Encoding data using visual cues

Visual cues are any element of design that gives the viewer clues as to how to use the object. For instance, we can look at door handles like these

and know exactly what to do with them. We don’t even need the “PUSH” and “PULL” – approaching just the pull handle in the wild gives sufficient visual cues that you know the door is a “pull” door. Encountering a metal plate with no handle is going to imply “push”. If the door on the right were a “push” door, you’d be momentarily confused! It’s poor design. Your plots should use visual cues to help readers understand how to use them with no confusion.

We start by describing some principles for encoding data. There are several approaches at our disposal including position, aligned lengths, angles, area, brightness, and color hue.

To illustrate how some of these strategies compare, let’s 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. A widely used graphical representation of percentages, popularized by Microsoft Excel, is the pie chart:

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. The donut chart is an example of a plot that uses only area:

To see how hard it is to quantify angles and area, note that the rankings and all the percentages in the plots above changed from 2000 to 2015. Can you determine the actual percentages and rank the browsers’ popularity? Can you see how the percentages changed from 2000 to 2015? It is not easy to tell from the plot. In fact, the pie R function help file states that:

Pie charts are a very bad way of displaying information. The eye is good at judging linear measures and bad at judging relative areas. A bar chart or dot chart is a preferable way of displaying this type of data.

In this case, simply showing the numbers is not only clearer, but would also save on printing costs if printing a paper copy:

The preferred way to plot these quantities is to use length and position as visual cues, since humans are much better at judging linear measures. The barplot uses this approach by using bars of length proportional to the quantities of interest. By adding horizontal lines at strategically chosen values, in this case at every multiple of 10, we ease the visual burden of quantifying through the position of the top of the bars. Compare and contrast the information we can extract from the two figures.

Notice how much easier it is to see the differences in the barplot. In fact, we can now determine the actual percentages by following a horizontal line to the x-axis.

If for some reason you need to make a pie chart, label each pie slice with its respective percentage so viewers do not have to infer them from the angles or area:

In general, when displaying quantities, position and length are preferred over angles and/or area. Brightness and color are even harder to quantify than angles. But, as we will see later, they are sometimes useful when more than two dimensions must be displayed at once.

Avoid pseudo-three-dimensional plots

The figure below, taken from the scientific literature⁵, shows three variables: dose, drug type and survival. Although your screen/book page is flat and two-dimensional, the plot tries to imitate three dimensions and assigned a dimension to each variable.

(Image courtesy of Karl Broman)

Humans are not good at seeing in three dimensions (which explains why it is hard to parallel park) and our limitation is even worse with regard to pseudo-three-dimensions. To see this, try to determine the values of the survival variable in the plot above. Can you tell when the purple ribbon intersects the red one? This is an example in which we can easily use color to represent the categorical variable instead of using a pseudo-3D:

##First read data
url <- "https://github.com/kbroman/Talk_Graphs/raw/master/R/fig8dat.csv"
dat <- read.csv(url)

##Now make alternative plot
dat %>% gather(drug, survival, -log.dose) %>%
  mutate(drug = gsub("Drug.","",drug)) %>%
  ggplot(aes(log.dose, survival, color = drug)) +
  geom_line()

Notice how much easier it is to determine the survival values.

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. Here are two examples:

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

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. In this case, two significant figures is more than enough and clearly makes the point that rates are decreasing:

Useful ways to change the number of significant digits or to round numbers are signif and round. You can define the number of significant digits globally by setting options like this: options(digits = 3).

Another principle related to displaying tables is to place values being compared on columns rather than rows. Note that our table above is easier to read than this one:

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.

As a simple example, consider that for your own exploration it may be more useful to log-transform data and then plot it. However, for a general audience that is unfamiliar with converting logged values back to the original measurements, using a log-scale for the axis instead of log-transformed values will be much easier to digest.

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. Below is an illustrative example used by Peter Aldhous in this lecture: http://paldhous.github.io/ucb/2016/dataviz/week2.html.

(Source: Fox News, via Media Matters⁶.)

From the plot above, it appears that apprehensions have almost tripled when, in fact, they have only increased by about 16%. Starting the graph at 0 illustrates this clearly:

Here is another example, described in detail in a Flowing Data blog post:

(Source: Fox News, via Flowing Data⁷.)

This plot makes a 13% increase look like a five fold change. Here is the appropriate plot:

Finally, here is an extreme example that makes a very small difference of under 2% look like a 10-100 fold change:

(Source: Venezolana de Televisión via Pakistan Today⁸ and Diego Mariano.)

