Data Visualization and Exploration

scales: colors and numbers

Transition from last week

• Last week we looked at plots showing the distribution of raw data values.
• There are a variety of ways to do this - context and audience matter.
• Consider the sample data to the right with variables
• Replicate (1, 2, 3)
• Treatment (“Control”, “Drug”)
• Speed (decimal values)

Replicate	Treatment	Speed
1	Control	43.69202
1	Control	41.85664
1	Control	49.11707
1	Control	49.79331
…	…	…

Bar plots to “SuperPlots”

Figure 1: “SuperPlots” (from https://rupress.org/jcb/article/219/6/e202001064/151717/SuperPlots-Communicating-reproducibility-and)“.

Replacing bar plots¹

Figure 2: Evolution of a “SuperPlot”.

Do any of these panels stand out as familiar, helpful, confusing, surprising?

1. From https://rupress.org/jcb/article/219/6/e202001064/151717/SuperPlots-Communicating-reproducibility-and.

A final recommendation

Figure 3: A ggplot “SuperPlot” with beeswarm, showing more raw data and distribution information.

Current events

Figure 4: Colored bar chart showing weather patterns in Florida.

Weather in Florida

Figure 5: Colored bar chart showing weather patterns in Florida.

• What would you change?
• How would you do it?
• What data would you use?
• How would you get the data?

Weather in Florida

What data might go into the forecast graphic and how else could we represent that more effectively?

Color contrast

Color contrast measures the difference in luminance¹ between two colors. A few good options are below.

• coolors.co
• accessibleweb.com
• acquia
• Material Design (Google)

1. loosely how “bright” color is

Current WCAG 2.1 AA Recommendations

For text:

standard defines an acceptable contrast ratio as at least 3:1 for large or bold text and icons and 4.5:1 for general reading text.

For graphics:

shapes, icons, and large text relative to their background color meets a minimum ratio of 3:1.

Regardless of contrast, color alone should rarely be used. Encode redundantly with symbols, patterns, or labeling.

Built-in palette tools

Color is a complicated subject.

It helps to have a variety of tools, though ever-changing, to explore.

We can do a bit of experimentation with the palette() command to set in-session color defaults.

Figure 6: Threads screenshot discussing a new color model https://oklch.fyi/.

Pause to experiment.

OKLCH

The webpage has a great interactive tool showcasing one key achievement of this color model - lightness.

Style guides (as constraints)

Some companies have style or branding guides that could influence what colors are available for use in data visualizations.

To compensate you could

• use shapes or line styles
• directly annotate data

Enter log scales

Figure 7: Change as percent.

Figure 8: Change as a multiplier.

Properties of growth

Suppose we are interested in “percent change” as a metric.

Percent change	Multiplier
700%	8
100%	2
0%	1
-50%	\(\frac{1}{2}\)
-87.5%	\(\frac{1}{8}\)

• Which is “more important” doubling or halving?
• How should each change be represented in a graph?

Spacing

Figure 9: Spacing on linear and log scales.

Re-analysis Goals

Graph all three columns of the data in exponential.csv, first on linear scale and next on a log scale.

Observe how the use of vertical space draws attention to the “action” in the data. In other words, “what do you notice?”

Dealing with ugly

The default R axes are not necessarily pleasing.

par(mar = c(4.1, 5.1, 0.8, 0.8))
x <- 0:20
plot(x, 2^(x), ylab = "Doubling of values", xlab = "Number")

Figure 10

As it is, few things will change that.

Changing the scale

The default R axes are not necessarily pleasing.

par(mar = c(4.1, 5.1, 0.8, 0.8))
x <- 0:20
plot(x, 2^(x), ylab = "Doubling of values", xlab = "Number", log = 'y')

Figure 11

New questions

What to plot, what to label?

• Do we plot the logarithm and have a “nicer” axis?
• Do we plot the raw data and have more complex axis?

Regardless of choice, how do we make it user-friendly and “nice” aesthetically?

Improving aesthetics

Suppress axes with axes = F, but invite them back with the axis() command.

You’ll have to ask and answer

• “where are the ticks?”,
• “what are their labels?”, and
• “what is the vertical axis label?”.

Fortunately we do not have to worry about the horizontal axis (here representing “time”) because that pretty much only makes sense on a linear scale.

par(mar = c(4.1, 5.1, 0.8, 0.8))
x <- 0:20
plot(x, 2^(x), log = 'y')

Figure 12

Options for formatting (base R)

Suppose we wanted to show tick mark labels as powers of ten.

After setting axes = F, we could try a variety of things using axis(). We could

• list at locations
• list at locations and labels
• list at locations and labels (one at a time)

Or we could (and will) use more advanced tools or specialized packages.

Comparing values or growth rates

f <- function(x)exp(x)
g <- function(x)exp((1 + 0.5*x)*x)
par(mar = c(4.1, 5.1, 0.8, 0.8))
plot(f, xlim = c(0, 2), ylim = c(0, g(2)))
plot(g, xlim = c(0, 2), col = 2, add = T)

Change in value.

f <- function(x)exp(x)
g <- function(x)exp((1 + 0.5*x)*x)
par(mar = c(4.1, 5.1, 0.8, 0.8))
plot(f, xlim = c(0, 2), ylim = c(1, g(2)), log = 'y')
plot(g, xlim = c(0, 2), col = 2, add = T, log = 'y')

Change in slope.

A good rule of thumb

To illustrate value use a linear scale, to inspect rate of change use a log scale.

Consider the log-transformation of \(y = ae^{bt}\) which becomes \(\ln(y) = \ln(a) + bt\). (Verify this.)

For convenience we use the natural logarithm, but the rules work the same for any other choice of base.

This means the underlying exponential parameter \(b\) is emphasized as the slope when graphed on the log scale.