Categorical x Continuous data (2 of 2)

Sep 23, 2023

This chapter explores Categorical x Continuous data using the dplyr and ggplot2 packages.
Data: Suppose we run the following code to prepare the mtcars data for subsequent analysis and save it in a tibble called tb.

# Load the required libraries, suppressing annoying startup messages
library(dplyr, quietly = TRUE, warn.conflicts = FALSE)
library(tibble, quietly = TRUE, warn.conflicts = FALSE)
library(knitr) # For formatting tables
# Read the mtcars dataset into a tibble called tb
data(mtcars)
tb <- as_tibble(mtcars)
# Convert relevant columns into factor variables
tb$cyl <- as.factor(tb$cyl) # cyl = {4,6,8}, number of cylinders
tb$am <- as.factor(tb$am) # am = {0,1}, 0:automatic, 1: manual transmission
tb$vs <- as.factor(tb$vs) # vs = {0,1}, v-shaped engine, 0:no, 1:yes
tb$gear <- as.factor(tb$gear) # gear = {3,4,5}, number of gears
# Directly access the data columns of tb, without tb$mpg
attach(tb)

Visualizing Continuous Data using `ggplot2`

Let’s take a closer look at some of the most effective ways of visualizing continuous data, across one Category, using ggplot2, including

Bee Swarm plots, using ggplot2;
Histograms, using ggplot2;
PDF and CDF Density plots, using ggplot2;
Box plots, using ggplot2;
Violin plots, using ggplot2;

Bee Swarm Plot across one Category using `ggbeeswarm`

Visualizing Median using Box Plot – median weight of the cars broken down by cylinders (cyl=4,6,8)

library(ggplot2)


Attaching package: 'ggplot2'

The following object is masked from 'tb':

    mpg

library(ggbeeswarm)
# Create the beeswarm plot
ggplot(mtcars, 
       aes(x = factor(cyl), 
           y = mpg)) +
  geom_beeswarm() +
  labs(title = "Bee Swarm plot of Mileage (mpg) by Cylinders (cyl=4,6,8)",
       x = "Cylinders (cyl)",
       y = "Miles per gallon (mpg)") +
  theme_minimal()

Histograms across one Category using `ggplot2`

Visualizing histograms of car milegage (mpg) broken down by transmission (am=0,1)

ggplot(tb, aes(x = mpg, 
               fill = am)) +
  geom_histogram(binwidth = 5, color = "black") +
  scale_fill_manual(values = c("gold", "lightblue")) +
  theme_minimal() +
  labs(title = "Histogram of Miles Per Gallon (mpg) by Transmission Type (am)",
       x = "Miles Per Gallon (mpg)",
       y = "Frequency")

Discussion: If we want separate histograms, we can set facet_wrap(~ am)

ggplot(tb, aes(x = mpg, 
               fill = am)) +
  geom_histogram(binwidth = 5, color = "black") +
  scale_fill_manual(values = c("gold", "lightblue")) +
  facet_wrap(~ am) +
  theme_minimal() +
  labs(title = "Histogram of Miles Per Gallon (mpg) by Transmission Type (am)",
       x = "Miles Per Gallon (mpg)",
       y = "Frequency")

Histogram across one Category using `ggpubr`

library(ggpubr)
gghistogram(tb, 
            x = "mpg", 
            bins = 6,
            add = "mean", 
            rug = TRUE, 
            color = "am", 
            fill = "am", 
            alpha = 0.8,
            palette = c("gold", "lightblue"),
            title = "Histogram of Mileage (mpg) by Transmission (am=0,1)")

Histograms across two Categories using `ggplot2`

Visualizing histograms of car milegage (mpg) by transmission (am=0,1) and cylinders (cyl=4,6,8)

ggplot(tb, aes(x = mpg, 
               fill = am)) +
  geom_histogram(binwidth = 3, color = "black") +
  scale_fill_manual(values = c("gold", "lightblue")) +
  facet_grid(cyl ~ am) +
  theme_minimal() +
  labs(title = "Histogram of Mileage (mpg) by Transmission (am=0,1) and Cylinders (cyl=4,6,8)",
       x = "Miles Per Gallon (mpg)",
       y = "Frequency")

