Exploratory Data Analysis

A tutorial about data analysis using R (Website Version)

Author

Affiliation

Jon Yearsley

School of Biology and Environmental Science, UCD

Published

September, 2024

How to Read this Tutorial

This tutorial is a mixture of R code chunks and explanations of the code. The R code chunks will appear in boxes.

Below is an example of a chunk of R code:

# This is a chunk of R code. All text after a # symbol is a comment
# Set working directory using setwd() function
setwd('Enter the path to my working directory')

# Clear all variables in R's memory
rm(list=ls())    # Standard code to clear R's memory

Sometimes the output from running this R code will be displayed after the chunk of code.

Here is a chunk of code followed by the R output

2 + 4            # Use R to add two numbers

[1] 6

Objectives

The objectives of this tutorial are to use R for:

Numerical data summaries of
- central tendency
- spread
- correlation
Visualise qualitative data using
- contingency tables
- graphs
Visualise quantitative data using
- graphs
Save graphical output to a file

Introduction

Note

Exploratory data analysis is the first step in any data analysis. It involves visualising your data using graphical and numerical summaries

Exploratory data analysis is not technical. You can use your own creativity to explore your data in order to:

Gain a better understanding of the patterns in the data before you start a formal analysis
Spot any errors in the data, and correct them, before you start an analysis

This tutorial will look at the visualisation functions in the ggplot2 package and some of R’s basic data visualisation functions.

Before you continue:

Review this online lesson about data types.

Online Lesson

Data Types

This lesson is at https://DrJonYearsley.github.io/OnlineLessons/lesson1_datatypes_Website.html

Overview of the data

We will primarily be using two data sets: msleep, WOLF.CSV. Some examples will also use the dataset MALIN_HEAD.TXT. These data are described at https://DrJonYearsley.github.io/Resources/datasets.html

The wolf data set was used in the “Importing data into R” tutorial and the msleep data set was used in the “Getting started with R” worksheet.

Import data

Start by loading the two data sets. See the data import tutorial for more details on this.

# Import data ------------------

# Load the 'ggplot2' package (required to access msleep dataset)
library('ggplot2')

wolf <- read.table('WOLF.CSV', header=T, sep=',') # Import wolf data set
data(msleep)                                     # Load msleep data set

ALWAYS check that the data have been imported correctly. For this you can use functions such as: ls(), head(), tail() and `summary()

Once the data are imported we create a subset of the data that only contains data from populations 1 and 2. We also create a new qualitative variable (factor) that codes for hunting intensity in the different populations (light hunting intensity in population 1, heavy hunting intensity in population 2).

# Subset the wolf data frame and remove unwanted levels
wolf.sub <- droplevels(subset(wolf, Population!=3))


# Create a new variable called Hunting
wolf.sub$Hunting <- 'Heavy'
wolf.sub$Hunting[wolf.sub$Population==1] <- 'Light'

# Make the variable Hunting a factor
wolf.sub$Hunting <- as.factor(wolf.sub$Hunting)

Descriptive statistics

A descriptive statistic summarizes a set of observations with a single number. Examples of descriptive statistics are estimates of central tendency (e.g. mean, median, mode), spread (e.g. standard deviation, inter-quartile range) and extremes (e.g. max and min values).

Central tendency

Central tendency describes the middle of the data, where most observations lie.

Two measures of central tendency are the mean and the median.

# Measures of central tendency for all cortisol concentrations
# The argument na.rm=TRUE removes any missing values (NA's)
mean(wolf.sub$Cpgmg, na.rm=TRUE)               # Mean
median(wolf.sub$Cpgmg, na.rm=TRUE)             # Median
quantile(wolf.sub$Cpgmg, prob=0.5, na.rm=TRUE) # Median = 50% quantile

The mean is commonly used, but it is overly influenced by extreme outliers

Example: Does the mean of the numbers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1000 reflect the ‘middle’ of the data?

The median is a more robust estimator of central tendency that is less affected by extreme outliers (e.g. repeat the above example using the median instead of the mean).