Here is the appropriate plot:

When using position rather than length, it is then not necessary to include 0. This is particularly the case when we want to compare differences between groups relative to the within-group variability. Here is an illustrative example showing country average life expectancy stratified across continents in 2012:

Note that in the plot on the left, which includes 0, the space between 0 and 43 adds no information and makes it harder to compare the between and within group variability.

Do not distort quantities

During President Barack Obama’s 2011 State of the Union Address, the following chart was used to compare the US GDP to the GDP of four competing nations:

(Source: The 2011 State of the Union Address⁹)

Judging by the area of the circles, the US appears to have an economy over five times larger than China’s and over 30 times larger than France’s. However, if we look at the actual numbers, we see that this is not the case. The actual ratios are 2.6 and 5.8 times bigger than China and France, respectively. The reason for this distortion is that the radius, rather than the area, was made to be proportional to the quantity, which implies that the proportion between the areas is squared: 2.6 turns into 6.5 and 5.8 turns into 34.1. Here is a comparison of the circles we get if we make the value proportional to the radius and to the area:

gdp <- c(14.6, 5.7, 5.3, 3.3, 2.5)
gdp_data <- data.frame(Country = rep(c("United States", "China", "Japan", "Germany", "France"),2),
           y = factor(rep(c("Radius","Area"),each=5), levels = c("Radius", "Area")),
           GDP= c(gdp^2/min(gdp^2), gdp/min(gdp))) %>%
   mutate(Country = reorder(Country, GDP))
gdp_data %>%
  ggplot(aes(Country, y, size = GDP)) +
  geom_point(show.legend = FALSE, color = "blue") +
  scale_size(range = c(2,25)) +
  coord_flip() + 
  ylab("") + xlab("") # identical to labs(y = "", x = "")

Not surprisingly, ggplot2 defaults to using area rather than radius. Of course, in this case, we really should not be using area at all since we can use position and length:

gdp_data %>%
  filter(y == "Area") %>%
  ggplot(aes(Country, GDP)) +
  geom_bar(stat = "identity", width = 0.5) +
  labs(y = "GDP in trillions of US dollars")

Order categories by a meaningful value

When one of the axes is used to show categories, as is done in barplots, 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. In all the cases above, the barplots were ordered by the values being displayed. The exception was the graph showing barplots comparing browsers. In this case, we kept the order the same across the barplots to ease the comparison. Specifically, instead of ordering the browsers separately in the two years, we ordered both years by the average value of 2000 and 2015.

We previously learned how to use the reorder function, which helps us achieve this goal. To appreciate how the right order can help convey a message, suppose we want to create a plot to compare the murder rate across states. We are particularly interested in the most dangerous and safest states. Note the difference when we order alphabetically (the default) versus when we order by the actual rate:

data(murders)
p1 <- murders %>% mutate(murder_rate = total / population * 100000) %>%
  ggplot(aes(x = state, y = murder_rate)) +
  geom_bar(stat="identity") +
  coord_flip() +
  theme(axis.text.y = element_text(size = 8))  +
  xlab("")

p2 <- murders %>% mutate(murder_rate = total / population * 100000) %>%
  mutate(state = reorder(state, murder_rate)) %>% # here's the magic!
  ggplot(aes(x = state, y = murder_rate)) +
  geom_bar(stat="identity") +
  coord_flip() +
  theme(axis.text.y = element_text(size = 8))  +
  xlab("")

grid.arrange(p1, p2, ncol = 2) # we'll cover this later

We can make the second plot like this:

The reorder function lets us reorder groups as well. Earlier we saw an example related to income distributions across regions. Here are the two versions plotted against each other:

The first orders the regions alphabetically, while the second orders them by the group’s median.

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.

To motivate our first principle, “show the data”, we go back to our artificial example of describing heights to a person who is unaware of some basic facts about the population of interest (and is otherwise unsophisticated). This time let’s assume that this person is interested in the difference in heights between males and females. A commonly seen plot used for comparisons between groups, popularized by software such as Microsoft Excel, is the dynamite plot, which shows the average and standard errors.¹⁰ The plot looks like this:

The average of each group is represented by the top of each bar and the antennae extend out from the average to the average plus two standard errors. If all ET receives is this plot, he will have little information on what to expect if he meets a group of human males and females. The bars go to 0: does this mean there are tiny humans measuring less than one foot? Are all males taller than the tallest females? Is there a range of heights? ET can’t answer these questions since we have provided almost no information on the height distribution.

This brings us to our first principle: show the data. This simple ggplot2 code already generates a more informative plot than the barplot by simply showing all the data points:

For example, this plot gives us an idea of the range of the data. However, this plot has limitations as well, since we can’t really see all the 238 and 812 points plotted for females and males, respectively, and many points are plotted on top of each other. As we have previously described, visualizing the distribution is much more informative. But before doing this, we point out two ways we can improve a plot showing all the points.

