Data Visualization Principles

2024-10-07

Some motivation

Some motivation

Some motivation

Some motivation

Some motivation

Some motivation

Some motivation

Some motivation

Data visualization principles

Data visualization principles

  • Following Karl’s approach, we show some examples of plot styles we should avoid, explain how to improve them, and use these as motivation for a list of principles.

  • We compare and contrast plots that follow these principles to those that don’t.

Data visualization principles

  • The principles are mostly based on research related to how humans detect patterns and make visual comparisons.

  • The preferred approaches are those that best fit the way our brains process visual information.

  • When deciding on a visualization approach, it is also important to keep our goal in mind.

Data visualization principles

We may be comparing a

  • Viewable number of quantities.
  • Describing distributions for categories or numeric values.
  • Comparing the data from two groups.
  • Describing the relationship between two variables.

Encoding data using visual cues

We start by describing some principles for visualy encoding numerical values:

  • aligned lengths
  • position
  • angles
  • area
  • brightness
  • color hue

Encoding data using visual cues

Example:

  • Suppose we want to report the results from two hypothetical polls regarding browser preference taken in 2000 and then 2015.

  • For each year, we are simply comparing five quantities – the five percentages for Opera, Safari, Firefox,IE, and Chrome.

Encoding data using visual cues

A widely used graphical representation of percentages, popularized by Microsoft Excel, is the pie chart:

Encoding data using visual cues

  • Here we are representing quantities with both areas and angles, since both the angle and area of each pie slice are proportional to the quantity the slice represents.

  • This turns out to be a sub-optimal choice since, as demonstrated by perception studies, humans are not good at precisely quantifying angles and are even worse when area is the only available visual cue.

Encoding data using visual cues

The donut chart uses only area:

Compare 2000 to 2015

  • Can you determine the actual percentages and rank the browsers’ popularity?

  • Can you see how they changed from 2000 to 2015?

Show the numbers

A better approach is to simply show the numbers. It is not only clearer, but would also save on printing costs if printing a paper copy:

Browser 2000 2015
Opera 3 2
Safari 21 22
Firefox 23 21
Chrome 26 29
IE 28 27

Barplots

Length is the best visual cue:

If foreced to make a pie chart

Label each pie slice with its respective percentage so viewers do not have to infer them:

Know when to include 0

  • When using barplots, it is misinformative not to start the bars at 0.

  • This is because, by using a barplot, we are implying the length is proportional to the quantities being displayed.

  • By avoiding 0, relatively small differences can be made to look much bigger than they actually are.

  • This approach is often used by politicians or media organizations trying to exaggerate a difference.

Know when to include 0

Below is an illustrative example used by Peter Aldhous in this lecture.

(Source: Fox News, via Media Matters.)

Know when to include 0

Here is the correct plot:

Know when to include 0

Another examples:

(Source: Fox News, via Flowing Data.)

Know when to include 0

And here is the correct plot:

Know when to include 0

One more example:

(Source: Venezolana de Televisión via Pakistan Today and Diego Mariano.)

Know when to include 0

Here is the appropriate plot:

Know when to include 0

  • When using position rather than length, it is not necessary to include 0.

  • In particularly when comparing between to within groups variability.

Do not distort quantities

President Obama used the following chart to compare the US GDP to the GDP of four competing nations:

(Source: The 2011 State of the Union Address)

Do not distort quantities

Here is comparison of using radius versus area:

Do not distort quantities

  • ggplot2 defaults to using area rather than radius.

  • Of course, in this case, we really should be using length:

Order categories by a meaningful value

  • When one of the axes is used to show categories the default ggplot2 behavior is to order the categories alphabetically when they are defined by character strings.

  • If they are defined by factors, they are ordered by the factor levels.

  • We rarely want to use alphabetical order.

  • Instead, we should order by a meaningful quantity.

Order categories by a meaningful value

Note that the plot on the right is more informative:

Order categories by a meaningful value

Here is another example:

Show the data

  • We have focused on displaying single quantities across categories. We now shift our attention to displaying data, with a focus on comparing groups.

  • Suppose we want to describe height data to an extra-terrestrial.

Show the data

A commonly used plot, popularized by Microsoft Excel, is a barplot like this:

Show the data

Show the data

Use jitter to avoid over-plotting

Histograms

Since there are so many points, it is more effective to show distributions rather than individual points. We therefore show histograms for each group:

Ease comparisons

  • Use common axes

  • If horizontal comparison, stack graphs vertically

  • If vertical comparison, stack graphs horizontally

Stack vertically

Same axis

Boxplot is a vertical

Stack horizontally

Contrast and compare

Consider transformations

Here is a terrible plot comparing population across continents

Two countries drive average

Transformations

Here a log transformation provides a much more informative plot:

Visual cues to be compared should be adjacent

Note that it is hard to compare 1970 to 2020 by country:

Visual cues to be compared should be adjacent

Much easier if they are adjacent

Use color

The comparison becomes even easier to make if we use color to denote the two things we want to compare:

Think of the color blind

  • Approximately 1 in 12 men (8%) and 1 in 200 women (0.5%) worldwide are color blind.