Spread

Spread describes how far the data are scattered around the central tendency.

Three measures of spread are the standard deviation, the inter-quartile range (IQR) and the median absolute deviation (MAD).

# Measures of spread for all cortisol concentrations
sd(wolf.sub$Cpgmg, na.rm=T)                  # (Sample) Standard deviation
IQR(wolf.sub$Cpgmg, na.rm=T)                 # Inter-quartile range
mad(wolf.sub$Cpgmg, na.rm=T)                 # Median absolute deviation

The standard deviation quantifies spread about the mean. Like the mean it is influenced by outliers. The square of the standard deviation is called the variance.

Both the inter-quartile range and the median absolute deviation quantify spread about the median. Both are more robust to outliers than the standard deviation.

The inter-quartile range is defined as the difference between the 25% and 75% quantiles.

`summary()` of a data frame

Applying the summary() function to a data frame will automatically gives many of these descriptive statistics.

# Summarise the wolf.sub data frame
summary(wolf.sub)

   Individual         Sex              Population       Colour         
 Min.   :  1.00   Length:148         Min.   :1.000   Length:148        
 1st Qu.: 37.75   Class :character   1st Qu.:1.000   Class :character  
 Median : 74.50   Mode  :character   Median :2.000   Mode  :character  
 Mean   : 74.50                      Mean   :1.696                     
 3rd Qu.:111.25                      3rd Qu.:2.000                     
 Max.   :148.00                      Max.   :2.000                     
                                                                       
     Cpgmg           Tpgmg            Ppgmg        Hunting   
 Min.   : 4.75   Min.   : 3.250   Min.   :12.76   Heavy:103  
 1st Qu.:12.16   1st Qu.: 4.378   1st Qu.:19.50   Light: 45  
 Median :15.38   Median : 5.030   Median :25.00              
 Mean   :16.61   Mean   : 5.617   Mean   :25.89              
 3rd Qu.:19.98   3rd Qu.: 6.067   3rd Qu.:30.01              
 Max.   :40.43   Max.   :15.130   Max.   :53.28              
                                  NA's   :79

Note: the 1st and 3rd quartiles (1st Qu. and 3rd Qu.) are the 25% and 75% quantiles respectively. The 2nd quartile is the median (50% quantile).

Other descriptive statistics

Some functions for other descriptive statistic:

# Other descriptive statistics
quantile(wolf.sub$Cpgmg, prob=0.25, na.rm=T) # Quantiles (here 25% quantile)
max(wolf.sub$Cpgmg, na.rm=T)                 # Maximum
min(wolf.sub$Cpgmg, na.rm=T)                 # Minimum
range(wolf.sub$Cpgmg, na.rm=T)               # Range = Maximum - Minimum

The moments package must be loaded for descriptive statistics of skewness and kurtosis.

library(moments)                            # Load the moments package

skewness(wolf.sub$Cpgmg, na.rm=T)           # Skewness of cortisol data

Note: In the tutorial on distributions we’ll see that skew is the asymmetry of a distribution about its mean

Correlation

A correlation is a relationship between two variables. The strength of a relationship can be quantified using a correlation coefficient (we will look at this in more detail in the tutorial on regression).

Two common correlation coefficients are Pearson correlation coefficient and Spearman’s rank correlation coefficient.

Here is an example of calculating correlation coefficients between variables Cpgmg and Ppgmg in the wolf.sub data frame.

# Calculate Pearson's correlation coefficient
cor(wolf.sub$Cpgmg, wolf.sub$Ppgmg, use='complete.obs', method='pearson')

# Calculate Spearman's rank correlation coefficient
cor(wolf.sub$Cpgmg, wolf.sub$Ppgmg, use='complete.obs', method='spearman')

Both these coefficients can take values between -1 and 1.

Correlations close to -1 are very strong negative relationships
Correlations close to 0 are weak relationships
Correlations close to 1 are very strong positive relationships

Qualitative data

Contingency Tables

Qualitative variables can be described by contingency tables. Given a qualitative variable (e.g. types of mammals: herbivore, omnivore, …) a contingency table records how many observations there are in each category. A contingency table can easily display up to two qualitative variables. Higher numbers of variables quickly become difficult to represent (e.g. three qualitative variables would require the equivalent of a three dimensional table).

