Data visualization

Matt Bhagat-Conway

Why visualize data

• Many people are visual thinkers
• Data visualization can remove the need to understand exact numbers and show the big picture

• Data visualizations are less likely to put people to sleep than tables 😴

The power of data visualization

• Data visualization helps us make sense of large datasets
• We can make conclusions and hypotheses that would be difficult from looking at the data alone
• But, we can also mislead and misdirect

The power of data visualizations: Anscombe’s quartet

Anscombe (1973)

• These datasets all have the same means, standard deviations, correlation coefficients, regression lines, and \(R^2\)

Histograms

• A histogram visualizes a univariate (one variable) distribution

Creating a histogram in Excel

• Select the column you want to create a histogram of
• Choose Insert -> Charts -> Statistical -> Histogram
• By double-clicking on the bars you can edit the number of bins, bin size, how outliers are handled
• Histograms should not have gaps between the bars even though they do by default in Excel
  • After double-clicking on the bars, choose the Fill and Line tab (paint can icon) and set the border to “solid line” to fill the gaps

Boxplots/box and whisker plots

• Box plots visualize data by showing the median, 25th and 25th percentiles, tails, and outliers
• The center line is the median, the top of the box is the 75th percentile, and the bottom of the box is the 25th percentile
• Whiskers generally extend to largest/smallest data value less than 1.5 \(\times\) interquartile range from the ends of the box
  • Sometimes 5th/95th percentiles
• Points beyond these are plotted individually as outliers

Boxplots/box and whisker plots

Making a boxplot in Excel

• Select the data you want to create a boxplot for
• Insert -> Charts -> Statistical -> Box and Whisker

Multiple boxplots

• Often, you will see multiple boxplots presented next to one another

Multiple box plots in Excel

• If you select multiple columns, Excel will make multiple box plots
• Unfortunately, often you want to do this by separating out different observations in the same column
• This is inexplicably difficult in Excel
• Best way I’ve found is to make a table in Excel, filter by the attributes you want, and copy variables to a new sheet

Scatter plots

• Used when you have two continuous variables
• Simply plot the location of each data point
• In a regression context, the independent variable is customarily on the x axis

Scatter plots: other properties

• When there are many points, reducing the size or opacity can help show trends

Scatter plots in Excel

• Select the data you want, then Insert -> Chart -> Scatter plot
• To change the size, select Format tab, then the series name on the left, and open the format pane
• Click the Fill and Line tab (paint bucket), then select Marker, Marker options, Built-in, and edit the size
• Transparency

Trendlines

• It may occasionally be useful to add a trendline
• Format -> Add Chart Element -> Trendline

The curse of trendlines

• Excel provides many options for trendlines; don’t get carried away

© xkcd

Bar charts

• Used with one continuous and one categorical variable

Bar charts in Excel

• Select the column with labels and the column with values
• Insert -> Chart -> Bar chart

Error bars

• Error bars indicate a margin of error/confidence interval around the tops of the bars
  • Or occasionally just the standard error - be careful here!

Grouped bar charts

• A common variation of the bar chart is the grouped bar chart
• Used when you want to have multiple bars associated with each \(x\)-axis value

Grouped bar charts in Excel

• If you select multiple columns when creating a bar/column chart in Excel, a grouped bar chart is the default

Stacked bar charts

• Often used with percentages but can be used with other things as well

Stacked bar chart in Excel

• Each portion of the stacked bar should be in a different column
• Select all the columns and choose Insert -> Chart -> Stacked Column
  • or 100% stacked column to have Excel normalize to 100% for you

3D bar charts

• 3D bar charts look cool but they’re confusing
• Generally, the bar height represents the value being represented, but it is easy to misinterpret the area or volume as the value being represented

Line charts

• Line charts suggest change over time, so the \(x\) axis should always be time
• This graph also shows a common way graphs can mislead
• look at the extents of the \(y\) axis

Multiple lines

• It’s common to have multiple lines on line charts

Multiple \(y\) axes

• Occasionally, you’ll even see a graph with multiple \(y\) axes

Bhagat-Conway and Zhang (2023)