PDF across one Category using `ggplot2`

Visualizing the Probability Density Functions (PDF) of car milegage (mpg) by transmission (am=0,1)

ggplot(tb, aes(x = mpg, 
               fill = am)) +
  geom_density(color = "black") +
  scale_fill_manual(values = c("gold", "lightblue")) +
  facet_wrap(~ am) +
  theme_minimal() +
  labs(title = "Density Plot of Mileage (mpg) by Transmission (am=0,1)",
       x = "Miles Per Gallon (mpg)",
       y = "Density")

PDF across one Category using `ggpubr`

The provided R code creates a Boxplot of the mpg (miles per gallon) variable in the tb dataset, using the ggboxplot() function from the ggpubr package.

library(ggpubr)
ggdensity(tb, 
          x = "mpg", 
          color = "am" ,
          fill = "am",
          add = "mean",
          rug = TRUE,
          palette = c("gold", "skyblue"),
          title = "PDF of Mileage (mpg) by Transmission (am=0,1), using ggpubr::ggdensity()",
          ylab = "Miles Per Gallon (mpg)",
          xlab = "Transmission (am)"
)

CDF across one Category using `ggplot2`

Visualizing the Cumulative Density Functions (CDF) of car milegage (mpg) by transmission (am=0,1)

library(ggplot2)
# Create separate CDFs for 'am = 0' and 'am = 1'
ggplot(tb, aes(x = mpg, 
               color = factor(am))) +
  stat_ecdf(geom = "line") +
  scale_color_manual(values = c("blue", "black")) +
  labs(x = "Miles Per Gallon (mpg)", y = "CDF", 
       title = "Cumulative Distribution Function (CDF) of Mileage (mpg) by Transmission (am=0,1)",
       color = "am") +
  theme_minimal()

Box Plot across one Category using `ggplot2`

Visualizing Boxplots of car milegage (mpg) broken down by cylinders (cyl=4,6,8)

library(ggplot2)
ggplot(tb, aes(x = cyl, 
               y = mpg)) +
  geom_boxplot(fill = c("gold","lightblue","lightpink"), 
               color = "black") +
  coord_flip() +
  labs(title = "Boxplot of Mileage (mpg) by Cylinders (cyl=4,6,8)",
       y = "Miles Per Gallon (mpg)",
       x = "Cylinders") +
  theme_minimal()

Box Plot across one Category using `ggpubr`

The provided R code creates a Boxplot of the mpg (miles per gallon) variable in the tb dataset, using the ggboxplot() function from the ggpubr package.

library(ggpubr)
ggboxplot(tb, 
          y = "mpg", 
          x = "cyl",
          color = "cyl",
          fill = "white",
          palette = c("black","blue","red"),
          shape = "cyl",
          orientation = "horizontal",
          add = "jitter", #jitter helps display the data points
          title = "Boxplot of Mileage (mpg) by Cylinders (cyl=4,6,8), using ggpubr::ggboxplot()",
          ylab = "Miles Per Gallon (mpg)",
          xlab = "Cylinders"
)

Box Plot across two Categories using `ggplot2`

Visualizing Boxplots of car milegage (mpg) broken down by cylinders (cyl=4,6,8) and Transmission (am=0,1)

ggplot(tb, aes(x = as.factor(am), y = mpg, fill = as.factor(am))) +
  geom_boxplot() +
  scale_fill_manual(values = c("gold", "lightblue"), name = "Transmission") +
  facet_grid(~ cyl) +
  theme_minimal() +
  labs(title = "Boxplot of Mileage (mpg) by Cylinders (cyl=4,6,8) and Transmission (am=0,1)",
       x = "Transmission Type (am)",
       y = "Miles Per Gallon (mpg)")

Alternately:

ggplot(tb, aes(x = as.factor(cyl), y = mpg, fill = as.factor(cyl))) +
  geom_boxplot() +
  scale_fill_manual(values = c("gold", "lightblue", "lightpink"), name = "Cylinders") +
  facet_grid(~ am) +
  theme_minimal() +
  coord_flip() +
  labs(title = "Boxplot of Mileage (mpg) by Transmission (am=0,1) and Cylinders (cyl=4,6,8)",
       x = "Number of Cylinders (cyl)",
       y = "Miles Per Gallon (mpg)")

