Lecture 3
Displaying Data

ABD 3e Chapter 2

Chris Merkord

Key Learning Objectives

  • Distinguish between explanatory and exploratory figures
  • Identify what makes a good graph
  • Understand how data types drive figure design
  • Understand how to make effective tables
  • Identify best practices in figure design

Displaying data helps you understand your data and communicate your results

Exploratory vs. Explanatory Plots

Exploratory

  • Purpose: find the story in the data
  • Audience: you (the analyst)
  • Minimal concern for aesthetics
    • Rough labels
    • Default colors
    • Rapid iteration
  • Focused on understanding patterns and relationships

Explanatory

  • Purpose: share the story of the data
  • Audience: others
  • Careful design choices
    • Clear labels and scales
    • Thoughtful color use
    • Accessible in grayscale
  • Assumes the audience may be unfamiliar with the data

Data Visualization Example: Anscombe’s Quartet

  • Four data sets with identical summary statistics.
  • Same means, standard deviations, and correlations
Dataset \(\\bar{x}\) \(\\bar{y}\) \(s_x\) \(s_y\) \(r_{x,y}\)
I 9.0 7.5 3.316 2.031 0.816
II 9.0 7.5 3.316 2.031 0.816
III 9.0 7.5 3.316 2.031 0.816
IV 9.0 7.5 3.316 2.031 0.816

Trendlines for Anscombe’s quartet show exactly the same pattern

  • A fitted trendline looks essentially identical across datasets

Visualizing the Data Reveals What Statistics Miss

  • The underlying data distributions are very different
  • Patterns include nonlinearity, outliers, and leverage points
  • Graphs expose structure that summary statistics conceal

What Makes a Plot Effective (or Misleading)

Good plots

  • Show the data, not just summaries
  • Make patterns easy to see
  • Represent magnitudes accurately
  • Use clear, readable graphics

Bad plots

  • Hide or obscure the data
  • Make patterns difficult to detect
  • Distort magnitudes
  • Use cluttered or unclear graphics

Show the data, not just the summaries

  • Shows means only

  • Variation within positions is hidden

  • Shows individuals

  • Points are overplotted

  • Obscures density of points

  • Shows all of the observations.
  • Jittering - shifting points horizontally (random)

Make Patterns Easy to See

How patterns get hidden

  • Rely on a single plot
  • Use inappropriate or misleading scales
  • Arrange groups arbitrarily
  • Ignore meaningful ordering

How patterns are revealed

  • Explore multiple plot types
  • Choose scales that match the data
  • Arrange factors intentionally
  • Order groups:
    • By level for ordinal variables
    • By mean (or another summary) for nominal variables

Nonsensical Order Hides Patterns

Non-intuitive ordering of factors hides patterns.

Inappropriate scales hides patterns

Transform Data to Reveal Patterns

In this plot, a log-log scale reveals a pattern hidden on the linear scale. Lifespan by body size in mammals, data from Allison & Cicchetti 1976

Mistake: Display Magnitudes Dishonestly

How to represent magnitudes dishonestly:

  • Start bar plots at a non-zero value

How to represent magnitudes honestly:

  • Start bar plots at zero Why? The weight of a bar plot makes us think in magnitudes.

Present Magnitudes Dishonestly (1 of 2)

This plot suggests that centers are 20X taller than guards.

Present Magnitudes Dishonestly (2 of 2)

Note: This applies to bar plots that naturally start at zero. Not all plots need to start at zero.

Mistake: Draw Elements Unclearly

How to draw graphical elements unclearly:

  • Unthinkingly accept default options from plotting programs.
  • Do not consider how a diverse audience will interpret your figure.

How to draw graphical elements clearly:

  • Reflect on plot design.

  • Consider the diverse audience you are reaching and how they may interact with your plot.

Draw Graphics Unclearly

In this plot, x-axis labels obscure one another.

Flip Axes to Present Graphics Clearly

Flipping axes makes categories readable.

Always consider color-blind readers

Simulated view of the graph on the left for two types of color-blindness

Direct Labeling Clarifies Graphics