The first is to add jitter, which adds a small random shift to each point. In this case, adding horizontal jitter does not alter the interpretation, since the point heights do not change, but we minimize the number of points that fall on top of each other and, therefore, get a better visual sense of how the data is distributed. A second improvement comes from using alpha blending: making the points somewhat transparent. The more points fall on top of each other, the darker the plot, which also helps us get a sense of how the points are distributed. Here is the same plot with jitter and alpha blending:

heights %>%
  ggplot(aes(sex, height)) +
  geom_jitter(width = 0.1, alpha = 0.2)

Now we start getting a sense that, on average, males are taller than females. We also note dark horizontal bands of points, demonstrating that many report values that are rounded to the nearest integer.

Faceting

Looking at the previous plot, it’s easy to tell that males tend to be taller than females. Before, we showed how we can plot two distributions over each other using an aesthetic mapping. Something like this:

heights %>%
  ggplot(aes(x = height, fill = sex)) +
  geom_histogram(alpha = .5, show.legend = TRUE) +
  labs(fill = 'Sex')

Sometimes, putting the plots on top of each other, even with a well-chosen alpha, does not clearly communicate the differences in the distribution. When we want to compare side-by-side, we will often use facets. Facets are a bit like supercharged aesthetic mapping because they let us separate plots based on categorical variables, but instead of putting them together, we can have side-by-side plots.

Two functions in ggplot give facets: facet_wrap and facet_grid. We’ll use facet_grid as this is a little more powerful.

Facets are added as an additional layer like this: + facet_grid(. ~ sex). Inside the function, we have a “formula” that is written without quotes (which is unusual for R). Since facet_grid takes a “formula”, all we have to do to facet is decide how we want to lay out our plots. If we want each of the faceting groups to lie along the vertical axis, we put the variable on which we want to facet before the “~”, and after the “~” we simply put a period. If we want the groups to lie along the horizontal axis, we put the variable after the “~” and the period before. In the example, we’ll separate the histogram by drawing them side by side along the horizontal axis.

heights %>%
  ggplot(aes(x = height)) +
  geom_histogram(binwidth = 1, color="black") +
  facet_grid(.~sex)

This would be the result if we took the females, plotted the histogram, then took the males, made another histogram, and then put them side by side. But we do it in one command by adding +facet_grid(...)

heights %>%
  ggplot(aes(height)) +
  geom_histogram(binwidth = 1, color="black") +
  facet_grid(. ~ sex, scales = "free_x")

heights %>%
  ggplot(aes(height)) +
  geom_histogram(binwidth = 1, color="black") +
  facet_grid(. ~ sex)

p2 <- heights %>%
  ggplot(aes(height)) +
  geom_histogram(binwidth = 1, color="black") +
  facet_grid(sex~., scales = 'free_y')
p2

p3=heights %>%
  ggplot(aes(sex, height)) +
  geom_boxplot(coef=3) +
  geom_jitter(width = 0.1, alpha = 0.2) +
  ylab("Height in inches")

p3

gapminder::gapminder %>%
  filter(year %in% c(1952,1972, 1992, 2002)) %>%
  filter(continent != 'Oceania') %>%
  ggplot(aes(x = lifeExp)) + 
  geom_density() +
  facet_grid(continent ~ year)

dslabs::gapminder %>%
  filter(year %in% c(1970, 2010) & !is.na(gdp)) %>%
  mutate(dollars_per_day = gdp/population/365) %>%
  mutate(labels = paste(year, continent)) %>%  # creating text labels
  ggplot(aes(x = labels, y = dollars_per_day)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.25)) +
  scale_y_continuous(trans = "log2") +
  ylab("Income in dollars per day")

dslabs::gapminder %>%
  filter(year %in% c(1970, 2010) & !is.na(gdp)) %>%
  mutate(dollars_per_day = gdp/population/365) %>%
  mutate(labels = paste(continent, year)) %>%
  ggplot(aes(labels, dollars_per_day)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = .25)) +
  scale_y_continuous(trans = "log2") +
  ylab("Income in dollars per day") + xlab('Continent and Year') 

dslabs::gapminder %>%
  filter(year %in% c(1970, 2010) & !is.na(gdp)) %>%
  mutate(dollars_per_day = gdp/population/365) %>%
  mutate(labels = paste(continent, year)) %>%
  ggplot(aes(labels, dollars_per_day)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = .25)) +
  scale_y_continuous(trans = "log2") +
  ylab("Income in dollars per day") + xlab('Continent and Year') +
  theme(plot.margin = margin(t=2, r = 2, b = 2, l = 2, unit = 'cm'),
        plot.background = element_rect(color = 'black', size = 1)) # Adds black border