Box Plot across two Categories using `ggpubr`

The provided R code creates Boxplots of the mpg (miles per gallon) variable in the tb dataset, using the ggboxplot() function from the ggpubr package.

library(ggpubr)
ggboxplot(tb, 
          y = "mpg", 
          x = "cyl",
          color = "cyl",
          fill = "white",
          palette = c("black","blue","red"),
          shape = "cyl",
          orientation = "horizontal",
          add = "jitter", #jitter helps display the data points
          facet.by = "am", #split data by "am"
          title = "Boxplot of Mileage by Cylinders, Transmission, with ggpubr::ggboxplot()",
          ylab = "Miles Per Gallon (mpg)",
          xlab = "Cylinders"
)

library(ggpubr)
ggboxplot(tb, 
          y = "mpg", 
          x = "am",
          color = "am",
          fill = "white",
          palette = c("black", "blue"),  # assuming am has 2 levels; adjust as needed
          shape = "am",
          orientation = "horizontal",
          add = "jitter", #jitter helps display the data points
          facet.by = "cyl", #split data by "cyl"
          title = "Boxplot of Mileage by Transmission, Cylinders, with ggpubr::ggboxplot()",
          ylab = "Miles Per Gallon (mpg)",
          xlab = "Transmission"
)

Violin Plot across one Category using `ggplot2`

We can embed boxplots within the above Violin plots, as follows.

library(ggplot2)
ggplot(tb, aes(x = factor(cyl), 
               y = mpg)) +
  geom_violin(aes(fill = factor(cyl)), 
              color = "black") +
  scale_fill_manual(values = c("gold","lightblue","lightpink"), 
                    name = "Cylinders") +
  geom_boxplot(width=0.2, 
               fill="white") +
  coord_flip() +
  labs(title = "Violin Plot and Box Plot of Mileage (mpg) by Cylinders (cyl=4,6,8)",
       y = "Miles Per Gallon (mpg)",
       x = "Cylinders") +
  theme_minimal()

Summarizing Continuous Data using `dplyr` and `ggplot2`

Across one Category using `dplyr` and `ggplot2`

Calculating the mean and standard deviation

We demonstrate the bivariate relationship between Miles Per Gallon (mpg) and Cylinders (cyl) using ggplot2.

suppressPackageStartupMessages(library(dplyr))
s1 <- tb %>%
  group_by(cyl) %>%
  summarise(Mean_mpg = mean(mpg, na.rm = TRUE),
            SD_mpg = sd(mpg, na.rm = TRUE))
  
kable(s1, digits=2, caption = "Summary Statistics of Mileage (mpg) by Cylinders (cyl=4,6,8)")

Summary Statistics of Mileage (mpg) by Cylinders (cyl=4,6,8)
cyl	Mean_mpg	SD_mpg
4	26.66	4.51
6	19.74	1.45
8	15.10	2.56

Discussion:

In this code, we use the pipe operator %\>% to perform a series of operations. We first group the data by the cyl column using the group_by() function. We then use summarise() to apply the mean() and sd() functions to the mpg column.
The results are stored in new columns, aptly named Mean_mpg and SD_mpg.
We set na.rm = TRUE in both mean() and sd() function calls, to remove any missing values before calculation.
The data resulting from the above code consists of grouped cylinder counts (cyl), their corresponding mean miles per gallon (Mean_mpg), and the standard deviation of miles per gallon (SD_mpg).[1]

Visualizing the mean and standard deviation

A simple way to visualize this data is to create a line plot for the mean miles per gallon with error bars indicating the standard deviation. Here is an example of how we could do this with ggplot2:

suppressPackageStartupMessages(library(ggplot2))
ggplot(s1, 
       aes(x = cyl, y = Mean_mpg)) +
  geom_line(group=1, color = "blue") +
  geom_point(size = 2, color = "red") +
  geom_errorbar(aes(ymin = Mean_mpg - SD_mpg, 
                    ymax = Mean_mpg + SD_mpg), 
                width = .2, colour = "black") +
  labs(x = "Cylinders", y = "Mean mpg",
       title = "Mean and SD of Mileage(mpg) by #Cylinders") +
  theme_minimal()

Discussion:

aes(x = cyl, y = Mean_mpg) assigns the cyl values to the x-axis and Mean_mpg to the y-axis.
geom_line(group=1, color = "blue") adds a blue line connecting the data points.
geom_point(size = 2, color = "red") adds red points for each data point.
geom_errorbar(aes(ymin = Mean_mpg - SD_mpg, ymax = Mean_mpg + SD_mpg), width = .2, colour = "black") adds error bars, where the error is the standard deviation.
The ymin and ymax arguments define the range of the error bars.
labs(x = "Cylinders", y = "Mean mpg") labels the x and y axes.
theme_minimal() applies a minimal theme to the plot.

