## 8.2 Visualizing association between two categorical variables

We’ll cover three ways to visualize associations between two categorical variables:

• a contingency table
• a grouped bar graph
• a mosaic plot

### 8.2.1 Constructing a contingency table

New tool The tabyl function from the janitor package is useful for creating contingency tables, or more generally, cross-tabulating frequencies for multiple categorical variables.

You can check out more about the tabyl function at this vignette.

Let’s use the bird.malaria dataset for our demonstration.

If you got an overview of the dataset, as suggested as part of the activity in the preceding section, you would have seen that the bird.malaria tibble includes two categorical variables: treatment and response, each with 2 categories.

The dataset includes 65 rows. Each row corresponds to an individual (unique) bird. Thirty of the birds were randomly assigned to the “Control” treatment group, and 35 were randomly assigned to the “Egg removal” treatment group.

The response variable includes the categories “Malaria” and “No Malaria”, indicating whether the bird contracted Malaria after the treatment.

Our goal is to visualize the frequency of birds that fall into each of the four unique combinations of category:

• Control + No Malaria
• Control + Malaria
• Egg removal + No Malaria
• Egg removal + Malaria

More specifically, we are interested in comparing the incidence of malaria among the Control and Egg removal treatment groups. We’ll learn in a later tutorial how to conduct this comparison statistically.

Let’s provide the code, then explain after. We’ll again make use of the kable function from the knitr package to help present a nice table. So first we create the table (“bird.malaria.table”), then in a later code chunk we’ll output a nice version of the table using the kable function.

First create the basic contingency table:

bird.malaria.freq <- bird.malaria %>%
tabyl(treatment, response)

Code explanation:

• the first line is telling R to assign any output from our commands to the object called “bird.malaria.freq”
• the first line is also telling R that we’re using the bird.malaria object as input to our subsequent functions, and the pipe (%>%) tells R there’s more to come.
• the second line uses the tabyl function, and we provide it with the names of the variables from the bird.malaria object that we want to use for tabulating frequencies. Here we provide the variable names “treatment”, and “response”

Let’s look at the table:

bird.malaria.freq
##    treatment Malaria No Malaria
##      Control       7         28
##  Egg removal      15         15

It is typically a good idea to also include the row and column totals in a contingency table.

To do this, we use the adorn_totals function, from the janitor package, as follows, and we’ll create a new object called “bird.malaria.freq.totals”:

bird.malaria.freq.totals <- bird.malaria %>%
tabyl(treatment, response) %>%
adorn_totals(where = c("row", "col"))
• the last line tells the adorn_totals function that we want to add the row and column totals to our table

Now let’s see what the table looks like before using the kable function. To do this, just provide the name of the object:

bird.malaria.freq.totals
##    treatment Malaria No Malaria Total
##      Control       7         28    35
##  Egg removal      15         15    30
##        Total      22         43    65

Now let’s use the kable function to improve the look, and add a table heading.

bird.malaria.freq.totals %>%
kable(caption = "Contingency table showing the incidence of malaria in female great tits in relation to experimental treatment", booktabs = TRUE)
Table 8.1: Contingency table showing the incidence of malaria in female great tits in relation to experimental treatment
treatment Malaria No Malaria Total
Control 7 28 35
Egg removal 15 15 30
Total 22 43 65

Relative frequencies

Often it is useful to also present a contingency table that shows the relative frequencies. However, it’s important to know how to calculate those relative frequencies.

For instance, recall that in this malaria example, we are interested in comparing the incidence of malaria among the Control and Egg removal treatment groups. Thus, we should calculate the relative frequencies using the row totals. This will become clear when we show the table.

We can get relative frequencies, which are equivalent to proportions, using the adorn_percentages function (the function name is a misnomer, because we’re calculating proportions, not percentages!), and telling R to use the row totals for the calculations.

First create the new table object “bird.malaria.prop”:

bird.malaria.prop <- bird.malaria %>%
tabyl(treatment, response) %>%
adorn_percentages("row")

Now present it using kable:

bird.malaria.prop %>%
kable(caption = "Contingency table showing the relative frequency of malaria in female great tits in relation to experimental treatment", booktabs = TRUE)
Table 8.2: Contingency table showing the relative frequency of malaria in female great tits in relation to experimental treatment
treatment Malaria No Malaria
Control 0.2 0.8
Egg removal 0.5 0.5

### 8.2.2 Constructing a grouped bar graph

To construct a grouped bar graph, we first need wrangle (reformat) the data to be in the form of a frequency table.

