Most statistical data analysis, and thus most graphical data analysis, is directed towards modelling of relationships, but many statistical problems have a different flavour: their focus is comparison, and the key question is assessing agreement or disagreement between two or more data sets or subsets with variables measured in the same units. I survey the range of official and user-written graphical programs available in Stata 8 for such problems, with emphasis on making use of all the information in the data. Recurrent themes include (1) the use of reference lines, especially horizontal reference lines, indicating benchmark cases; (2) the relative merits of superimposition and juxtaposition; (3) how far methods work well at a range of sample sizes; ( 4) standing on giant's shoulders by writing wrappers around existing Stata commands; (5) use (and abuse) of summary statistics appropriate for such problems.

Nicholas J. Cox

English

Research Papers in Economics

Graphics (and numerics) for comparison
Nicholas J. Cox
University of Durham
n.j.cox@durham.ac.ukSynopsis
Most statistical data analysis, and thus
most graphical data analysis, is directed
towards modelling of relationships, but
many statistical problems have a diﬀerent
ﬂavour: their focus is comparison, and
the key question is assessing agreement or
disagreement between two or more data
sets or subsets with variables measured in
the same units.
Here I survey (some of) the range
of oﬃcial and user-written graphical
programs available in Stata 8 for such
problems, with emphasis on making use
of all the information in the data.Themes
Recurrent themes include
 use reference lines, especially horizontal
reference lines, to indicate benchmark
cases
 don’t juxtapose, superimpose!
 what methods work well at a range of
sample sizes?
 stand on giant’s shoulders: write
wrappers around existing Stata commands
 what summary statistics are
appropriate for comparison?
The biggest message of all is thatStata
8
isout
withall-new
graphicsPreviously...
I talked in London last year on graphics
before (and especially after) modelling,
particularly about a suite of commands
which can follow a variety of modelling
commands, not just regress or anova.
That project involved graphics for Stata 7,
now obsolete. There is an ongoing project
revising programs for Stata 8 and some
results were shown at the Boston meeting.
Overheads for the Boston talk can be
found at
http://fmwww.bc.edu/repec/nasug2003/
CoxNASUG2003.pdfHomilies I
A good graph is a good answer to a good
question...
The question could be general, often one
of
 what are these data like?
 what patterns, trends, similarities,
diﬀerences?
 what interesting, informative, puzzling
detail?
⇒ we want graphs to provide summary
and exposure and to show both coarse
and ﬁne structure
The best general graphs allow both:
e.g. dot plots or scatter plots, but
arguably less so e.g. box plots or
histograms.Homilies II
A good graph is a good answer to a good
question...
The question could be speciﬁc, as for
example
 are these variables or subsets identical
(as a reference case)?
 is diﬀerence constant (e.g. 0)?
is ratio constant (e.g. 1)?
 has a transformation done what we
wanted? is distribution more nearly
symmetric, Gaussian, homoscedastic?
⇒ we want graphs to answer the question
directly without posing too many
challenges (e.g. decoding or mental
rotation)An emerging issue
No dialogs∗ have been written for the
user-written commands discussed in this
talk.
Ars longa, vita brevis...
How many users (really) want dialogs?
How many user-programmers will write
dialogs?
A possible and valuable new role in the
Stata user community – a new ecological
niche – would be writing dialogs for other
people’s programs.
∗ dialogues, if you preferGeneral: Distribution functions
cumulative probability or frequency as y
is plotted versus
value of variable as x
OS∗ cumul will calculate
SSC† distplot will graph for
 several variables
 or several subsets
 reverse (a.k.a. survival) functions
 transformed vertical scale
 diﬀerent plot types
∗ OS means ‘oﬃcial Stata’
† SSC means Boston archive: use sscGeneral: Quantile functions
quantile as y
is plotted versus
‘plotting position’ as x
OS quantile is limited
STB-61∗ quantil2 for Stata 7 is more
ﬂexible
qplot (under development) will graph
 several variables
 or several subsets
 reverse order
 transformed horizontal scale
 ranks
 diﬀerent plot types
∗ STB means Stata Technical BulletinTwo novel details
Diﬀerent plot types may be obtained by a
syntax of
command subcommand ...
Here we can exploit the structure of
graph twoway, as for example with
distplot line ... or
qplot spike ...
The menu is area, bar, connected, dot,
dropline line, scatter, spike for these
two commands.
Transformed scales can be shown on any
user-speciﬁed scale supplied e.g.
tscale(invnorm(@))
with @ as placeholder for transformand
SSC mylabels is a utility to produce
labels in the original scale
The idea goes back to Patrick Royston
(STB-34, 1996)Speciﬁc: Symmetry of distribution
OS symplot plots
(upper quantile − median) as y
versus
(median − lower quantile) as x
Symmetry implies that y = x