Visualizing the mean and standard deviation - Alternate Method

An alternate method is to visualize this mean by creating a bar plot, with error bars indicating the standard deviation. Here is an example of how we could do this with ggplot2:

library(ggplot2)
# mpg plot
ggplot(s1, 
       aes(x = cyl, 
           y = Mean_mpg)) +
  geom_bar(stat = "identity", 
           fill = "gold") +
  geom_errorbar(aes(ymin = Mean_mpg - SD_mpg, 
                    ymax = Mean_mpg + SD_mpg), 
                width = .2) +
  labs(x = "Cylinders", y = "Mean mpg",
       title = "Mean and SD of Mileage(mpg) by #Cylinders") +
  theme_minimal()

Discussion:

ggplot(s1, aes(x = cyl, y = Mean_mpg)): The ggplot() function initializes a ggplot object using dataframe s1 and mapping aesthetic elements. Here, aes(x = cyl, y = Mean_mpg) specifies that the x-axis represents cyl (number of cylinders) and the y-axis represents Mean_mpg (mean miles per gallon).
geom_bar(stat = "identity", fill = "gold"): The geom_bar() function is used to create a bar chart. Setting stat = "identity" indicates that the heights of the bars represent the values in the data (in this case, Mean_mpg). The fill = "gold" argument sets the color of the bars.
geom_errorbar() adds error bars to the plot. The arguments aes(ymin = Mean_mpg - SD_mpg, ymax = Mean_mpg + SD_mpg) set the bottom (ymin) and top (ymax) of the error bars to represent one standard deviation below and above the mean, respectively. width = .2 sets the horizontal width of the error bars.
labs(x = "Cylinders", y = "Mean mpg"): The labs() function is used to specify the labels for the x-axis and y-axis.
theme_minimal(): The theme_minimal() function is used to set a minimalistic theme for the plot.

We extend this code to demonstrate how to measure the bivariate relationships between multiple continuous variables from the mtcars data and the categorical variable number of Cylinders (cyl), using ggplot2. Specifically, we want to measure the mean and SD of continuous variables (i) Miles Per Gallon (mpg); (ii) Weight (wt); (iii) Horsepower (hp) across the number of Cylinders (cyl).

library(dplyr)
s3 <- tb %>%
  group_by(cyl) %>%
  summarise(
    Mean_mpg = mean(mpg, na.rm = TRUE),
    SD_mpg = sd(mpg, na.rm = TRUE),
    Mean_wt = mean(wt, na.rm = TRUE),
    SD_wt = sd(wt, na.rm = TRUE),
    Mean_hp = mean(hp, na.rm = TRUE),
    SD_hp = sd(hp, na.rm = TRUE)
    ) 
kable(s3, 
      digits=2, 
      caption = "Summary of Mileage (mpg), Weight (wt), Horsepower (hp) by Cylinders (cyl=4,6,8)")

Summary of Mileage (mpg), Weight (wt), Horsepower (hp) by Cylinders (cyl=4,6,8)
cyl	Mean_mpg	SD_mpg	Mean_wt	SD_wt	Mean_hp	SD_hp
4	26.66	4.51	2.29	0.57	82.64	20.93
6	19.74	1.45	3.12	0.36	122.29	24.26
8	15.10	2.56	4.00	0.76	209.21	50.98

Discussion:

