kstock
496
162
87.94
3.23
mvalue
213.3
66.11
6.53
58.12
invest
20.89
.93
1935 1940 1945 1950 1955 1935 1940 1945 1950 1955
60
Nightingale’s data
Florence Nightingale (1820-1910) is well
remembered for her nursing in the Crimean war
and less so as a pioneer in data analysis.
Her most celebrated dataset is often reproduced
using her polar diagram, but is easier to think
about as time series.
Zymotic (loosely, infectious) disease mortality
dominates other kinds, so much so that a square
root scale helps comparison. (A logarithmic scale
over-transforms here.)
61
Nightingale's data on mortality in the Crimea
1000
zymotic disease
wounds and injuries
all other causes
800
600
400
200
0
1854
1855
1856
annualised rates per 1000
62
Nightingale's data on mortality in the Crimea
zymotic disease
wounds and injuries
all other causes
900
625
400
225
100
25
0
1854
1855
1856
annualised rates per 1000
63
Sparkline?
A sparkline display is useful to show relative shape,
such as times of peaks.
We see that seasonality is only part of what is being
seen. The harsh winter of 1854–5 coincided with
some of the hardest battles of the war.
64
Nightingale's data on mortality in the Crimea
140.1
all other causes
2.5
115.8
wounds and injuries
.4
1022.8
zymotic disease
1.4
1854
1855
1856
annualised rates per 1000
65
Arctic sea ice
Another time series example concerns seasonal
variation in Arctic sea ice for 2002-13, just 12
annual series.
The usual spaghetti plot shows the similarity of
series well, but makes comparing them difficult.
Although some people try using a key or legend,
that rarely works well beyond a very few series.
Separating out the series runs into the opposite
problem.
66
Arctic sea ice extent (million km²) 2002-13
15
10
5
0
1 Jan
1 Apr
1 Jul
1 Oct
31 Dec
67
Arctic sea ice extent (million km²)
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
15
10
5
15
10
5
15
10
5
1 Jan
1 Apr
1 Jul
1 Oct 31 Dec 1 Jan
1 Apr
1 Jul
1 Oct 31 Dec
1 Jan
1 Apr
1 Jul
1 Oct 31 Dec 1 Jan
1 Apr
1 Jul
1 Oct 31 Dec
68
Combine: backdrop as context
So, use both ideas:
Plot all data as a backdrop
(subdued, say using grayscale).
Plot each series within its context
(with stronger colour, thicker line).
See for discussion Cox, N. J. 2010. Graphing
subsets. Stata Journal 10: 670–681.
69
Arctic sea ice extent (million km²)
2002
2003
2004
2005
15
15
15
15
10
10
10
10
5
5
5
5
0
0
1 Jan 1 Apr
1 Jul
1 Oct 31 Dec
0
1 Jan 1 Apr
2006
1 Jul
1 Oct 31 Dec
0
1 Jan 1 Apr
2007
1 Jul
1 Oct 31 Dec
1 Jan 1 Apr
2008
15
15
15
10
10
10
10
5
5
5
5
0
0
0
0
1 Jul
1 Oct 31 Dec
1 Jan 1 Apr
2010
1 Jul
1 Oct 31 Dec
1 Jan 1 Apr
2011
1 Jul
1 Oct 31 Dec
1 Jan 1 Apr
2012
15
15
15
10
10
10
10
5
5
5
5
0
1 Jan 1 Apr
1 Jul
1 Oct 31 Dec
0
1 Jan 1 Apr
1 Jul
1 Oct 31 Dec
1 Jul
1 Oct 31 Dec
2013
15
0
1 Oct 31 Dec
2009
15
1 Jan 1 Apr
1 Jul
0
1 Jan 1 Apr
1 Jul
1 Oct 31 Dec
1 Jan 1 Apr
1 Jul
1 Oct 31 Dec
70
Cross-fertilisation
71
Titanic data
The Titanic sank in 1912. Statistically, we want to
explain fraction survived in terms of age, sex and
class of those on board.
A standard graph is a stacked or divided bar graph,
but it lacks punch. The command used was
catplot (SSC).
So, we end with something rather different,
produced with devnplot.
72
adult
child
1
0.8
fraction
0.6
0.4
0.2
0
f
m
first
f
m
second
f
m
third
died
f
m
first
f
m
second
f
m
third
f
m
crew
survived
73
level is weighted mean for age and sex
age
child
1
1 2
adult
1 2
1
C
2
0.8
0.6
0.4
3
3
1
3
0.2
3
C
2
0
female
male
female
male
sex
1,2,3,C = first, second, third class and crew
74