Data Visualization

April 3, 2015

• When you should graph

• What you should graph

• Given some data, how would you graph it

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When should you graph your data?

Data Visualization

AlwaysDon’t just make graphs for client reports -- graph your data for yourself, so you understand it.

If you use a table in a report, see if you can make it into a graph.

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Why graphs?

Because of the environment that humans evolved in, we are much

better at getting info from color, size, shape, and position than from reading text.

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Find the dangerous creatures!

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Why graphs work

• Color

• Size• Shape

• Position

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Why else do people like graphs?

People like cool-looking stuff.

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Not cool Cool

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What are we currently doing?

• Making lots of tables

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Group Mean 25% 50% 75%

Bananas 11.3 2.7 4.6 23.1

Kittens 4.0 0.9 3.6 7.5

Phones -3.1 -11.0 -2.9 2.2

Variable Parameter Estimate

Cuteness 0.6***

Ability to Fly 1.4***

Deadliness 11.2***

Telepathy -9.8***

Big Ears -17.3***

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What is wrong with tables?

Tables give only a partial picture – means only tell us so much.

Figuring out what’s bigger, and by how much, requires more work.

The information is not necessarily in any order, so we need to read all the numbers.

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What kinds of graphs should you make?

• The distribution, instead of giving just mean, median, etc.

• The relationship between two variables – the conditional distribution

• Graph estimation results’ point estimates and confidence intervals

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What to expect out of this presentation

1. Discussion of the type of graph (e.g. distributions)

2. How the type of graph applies to continuous vs. categorical data

3. Extensions (e.g. graphing more than one at a time)

What not to expect: how to do these in any particular software.

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Distributions

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Distributions – Continuous variables

Make density plots/histograms for continuous variables. These give much more information than means, medians, etc.

Two distributions with the same mean, but which are dramatically different.

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Density vs. histogram

A density plot is basically a smoothed histogram.

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Distributions – Categorical variables

Make bar charts for categorical variables.

Tip: if your categories don’t have any inherent order, order them from largest to smallest.

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Compare distributions using color

Suppose we want to compare the distribution of income among different occupations. Plot all the distributions, distinguished by color, and use transparency to make them all visible simultaneously.

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Highlighting important facts

Add vertical lines to highlight the means.

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Relationships

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Relationships between variables

If we’re asking, for example, what GDP growth looks like at different levels of government spending, we can show this using a scatterplot.

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How to show trends

We can highlight the trend using scatterplot smoothing, which adapts the shape of the trend line to the data.

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How to show multiple groups

We can see if the relationship differs among groups by giving each group a color.

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Another use for colors

Suppose we want to come up with rules to identify people’s favorite food based on population density and elevation (bear with me)

Can we see this on a graph?

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Graphing relationships with categorical data

With categorical data, you typically can’t use scatterplots because points fall right on top of each other (‘overplotting’).However! We can use jittering to move the plotted points slightly.

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Without jittering With jittering

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Graphing relationships with categorical data

The next step beyond jittering is to use a boxplot, which shows– The mean, – 25th and 75th percentiles, – 1.5 times the inter-quartile range (IQR)– outliers (plotted as points)

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mean

75th pctile

mean + 1.5 *IQR

outlier

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Looping back

A boxplot isn’t, after all, all that different from the multi-colored density plot we showed earlier. Which is better depends on what you’re trying to show.

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Use log scale if your data spans a wide range

Let’s say you have a large range of values, but most of your data is concentrated to one part of the range.

It’s easier to see what’s going when we use log scale.

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Estimation results

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Graphing estimation results

We make a lot of regression tables, but we can make them easier to understand by putting them into graphs.

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ggplot(df, aes(population_density, elevation, color = favorite_food)) + geom_point()

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dataset x variable y variable

make scatterplot

color variable

All graphs made in R and ggplot2

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Data Visualization Checklist

• Always graph

• Use color, size, shape, and position

• Three important types of graph:– Distribution– Relationship– Estimation results

• Highlight important facts

• Make it cool-looking

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