With tb %>%, we indicate that we are going to perform a series of operations on the tb data frame. The group_by(cyl) groups the data by the cyl variable.
The summarise() function calculates the mean and standard deviation (SD) of three variables (mpg, wt, and hp). Thena.rm = TRUE argument inside mean() and sd() functions is used to exclude any NA values from these calculations.
The resulting calculations are assigned to new variables (Mean_mpg, SD_mpg, Mean_wt, SD_wt, Mean_hp, and SD_hp) which will be the columns in the summarised data frame.
To summarize, this script groups the data in the tb tibble by cyl and then calculates the mean and standard deviation of the mpg, wt, and hp variables for each group. [1]

Across two Categories using `ggplot2`

We demonstrate the relationship between Miles Per Gallon (mpg) and Cylinders (cyl) and Transmission type (am) using ggplot2. Recall that a car’s transmission may be automatic (am=0) or manual (am=1).

s4 <- tb %>%
  group_by(cyl, am) %>%
  summarise(Mean_mpg = mean(mpg, na.rm = TRUE),
            SD_mpg = sd(mpg, na.rm = TRUE))

`summarise()` has grouped output by 'cyl'. You can override using the `.groups`
argument.

kable(s4, 
      digits=2, 
      caption = "Summary of Mileage (mpg) by Cylinders (cyl=4,6,8) and Transmission (am=0,1)")

Summary of Mileage (mpg) by Cylinders (cyl=4,6,8) and Transmission (am=0,1)
cyl	am	Mean_mpg	SD_mpg
4	0	22.90	1.45
4	1	28.08	4.48
6	0	19.12	1.63
6	1	20.57	0.75
8	0	15.05	2.77
8	1	15.40	0.57

Discussion:

The above code provides the mean and standard deviation of mpg for each unique combination of cyl and am.
Here is how it can be visualized:

# Create the plot
ggplot(s4, aes(x = interaction(cyl, am), 
               y = Mean_mpg, 
               fill = as.factor(am))) +
  geom_bar(stat = "identity", 
           position = position_dodge()) +
  geom_errorbar(aes(ymin = Mean_mpg - SD_mpg, 
                    ymax = Mean_mpg + SD_mpg), 
                width = .2, 
                position = position_dodge(.9)) +
  labs(x = "Cylinders and Transmission", 
       y = "Mean mpg", 
       fill = "Transmission",
       title = "Summary of Mileage (mpg) by Cylinders (cyl=4,6,8) and Transmission (am=0,1)") +
  theme_minimal()

In the below code, the order of the variables is reversed - the data is first grouped by am, then by cyl. So, the function first sorts the data by the am variable, and within each am group, it further groups the data by cyl.

library(dplyr)
s5 <- tb %>%
  group_by(am, cyl) %>%
  summarise(Mean_mpg = mean(mpg, na.rm = TRUE),
            SD_mpg = sd(mpg, na.rm = TRUE))

`summarise()` has grouped output by 'am'. You can override using the `.groups`
argument.

kable(s5, 
      digits=2, caption = "Summary of Mileage (mpg) by Transmission (am=0,1) and Cylinders (cyl=4,6,8)")

Summary of Mileage (mpg) by Transmission (am=0,1) and Cylinders (cyl=4,6,8)
am	cyl	Mean_mpg	SD_mpg
0	4	22.90	1.45
0	6	19.12	1.63
0	8	15.05	2.77
1	4	28.08	4.48
1	6	20.57	0.75
1	8	15.40	0.57

Here is how it can be visualized:

# Create the plot
ggplot(s5, 
       aes(x = interaction(am, cyl), 
           y = Mean_mpg, 
           fill = as.factor(cyl))) +
  geom_bar(stat = "identity", 
           alpha = 0.7, 
           position = position_dodge()) +
  geom_errorbar(aes(ymin = Mean_mpg - SD_mpg, 
                    ymax = Mean_mpg + SD_mpg), 
                width = .2, 
                position = position_dodge(.9)) +
  labs(x = "Transmission and Cylinders", 
       y = "Mean mpg", 
       fill = "Cylinders",
       title = "Summary of Mileage (mpg) by Transmission (am=0,1) and Cylinders (cyl=4,6,8)") +
  theme_minimal()

