STA 490H1S: Tabular and Graphical Display of
Data
Alison L. Gibbs
Department of Statistics
University of Toronto
Winter 2011
Gibbs
STA 490H1S
Notes from Altman and Bland
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Continuous data:
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Summary statistics such as means should not be given to more
than one extra decimal place over the raw data.
Greater precision may be warranted for measures of variability
such as the standard deviation or standard error as they are
often used in further calculations.
Categorical data:
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Summarize as frequencies or percentages.
Percentages alone can be confusing if the denominator is
unclear.
Percentages should usually be given as integers; one decimal
place may sometimes be reasonable but not in small samples.
There is rarely a need to show categorical data graphically.
Gibbs
STA 490H1S
Notes from Altman and Bland 2
I
Test statistics, correlation coefficients, and p-values:
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No more than two decimal places for test statistics and
correlation coefficients.
p-values to one or two significant figures.
Tables versus figures:
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A figure that displays only two means with their standard
errors or confidence intervals is a waste of space.
Gibbs
STA 490H1S
Ehrenberg’s rules for tables
(with contributions from Wainer)
1. Round to two significant or effective digits.
Humans cannot understand more than two digits very easily.
And who cares about more digits? “This year’s school budget
is $27,329,681.”
2. Frame the display with suitable summary statistics.
3. Figures are easier to compare in columns than rows.
4. Order by size or some other way that makes sense.
5. Use spacing to aid perception.
6. Graphs versus tables: Graphs are of little use in
communicating the quantitative aspects of the data but they
can highlight qualitative results.
Gibbs
STA 490H1S
An example from Wainer
Version 1:
Battery Life in Hours
Battery
Brands
Constant Charge
PowerBat
Servo-Cell
Never Die
Electro-Blaster
Cassette
Player
5
7
4
8
10
Gibbs
Radio
19
24
21
28
26
Flashlight
10
13
12
16
15
STA 490H1S
Portable
Computer
3
5
2
6
4
An example from Wainer
Version 2:
Battery
Brands
Never Die
Electro-Blaster
PowerBat
Servo-Cell
Constant Charge
Radio
28
26
24
21
19
Battery Life in Hours
Cassette Portable
Flashlight
Player
Computer
16
8
6
15
10
4
13
7
5
12
4
2
10
5
3
Gibbs
STA 490H1S
An example from Wainer
Version 3:
Battery
Brands
Never Die
Electro-Blaster
PowerBat
Servo-Cell
Constant Charge
Usage averages
Radio
28
26
24
21
19
24
Battery Life in Hours
Cassette
Portable
Flashlight
Player
Computer
16
8
6
15
10
4
13
7
5
12
4
2
10
5
3
13
7
4
Gibbs
STA 490H1S
Battery
Averages
15
14
12
10
9
12
An example from Wainer
Version 4:
Battery
Brands
Never Die
Electro-Blaster
PowerBat
Servo-Cell
Constant Charge
Usage averages
Radio
28
26
24
21
19
24
Battery Life in Hours
Cassette
Portable
Flashlight
Player
Computer
16
8
6
15
10
4
13
7
5
12
10
13
Gibbs
4
5
7
STA 490H1S
2
3
4
Battery
Averages
15
14
12
10
9
12
An example from Wainer
An alternative?
25
battery
15
10
5
Battery Life (hours)
20
Never Die
PowerBat
Electro-Blaster
Constant Charge
Servo-Cell
Radio
Flashlight
Cassette
Computer
Appliances
Gibbs
STA 490H1S
Burn’s ACCENT Principles for effective graphical display
The essence of a graph is the clear communication of quantitative
information.
I Apprehension
Ability to correctly perceive relations among variables.
I Clarity
Ability to visually distinguish all the elements of a graph.
I Consistency
Ability to interpret a graph based on similarity to previous
graphs.
I Efficiency
Ability to portray a possibly complex relation in as simple a
way as possible.
I Necessity
The need for the graph, and the graphical elements.
I Truthfulness
Ability to determine the true value represented by any
graphical element by its magnitude relative.
Gibbs
STA 490H1S
Pie Charts?
Edward Tufte:
“Pie charts are bad and that the only thing worse than one pie
chart is lots of them.”
Gibbs
STA 490H1S
Pie Charts?
Edward Tufte:
“Pie charts are bad and that the only thing worse than one pie
chart is lots of them.”
Studies have shown that piecharts are hard to read if you actually
have to answer questions about the numbers they represent. This
is mostly because differences in angles are not easy to judge for the
human eye.
Gibbs
STA 490H1S
References
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D.G. Altman and J.M. Bland (1996) Presentation of
numerical data. BMJ 312, 572.
I
D. A. Burn (1993), ”Designing Effective Statistical Graphs”.
In C. R. Rao, ed., Handbook of Statistics, vol. 9, Chapter 22.
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A.S.C. Ehrenberg (1977) Rudiments of Numeracy. Journal of
the Royal Statistical Society A 140, 277-297.
I
A.S.C. Ehrenberg (1978) Graphs or Tables? The Statistician
27, 87-96.
I
H. Wainer (1997) Improving Tabular Displays, With NAEP
Tables as Examples and Inspirations. Journal of Educational
and Behavioral Statistics, 22, 1-30.
Gibbs
STA 490H1S