Let’s revisit what the bird.malaria tibble looks like:

bird.malaria
## # A tibble: 65 × 3
##     bird treatment   response
##    <dbl> <chr>       <chr>
##  1     1 Control     Malaria
##  2     2 Control     Malaria
##  3     3 Control     Malaria
##  4     4 Control     Malaria
##  5     5 Control     Malaria
##  6     6 Control     Malaria
##  7     7 Control     Malaria
##  8     8 Egg removal Malaria
##  9     9 Egg removal Malaria
## 10    10 Egg removal Malaria
## # … with 55 more rows

To wrangle this into the appropriate format, here’s the appropriate code:

bird.malaria.tidy <- bird.malaria %>%
group_by(treatment) %>%
count(response)

This is similar to what you learned in a previous tutorial, but here we’ve added a new function!

New tool The group_by function from the dplyr package enables one to apply a function to each category of a categorical variable. See more help using “?group_by”.

In the preceding code chunk, we’re tallying the observations in the two “treatment” variable categories, but also keeping track of which category of “response” the individual belongs to.

Let’s have a look at the result:

bird.malaria.tidy
## # A tibble: 4 × 3
## # Groups:   treatment 
##   treatment   response       n
##   <chr>       <chr>      <int>
## 1 Control     Malaria        7
## 2 Control     No Malaria    28
## 3 Egg removal Malaria       15
## 4 Egg removal No Malaria    15

We now have what we need for a grouped bar chart, using the ggplot function:

ggplot(data = bird.malaria.tidy, aes(x = treatment, y = n, fill = response)) +
geom_bar(stat = "identity", position = position_dodge()) +
ylab("Frequency") +
xlab("Treatment group") +
theme_bw() This code is similar to what we used previously to create a bar graph, but there are two key differences:

• in the first line within the aes function, we include a new argument fill = response, telling R to use different bar fill colours based on the categories in the “response” variable.
• in the second line, we provide a new argument to the geom_bar function: position = position_dodge(), which tells R to use separate bars for each category of the “fill” variable (if we did not include this argument, we’d get a “stacked bar graph” instead)

It is best practice to use the response variable as the “fill” variable in a grouped bar graph, as we have done in the malaria example.

If we wished to provide an appropriate figure heading, this would be the code: Figure 8.1: Example code chunk for producing a good grouped bar graph

And the result:

ggplot(data = bird.malaria.tidy, aes(x = treatment, y = n, fill = response)) +
geom_bar(stat = "identity", position = position_dodge()) +
ylab("Frequency") +
xlab("Treatment group") +
theme_bw() Figure 8.2: Grouped bar graph showing the incidence of malaria in female great tits in relation to control (N = 35) and Egg-removal (N = 30) treatment groups.

### 8.2.3 Constructing a mosaic plot

An alternative and often more effective way to visualize the association between two categorical variables is a mosaic plot.

For this we use the geom_mosaic function, from the ggmosaic package, in conjunction with the ggplot function.

For more information about the ggmosaic package, see this vignette.

For the geom_mosaic function, we actually use the original (raw) bird.malaria tibble, which has a row for every observation (i.e. it isn’t summarized first into a frequency table).

Here’s the code, and we’ll explain after:

ggplot(data = bird.malaria) +
geom_mosaic(aes(x = product(treatment), fill = response)) +
scale_y_continuous() +
xlab("Treatment group") +
ylab("Relative frequency") +
theme_bw() In the code chunk above we see one key difference from previous uses of the ggplot function is that the aes function is not provided in the arguments to ggplot in the first line, but is instead provided to the arguments of the geom_mosaic function on the second line.

We also see product(treatment), which is difficult to explain, so suffice it to say that it’s telling the geom_mosaic function to calculate relative frequencies based on the “treatment” variable, and in conjunction with the fill variable “response”.

The scale_y_continuous function tells ggplot to add a continuous scale for the y-axis, and here, this defaults to zero to one for relative frequencies.

We’ll learn about interpreting mosaic plots next.

1. Using the penguins dataset, try creating a mosaic plot for comparing the relative frequency of penguins belonging to the three different “species” across the three different islands (variable “island”).

### 8.2.4 Interpreting mosaic plots

Let’s provide the mosaic plot again, and this time we’ll provide an appropriate figure heading in the chunk header, as we learned previously:

ggplot(data = bird.malaria) +
geom_mosaic(aes(x = product(treatment), fill = response)) +
scale_y_continuous() +
xlab("Treatment group") +
ylab("Relative frequency") +
theme_bw() Figure 8.3: Relative frequency of the incidence of malaria in female great tits in relation to control (N = 35) and Egg-removal (N = 30) treatment groups.

Here’s the code: Figure 8.4: Example code chunk for producing a good mosaic plot

When interpreting a mosaic plot, the key is to look how the relative frequency of the categories of the response variable - denoted by the “fill” colours - varies across the explanatory variable, which is arranged on the x-axis.

For example, in the malaria example above:

“The mosaic plot shows that the incidence (or relative frequency) of malaria is comparatively greater among birds in the egg removal treatment group compared to the control group. Only about 20% of birds in the control group contracted malaria, whereas 50% of the birds in the the egg-removal group contracted malaria.”