Signal & Noise

Jon Reades - j.reades@ucl.ac.uk

1st October 2025

What is it?

What is it?

What is it?

Start with a Chart

The problem of relying on statistics alone was amply illustrated by Anscombe’s Quartet (1973)…

• We are not very good at looking at spreadsheets.
• We are very good at spotting patterns visually.

Sometimes, we are too good; that’s where the stats comes in. Think of it as the ‘tiger in the jungle’ problem..

Anscombe’s Quartet

X1	Y1	X2	Y2	X3	Y3	X4	Y4
10.0	8.04	10.0	9.14	10.0	7.46	10.0	6.58
8.0	6.95	8.0	8.14	8.0	6.77	8.0	5.76
13.0	7.58	13.0	8.74	13.0	12.74	13.0	7.71
9.0	8.81	9.0	8.77	9.0	7.11	9.0	8.84
11.0	8.33	11.0	9.26	11.0	7.81	11.0	8.47
14.0	9.96	14.0	8.10	14.0	8.84	14.0	7.04
6.0	7.24	6.0	6.13	6.0	6.08	6.0	5.25
4.0	4.26	4.0	3.10	4.0	5.39	4.0	12.5
12.0	10.84	12.0	9.13	12.0	8.15	12.0	5.56
7.0	4.82	7.0	7.26	7.0	6.42	7.0	7.91
5.0	5.68	5.0	4.74	5.0	5.73	5.0	6.89

Summary Statistics for the Quartet

Property	Value
Mean of x	9.0
Variance of x	11.0
Mean of y	7.5
Variance of y	4.12
Correlation between x and y	0.816
Linear Model	y = 3 + 0.5x

But What do They Look Like?

The Tiger that Isn’t

I would argue that the basic purpose of charts and of statistics as a whole is to help us untangle signal from noise. We are ‘programmed’ to see signals, so we need to set the standard for ‘it’s a tiger!’ quite high in research & in policy-making.

Or, as Albert Einstein reportedly said: “If I can’t picture it, I can’t understand it.”

Think it Through

You can make a lot of progress in your research without any advanced statistics!

• A ‘picture’ isn’t just worth 1,000 words, it could be a whole dissertation!
• The right chart makes your case eloquently and succinctly.

Always ask yourself:

• What am I trying to say?
• How can I say it most effectively?
• Is there anything I’m overlooking in the data?

A good chart is a good way to start!

What Makes a Good Plot?

A good chart or table:

1. Serves a purpose — it is clear how it advances the argument in a way that could not be done in the text alone.
2. Contains only what is relevant — zeroes in on what the reader needs and is not needlessly cluttered.
3. Uses precision that is meaningful — doesn’t clutter the chart with needless numbers.

Far too many charts or tables could be easily written up in a single sentence.

Far too many charts or tables contain redundancy, clutter, and ‘flair’.

Don’t report average height of your class to sub-millimeter level accuracy, or lat/long to sub-atomic scale.

For Example…

How much precision is necessary in measuring degrees at the equator?

Decimal Places	Degrees	Distance
0	1	111km
1	0.1	11.1km
2	0.01	1.11km
3	0.001	111m
4	0.0001	11.1m
5	0.00001	1.11m
6	0.000001	11.1cm
7	0.0000001	1.11cm
8	0.00000001	1.11mm

Goals by World Cup Final

Goals by World Cup Final

Average Goals by World Cup Final

In 1982 the number of teams went from 16 to 24, and in 1998 it went from 24 to 32!

How far from Equality?

How far from Equality?

The Purpose of a Chart

The purpose of a graph is to show that there are relationships within the data set that are not trivial/expected.

Choose the chart to highlight relationships, or the lack thereof:

• Think of a chart or table as part of your ‘argument’ – if you can’t tell me how a figure advances your argument (or if your explanation is more concise than the figure) then you probably don’t need it.
• Identify & prioritise the relationships in the data.
• Choose a chart type/chart symbology that gives emphasis to the most important relationships.

If a picture is worth 1,000 words, make sure those words aren’t “blah, blah, blah…”

Not Everyone Likes Tables

Getting information from a table is like extracting sunlight from a cucumber. Arthur & Henry Fahrquhar (1891)

Real Numbers

Consider the difference in emphasis between:

• 11316149
• 11,316,149
• 11.3 million
• 11 x 10\(^{6}\)
• 22%
• 22.2559%

Always keep in mind the purpose of the number.

There’s Still a Role for Tables

Why a table is sometimes better than a chart:

• You need to present data values with greater detail
• You need to enable readers to draw comparisons between data values
• You need to present the same data in multiple ways (e.g. raw number and percentage)
• You want to show many dimensions for a small number of observations

e.g. percentage of people falling into each ethnic or income category for a small number of wards or boroughs.

Undergraduate Tables (Failing Grade)

Undergraduate Tables (Passing Grade)

Postgraduate Tables (Failing Grade)

Postgraduate Tables (Passing Grade)

Design for Tables

Principles:

• Reduce the number of lines to a minimum (and you should almost never need vertical lines).
• Use ‘white-space’ to create visual space between groups of unrelated (or less related) elements.
• Remove redundancy (if you find yourself typing ‘millions’ or ‘GBP’ or ‘Male’ repeatedly then you’ve got redundancy).
• Ensure that meta-data is clearly separate from, but attached to, the graph (i.e. source, title, etc.).

Additional Resources

There’s so much more to find, but:

• 26 Ways to Enhance your Tables in Tableau
• Tables Aren’t Boring, You Are

• The Visual Display of Quantitative Information (the Tufte and Graves-Morris 1983 classic)
• Why Tufte’s Wrong…
• Tufte is Dead; Long Live Tufte

Thank You

References

Tufte, Edward R, and Peter R Graves-Morris. 1983. The Visual Display of Quantitative Information. Vol. 2. 9. Graphics press Cheshire, CT.