i.e. reference case plots as a sloping line
SSC skewplot plots
1
2 (upper quantile + lower quantile) as y
versus
(upper quantile − lower quantile) as x
Symmetry implies that y = median
i.e. reference case plots as a horizontal line
You can plot several variables or several
subsets
skewplot shows more detail than box
plots!Speciﬁc: Paired observations I
We often ask speciﬁc questions:
can the means be considered identical?
With scatter plots, it is easy to forget the
precise question, especially as linearity
y = a + bx is more general than equality
y = x or constant diﬀerence y = a + x or
constant ratio y = bx.
The concordance correlation coeﬃcient
measures agreement (is y = x?). In many
problems correlation is used as a measure
of agreement, whereas it is a measure of
linearity (is y = a + bx?).
See Stata Journal 2(2) (Tom Steichen and
NJC) for concord. A Stata 8 version is in
preparation.Speciﬁc: Paired observations II
It is not easy to read oﬀ y − x or y/x from
a scatter plot.
John Tukey (and Doug Altman and
Martin Bland) urged plotting diﬀerence
versus mean, so that equality plots as a
horizontal line.
SSC pairplot gives this as one of various
choices. Others are ratio versus geometric
mean, diﬀerences or ratios in speciﬁed sort
order, etc.
pairplot is a wrapper around
twoway rspike || function.
If diﬀerences or ratios answer the question
of interest, show them directly!General: Frequencies of categorical data
OS histogram is geared towards
continuous variables, and must be coaxed
when given categorical data.
OS graph bar, hbar, dot oﬀer more scope,
but for some basic problems (e.g. showing
percents) you must calculate the variables
to be shown beforehand.
This cries out for a wrapper.
SSC catplot∗ was originally written for
teaching and can be used for 1, 2 or 3
categorical variables.
A structure of command subcommand
allows bar, hbar, dot with almost
identical syntax. Horizontal displays are
preferable unless value labels are very
short.
∗ Names can be diﬃcult! A liking for cats
was decisive here.Speciﬁc: Frequencies of graded data
Graded data (e.g. opinion scales) are often
plotted as stacked bars. A reﬁnement is to
split grades into those shown as positive
and those shown as negative, i.e. to slide
each bar so that it straddles zero.
Calculating frequencies or percents,
adjusting some to negative values and
stacking in a sensible order are trivial but
also ﬁddly, so a wrapper saves the busy
work.
SSC∗ slideplot does the graphics.
Subcommands are hbar and bar.
A twin program, SSC∗ majority, shows
tables of majorities, calculated from
‘votes’ deemed positive and negative.
∗ soon!Speciﬁc: Conﬁdence intervals
Plotting a bundle of conﬁdence intervals
vertically or horizontally is a standard
tool.
SSC ciplot allows you to ﬁre up OS
ci and plot intervals for several subsets
and/or several variables, all in one. Thus
ciplot is a wrapper for ci as well as for
graph.
A single option horizontal ﬂips axes,
courtesy of a handle provided by graph
twoway rcap.
Roger Newson is developing a more
general and very much complementary
approach, plotting conﬁdence intervals
from a reduced data set prepared
beforehand.0
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scatter || function
Percent literate for African countries 2000-
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Percent literate for African countries 2000Benin
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Burkina Faso
Burundi
Cameroon
Cape Verde
Central Aﬁcan Republic Chad
Comoros
Congo
Congo, Democratic Republic
Cote d'Ivoire
Djibouti
Equatorial Guinea
Ethiopia
Gabon
Gambia
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
Madagascar
Malawi
Maldives
Mali
Mauritania
Mauritius
Mozambique
Namibia
Niger Nigeria
Rwanda
Senegal
Seychelles
Sierra Leone
South Africa
Sudan
Swaziland
Tanzania
Togo
Uganda
Zambia
Zimbabwe
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pairplot
Percent literate for African countries 20000 20 40 60 80
percent of category
black
dark
medium
red
fair
catplot hbar
Eye and hair colour, Caithness
blue light medium dark0 20 40 60 80
percent of category
black
dark
medium
red
fair
catplot dot
Eye and hair colour, Caithness
blue light medium dark0 20 40 60 80 100
percent of category
black
dark
medium
red
fair
catplot hbar with stack
Eye and hair colour, Caithness
blue light medium dark-100 -50 0 50 100
percent
black
dark
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slideplot hbar
Eye and hair colour, Caithness
blue light medium dark-100
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Eye and hair colour, Caithness
blue light medium dark-60 -40 -20 0 20 40
percent votes
$75k+
$50-75k
$30-50k
$15-30k
<$15k
slideplot hbar
U.S. election 1992
Clinton BushN. Eng.
Mid Atl
E.N.C.
W.N.C.
S. Atl.
E.S.C.
W.S.C.
Mountain
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Cooling degree days
95% conﬁdence intervals
ciplot with hor
U.S. cities

Graphics (and numerics) for comparison

http://fmwww.bc.edu/repec/usug2003/compare_gph.pdf

Graphics (and numerics) for comparison

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Research Papers in Economics