The function table() can be used to create contingency tables. Below are examples with the msleep data frame

# A one dimensional contingency table
# The distribution of observations across mammalian foraging types
table(msleep$vore)


  carni   herbi insecti    omni 
     19      32       5      20

A two dimensional contingency table showing the number of species from each feeding type in each category of conservation status (cd=critically endangered, en=endangered, lc=least concern, nt=near threatened, vu=vulnerable).

# A two dimensional contingency table
table(msleep$conservation, msleep$vore)

              
               carni herbi insecti omni
  cd               1     1       0    0
  domesticated     2     7       0    1
  en               1     2       1    0
  lc               5    10       2    8
  nt               1     3       0    0
  vu               4     3       0    0

Barplots

A barplot is a one way to displaying how data are distributed across a qualitative variable. Each bar represents one category of the variable and the height of each bar usually represents the number of data points in each category.

A barplot is a graphical representation of a contingency table.

In Figure 1 we use the package ggplot2 to produce a bar plot of the feeding types of species in the msleep data.

Video Tutorial

The anatomy of a ggplot command (3 mins)

library(ggplot2)      # Load ggplot2 graphics library

# Define labels for the bars
labs <- c('herbi'='Herbivore',
         'carni'='Carnivore',
         'omni'='Omnivore',
         'insecti'='Insectivore')

# Use ggplot2 to produce a ...
# Bar plot of the distribution of feeding types in the msleep data set
ggplot(data=msleep,                   # Define the data to plot
       aes(x=vore)) + 
  geom_bar() +                        # Draw a bar plot
  scale_x_discrete(labels=labs) +     # Set x-axis labels
  labs(x='Feeding Type',              # Set axis titles
       y='Number of Species') + 
  theme_bw()                          # Set background to white

Figure 1: A bar plot of the distribution of feeding types in the msleep data set

Notice that we have relabeled the bars with more meaningful names. Graphical output should be styled so that it is easy to read.

We will see how the font size of the text can be increased later. For now we will tweak the plot to use different colours to fill the bars (Figure 2).

# Bar plot of the distribution of feeding types in the msleep data set
# with different colours for the different bars
ggplot(data=msleep,                             # Define the data to plot
       aes(x=vore, 
           fill=vore)) +                        # Define how bars are coloured
  geom_bar() +                                 
  scale_x_discrete(name = 'Feeding Type',       # Modify x axis labels   
                   labels=labs) + 
  scale_fill_discrete(name = 'Feeding Type',    # Modify the legend (colour) labels  
                      labels=labs) + 
  labs(x='Feeding Type',                        # Define the axis titles
       y='Number of Species') + 
  theme_bw()

Figure 2: A bar plot of the distribution of feeding types in the msleep data set with different colours for the different bars

ggplot2 help pages are available at https://ggplot2.tidyverse.org

Tip

R’s basic plotting command barplot() also produces a barplot.

Pie charts

Pie charts are sometimes used for displaying how a whole quantity is divided into proportions. They are another way of representing the data’s distribution across a qualitative variable. Each section of a pie chart is one category of the qualitative variable and the size of the section represents the proportion of data points out of the entire data set that have that value.

Figure 3 displays the above barplot as a pie chart using R’s pie() function

# Display a pie chart

# Plot the proportions of foraging types in the msleep dataset
pie(table(msleep$vore))

Figure 3: A pie chart created using R’s `pie()` function

Warning

A bar chart is usually preferred over a pie chart.

Issues with a pie chart:

does not communicate the number of data points used to calculate the proportions
can misrepresent the data because humans are bad at perceiving angles

Quantitative data

Histograms

The distribution of data across a quantitative data can be visualised using a histogram.

Figure 4 visualises the distribution of the daily time spent asleep for the mammals (from the msleep data set) using a histogram with approximately 20 bins.