  • The most common type of color blindness is red-green color blindness, which affects around 99% of all color blind individuals.

  • The prevalence of blue-yellow color blindness and total color blindness (achromatopsia) is much lower.

  • An example of how we can use a color blind friendly palette is described here.

Think of the color blind

  • Example of color-blind-friendly color palette:

Plots for two variables

In general, you should use scatterplots to visualize the relationship between two variables.

However, there are some exceptions.

  • We describe two alternative plots here:
    • slope chart
    • Bland-Altman plot

Slope charts

Slope charts adds angle as a visual cue, useful when comparing two groups and each element across two variables, such as years.

Scatterplot version

Bland-Altman plot

Shows difference in the y-axis and average on the x-axis.

Encoding a third variable

We can use

  • different colors or shapes for categoris

  • areas, brightness or hue for continuous values

Encoding a third variable

We encode OPEC membership, region, and population.

Point shapes available in R

Using intensity or hue

When selecting colors to quantify a numeric variable, we choose between two options: sequential and diverging.

Sequential colors

Sequential colors are suited for data that goes from high to low. High values are clearly distinguished from low values. Here are some examples offered by the package RColorBrewer:

Diverging colors

Diverging colors are used to represent values that diverge from a center. We put equal emphasis on both ends of the data range: higher than the center and lower than the center.

Avoid pseudo-3D plots

The figure below, taken from the scientific literature, shows three variables: dose, drug type and survival:

Avoid pseudo-3D plots

  • Humans are not good at seeing in three dimensions and our limitation is even worse with regard to pseudo-three-dimensions.

Avoid pseudo-3D plots

  • When does the purple ribbon intersects the red?

Avoid pseudo-3D plots

Color is enough to represent the categorical variable:

Avoid pseudo-3D plots

Pseudo-3D is sometimes used completely gratuitously: plots are made to look 3D even when the 3rd dimension does not represent a quantity. This only adds confusion and makes it harder to relay your message. We show two examples:

Avoid pseudo-3D plots

(Images courtesy of Karl Broman)

Avoid too many significant digits

  • By default, statistical software like R returns many significant digits.

  • The default behavior in R is to show 7 significant digits.

  • That many digits often adds no information and the added visual clutter can make it hard for the viewer to understand the message.

Avoid too many significant digits

As an example, here are the per 10,000 disease rates, computed from totals and population in R, for California across the five decades:

state year Measles Pertussis Polio
California 1940 37.8826320 18.3397861 0.8266512
California 1950 13.9124205 4.7467350 1.9742639
California 1960 14.1386471 NA 0.2640419
California 1970 0.9767889 NA NA
California 1980 0.3743467 0.0515466 NA

Avoid too many significant digits

  • We are reporting precision up to 0.00001 cases per 10,000, a very small value in the context of the changes that are occurring across the dates.
state year Measles Pertussis Polio
California 1940 37.8826320 18.3397861 0.8266512
California 1950 13.9124205 4.7467350 1.9742639
California 1960 14.1386471 NA 0.2640419
California 1970 0.9767889 NA NA
California 1980 0.3743467 0.0515466 NA

Avoid too many significant digits

  • In this case, two significant figures is more than enough and clearly makes the point that rates are decreasing:
state year Measles Pertussis Polio
California 1940 37.9 18.3 0.8
California 1950 13.9 4.7 2.0
California 1960 14.1 NA 0.3
California 1970 1.0 NA NA
California 1980 0.4 0.1 NA

Avoid too many significant digits

Useful ways to change the number of significant digits or to round numbers are

  • signif

  • round

You can define the number of significant digits globally by setting options like this: options(digits = 3).

Values compared in columns

Another principle related to displaying tables is to place values being compared on columns rather than rows. Compare these two presentations:

state disease 1940 1950 1960 1970 1980
California Measles 37.9 13.9 14.1 1 0.4
California Pertussis 18.3 4.7 NA NA 0.1
California Polio 0.8 2.0 0.3 NA NA

Values compared in columns

Another principle related to displaying tables is to place values being compared on columns rather than rows. Compare these two presentations:

state year Measles Pertussis Polio
California 1940 37.9 18.3 0.8
California 1950 13.9 4.7 2.0
California 1960 14.1 NA 0.3
California 1970 1.0 NA NA
California 1980 0.4 0.1 NA

Know your audience

Graphs can be used for

  1. our own exploratory data analysis,

  2. to convey a message to experts, or

  3. to help tell a story to a general audience.

Make sure that the intended audience understands each element of the plot.