Think of the color blind

About 10% of the population is color blind. Unfortunately, the default colors used in ggplot2 are not optimal for this group. However, ggplot2 does make it easy to change the color palette used in the plots. An example of how we can use a color blind friendly palette is described here: http://www.cookbook-r.com/Graphs/Colors_(ggplot2)/#a-colorblind-friendly-palette:

color_blind_friendly_cols <-
  c("#999999", "#E69F00", "#56B4E9", "#009E73",
    "#F0E442", "#0072B2", "#D55E00", "#CC79A7")

Here are the colors

From Seafood Prices Reveal Impacts of a Major Ecological Disturbance:

There are several resources that can help you select colors, for example this one: http://bconnelly.net/2013/10/creating-colorblind-friendly-figures/.

gp = dslabs::gapminder %>% 
filter(year == 1990 | year == 1995 | year==2000 |  year == 2005 | year==2010 ) %>%
ggplot(aes(x = continent, y = gdp/population, fill = as.factor(year)))  + coord_flip()

gp + geom_boxplot()  + labs(title = 'Default')

gp = dslabs::gapminder %>% 
filter(year == 1990 | year == 1995 | year==2000 |  year == 2005 | year==2010 ) %>%
ggplot(aes(x = continent, y = gdp/population, fill = as.factor(year)))  + coord_flip() + labs(fill = 'Year')

viridis_a = gp + geom_boxplot()  + labs(title = 'Viridis A') + scale_fill_viridis_d(option = 'A')
viridis_b = gp + geom_boxplot()  + labs(title = 'Viridis B') + scale_fill_viridis_d(option = 'B')
viridis_c = gp + geom_boxplot()  + labs(title = 'Viridis C') + scale_fill_viridis_d(option = 'C')
viridis_d = gp + geom_boxplot()  + labs(title = 'Viridis D') + scale_fill_viridis_d(option = 'D')

grid.arrange(viridis_a, viridis_b, viridis_c, viridis_d)

gp = dslabs::gapminder %>% 
filter(year == 1990 | year == 1995 | year==2000 |  year == 2005 | year==2010 ) %>%
ggplot(aes(x = continent, y = gdp/population, fill = as.factor(year)))  + coord_flip() + labs(fill = 'Year') 

custom_a = gp + geom_boxplot()  + labs(title = 'Viridis A') + scale_fill_discrete(type = color_blind_friendly_cols)
custom_b = gp + geom_boxplot()  + labs(title = 'Viridis A') + scale_fill_discrete(type = color_blind_friendly_cols[1:3])

grid.arrange(custom_a, custom_b)

dslabs::gapminder %>%
  filter(country=='Romania' & year>1980) %>%
  ggplot(aes(x = year, y = gdp/population, color = life_expectancy)) + 
  geom_point(size = 5) +
  labs(x = 'Year', y = 'GDP Per Capita', fill = 'Life Expectancy')

dslabs::gapminder %>%
  filter(country=='Romania' & year>1980) %>%
  ggplot(aes(x = year, y = gdp/population, color = life_expectancy)) + 
  scale_color_gradient2(low = 'red', mid = 'white', high = 'blue', midpoint = 72.5) + 
  geom_point(size = 5) +
  labs(x = 'Year', y = 'GDP Per Capita', color = 'Life Expectancy')

dslabs::gapminder %>%
  filter(country=='Romania' & year>1980) %>%
  ggplot(aes(x = year, y = gdp/population, color = life_expectancy)) + 
  scale_color_gradient2(low = color_blind_friendly_cols[3], mid = color_blind_friendly_cols[4], high = color_blind_friendly_cols[5], midpoint = 72.5) + 
  geom_point(size = 5) +
  labs(x = 'Year', y = 'GDP Per Capita', color = 'Life Expectancy')

gridExtra and grid.arrange

The gridExtra package has been used a few times in this lesson to combine plots using the grid.arrange function. The use is pretty intuitive - you save your plots as objects plot1 <- ggplot(data, aes(x = var1)) and plot2 <- ggplot(data, aes(x = var2)), and then use grid.arrange(plot1, plot2) to combine. The function will align as best it can, and there are more advanced grob-based functions that can adjust and align axes between plots, but we won’t get into them. If we want to set the layout, we can specify nrow and ncol to set the rows and columns.

The very-useful patchwork package is quickly replacing grid.arrange and provides more flexibility.