Line charts in Excel

• In Excel, how you insert a line chart depends on your \(x\) axis
• If you want Excel to generate the \(x\) axis as 1, 2, 3…, you need to add a line chart
• If you have a column with the \(x\) axis values, you want an XY (scatter) plot with lines

Line charts and error bars

• You’ll occasionally see line charts with error bars on them

Line charts and error bars

• It’s more common to see line charts with error “ribbons”

Pie charts

• Pie charts are common in government and business but rare in academia
• Can be hard to compare relative sizes
• Should only be used with data that totals 100%
• Avoid 3D pie charts for similar reasons as 3D bar charts

Pie charts in Excel

• Let’s use the “Stacked bar” tab to make a pie chart of commute mode in the Triangle
• Select the row with the Triangle
• Insert -> Chart -> 2D pie chart
• The labels are probably wrong; click “Select data” and specify the range for the category labels

Other gimmicks kinds of charts

• There are lots of other kinds of charts that are occasionally useful
• But probably 95% of charting needs are covered by what we’ve seen today
• It’s easy to get carried away

Accessibility concerns: alternative text

• Charts are a graphical element, and are not accessible to all individuals
• Many visually-impaired individuals will use a screen reader, software that speaks the text on their screen out loud
• All charts should either have alternative (alt) text, or be fully described in the text of the report
  • Add alt text in Word by right-clicking and choosing “view alt text”
  • Also applies to non-decorative images
• For small charts, you can list the values in the alt text (e.g. the percentages drving alone, etc.)
• For larger charts, you should describe overall trends/findings
• For many organizations, ensuring accessibility is a legal requirement under Section 508 of the Americans with Disabilities Act

Thanks to Dhruti Bhagat-Conway for recommendations on this section

Accessibility concerns: color vision deficiency

• Color vision deficiencies (color-blindness) are very common, especially among White males (~8%) (Machado et al. 2009)
• This can make charts useless

Accessibility concerns: color vision deficiency

Deuteranomaly (red-green): very common

Protanomaly (red-green): less common

Tritanomaly (blue-yellow): rare

What to do about it

• Avoid presenting information only using color
• Avoid using red and green together
• Vary saturation and brightness in addition to color

Contrast

• Can you read this?
• Text and graphical elements should provide enough contrast that they are easily distinguishable
• You can check the contrast of two colors using the WebAIM contrast checker
• Or generate color schemes using Coolers

Logarithmic (log) scales

Linear scale

Palm and Bhagat-Conway, under review; data: IPUMS

Logarithmic (log) scales

Logarithmic scale

Palm and Bhagat-Conway, under review; data: IPUMS

Logarithmic (log) scales

© xkcd

Log-log scales

Arshad et al. (2018)

Other ways axes can mislead

More misleading axes

Reuters via LiveScience

And more…

Georgia Dept of Public Health via Columbia Climate Law/Atlanta Journal-Constitution

Chart formatting in Excel

• Most tools to customize your chart are on the “Chart Design” and “Format” toolbars
• Double-clicking on elements of a chart lets you format and edit them

Advanced charting tools

• In R, the ggplot package is widely known and used, and very powerful
• matplotlib is the go-to plotting library for Python

References

Anscombe, F. J. 1973. “Graphs in Statistical Analysis.” The American Statistician 27 (1): 17–21. https://doi.org/10.2307/2682899.

Arshad, Sidra, Shougeng Hu, and Badar Nadeem Ashraf. 2018. “Zipf’s Law and City Size Distribution: A Survey of the Literature and Future Research Agenda.” Physica A: Statistical Mechanics and Its Applications 492 (February): 75–92. https://doi.org/10.1016/j.physa.2017.10.005.

Bhagat-Conway, Matthew Wigginton, and Sam Zhang. 2023. “Rush Hour-and-a-Half: Traffic Is Spreading Out Post-Lockdown.” PLoS One.

Machado, G. M., M. M. Oliveira, and L. Fernandes. 2009. “A Physiologically-based Model for Simulation of Color Vision Deficiency.” IEEE Transactions on Visualization and Computer Graphics 15 (6): 1291–98. https://doi.org/10.1109/TVCG.2009.113.

This work by Matthew Bhagat-Conway is licensed under a Creative Commons Attribution 4.0 International License.