The following code produces a new data frame that contains the mean and standard deviation of the continuous variables mpg, wt, and hp for each combination of the factor variables am and cyl. [1]

s6 <- tb %>%
  group_by(am, cyl) %>%
  summarise(
    Mean_mpg = mean(mpg, na.rm = TRUE),
    SD_mpg = sd(mpg, na.rm = TRUE),
    Mean_wt = mean(wt, na.rm = TRUE),
    SD_wt = sd(wt, na.rm = TRUE),
    Mean_hp = mean(hp, na.rm = TRUE),
    SD_hp = sd(hp, na.rm = TRUE)
    )

`summarise()` has grouped output by 'am'. You can override using the `.groups`
argument.

kable(s6, 
      digits=2, caption = "Summary of Mileage (mpg) by Transmission (am=0,1) and Cylinder (cyl=4,6,8)")

Summary of Mileage (mpg) by Transmission (am=0,1) and Cylinder (cyl=4,6,8)
am	cyl	Mean_mpg	SD_mpg	Mean_wt	SD_wt	Mean_hp	SD_hp
0	4	22.90	1.45	2.94	0.41	84.67	19.66
0	6	19.12	1.63	3.39	0.12	115.25	9.18
0	8	15.05	2.77	4.10	0.77	194.17	33.36
1	4	28.08	4.48	2.04	0.41	81.88	22.66
1	6	20.57	0.75	2.76	0.13	131.67	37.53
1	8	15.40	0.57	3.37	0.28	299.50	50.20

References

[1]

Wickham, H., François, R., Henry, L., & Müller, K. (2021). dplyr: A Grammar of Data Manipulation. R package version 1.0.7. https://CRAN.R-project.org/package=dplyr

Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. ISBN 978-3-319-24277-4, https://ggplot2.tidyverse.org.

[2]

Kassambara A (2023). ggpubr: ‘ggplot2’ Based Publication Ready Plots. R package version 0.6.0, https://rpkgs.datanovia.com/ggpubr/.

Appendix A

Appendix A1: Violin Plot across two Categories using `ggplot2`

We can embed boxplots within the above Violin plots, as follows.

library(ggplot2)

ggplot(tb, aes(x = factor(cyl), y = mpg)) +
  geom_violin(aes(fill = factor(cyl)), color = "black") +
  scale_fill_manual(values = c("gold", "lightblue", "lightpink"), name = "Cylinders") +
  geom_boxplot(width = 0.2, fill = "white") +
  coord_flip() +
  labs(title = "Violin Plot and Box Plot of Mileage (mpg) by Cylinders and Transmission",
       y = "Miles Per Gallon (mpg)",
       x = "Cylinders") +
  facet_grid(am ~ ., scales = "free_y", space = "free_y", labeller = labeller(am = function(x) ifelse(x == 0, "Automatic", "Manual"))) +
  theme_minimal()

Alternately, We can embed boxplots within the above Violin plots, as follows.

library(ggplot2)
library(dplyr)

# Modify the data first
tb_modified <- tb %>%
  mutate(am = factor(am, levels = c(0, 1), labels = c("Automatic", "Manual")))

# Create the plot
ggplot(tb_modified, 
       aes(x = factor(cyl), 
           y = mpg)) +
  geom_violin(aes(fill = factor(cyl)), 
              color = "black") +
  scale_fill_manual(values = c("gold", "lightblue", "lightpink"), 
                    name = "Cylinders") +
  geom_boxplot(width = 0.2, fill = "white") +
  coord_flip() +
  labs(title = "Violin Plot and Box Plot of Mileage (mpg) by Cylinders and Transmission",
       y = "Miles Per Gallon (mpg)",
       x = "Cylinders") +
  facet_grid(am ~ ., 
             scales = "free_y", 
             space = "free_y") +
  theme_minimal()

Categorical x Continuous data (2 of 2)

Visualizing Continuous Data using ggplot2

Bee Swarm Plot across one Category using ggbeeswarm

Histograms across one Category using ggplot2

Histogram across one Category using ggpubr

Histograms across two Categories using ggplot2

PDF across one Category using ggplot2

PDF across one Category using ggpubr

CDF across one Category using ggplot2

Box Plot across one Category using ggplot2

Box Plot across one Category using ggpubr

Box Plot across two Categories using ggplot2

Box Plot across two Categories using ggpubr

Violin Plot across one Category using ggplot2

Summarizing Continuous Data using dplyr and ggplot2

Across one Category using dplyr and ggplot2

Across two Categories using ggplot2