# Histogram of the number of hours per day mammals are asleep 
# (using 20 bins along the x axis)
ggplot(data=msleep,                        # Define the data to plot
       aes(x=sleep_total)) +       
  geom_histogram(bins=20) +                # Draw the histogram with 20 bins
  labs(x='Total time asleep per day (h)',  # Set axis titles
       y='Count') +
  theme_bw()                               # Set the background to white

Figure 4: A histogram showing the distribution of the number of hours per day mammals are asleep (using approximately 20 bins).

Histogram bins

A histogram divides up the x-axis into a number of segments, called bins. The height of a bar in a histogram represents the number of observations within the range covered by the bin.

In the histogram on the right each bin covers a range of times.

Note

R can also produce histograms without ggplot2 using the hist() command.

The number of bars used to represent the distribution can affect our interpretation. Too many bars or too few bars can both make the visualisation meaningless (Figure 5).

(a) A histogram with too many bars (300 bins). This plot shows little more than the individual data points.

Goldilocks and the number of bins

Pick the number of bins carefully so that the histogram visualises the distribution of the data. Too few or too many bins and the plot will not communicate the data fully.

Kernel density plots

These plots are another way to visualise the distribution of a continuous quantitative variable (see the ggplot2 function geom_density()).

Q-Q plots

Quantile-quantile plots (Q-Q plots) are a good way to compare the distribution of your data to a normal distribution (other distributions can also be used). Quantile-quantile plots are often used to test the assumptions of a data analysis (many common analysis methods assume the residuals from an analysis will be close to a normal distribution).

ggplot’s geom_qq() can be used to produce a quantile-quantile plot (R’s base function is qqnorm()). The points will lie on a straight line if data are close to being normal. geom_qq_line() can be used to add a line onto the ggplot2 plot.

Figure 6 is an example of a Q-Q plot (quantile-quantile plot) for the variable sleep_total in the msleep data set.

# A quantile-quantile plot for variable sleep_total in the msleep data set
# Add a title that reminds us which variable is being plotted
ggplot(data=msleep,                                # Define the data to plot
       aes(sample=sleep_total)) +    
  geom_qq() +                                      # Draw the QQ plot points
  geom_qq_line() +                                 # Draw the QQ plot line
  labs(title='Normal Q-Q Plot for sleep_total') +  # Add a title
  theme_bw()                               # Set the background to white

Figure 6: A quantile-quantile plot for the variable sleep_total in the msleep data set

The points lie along a fairly good straight line indicating that the distribution of total sleep across the mammal species in msleep data set is approximately normal.

Note

Q-Q plots can also be produced using the functions qqnorm() and qqline()

An example of a non-normal distribution

The distribution of mammal REM sleep times (variable msleep$sleep_rem) is not normally distributed. This variable is right-skewed (see the tutorial on data distributions for more details on skewed distributions).

# A quantile-quantile plot for variable sleep_rem in the msleep data set
# Add a title that reminds us which variable is being plotted
ggplot(data=msleep,                             # Define the data to plot
       aes(sample=sleep_rem)) +    
  geom_qq(na.rm=TRUE) +                         # Draw the QQ plot points
  geom_qq_line(na.rm=TRUE) +                    # Draw the QQ plot line
  labs(title='Normal Q-Q Plot for sleep_rem') + # Add a title
  theme_bw()                               # Set the background to white

Figure 7: A qq-plot for a variable that is right-skewed

Note

The Q-Q plot on the right has points that do not lie on a straight line, and so the variable is not well described by a normal distribution.

Box and whisker plots

A broad indication of a quantitative variable’s distribution can be seen by plotting quantiles (e.g. 0%, 25%, 50%, 75% and 100% quantiles correspond to minimum, 1st quartile, median, 3rd quartile and the maximum). Quantiles can be calculated using the quantile() function.

# Plot the 0%, 5%, 25%, 50%, 75%, 95% and 100% quantiles 
# for the Cpgmg variable in the wolf data frame
quantile(wolf.sub$Cpgmg, probs=c(0, 0.05, 0.25, 0.5, 0.75, 0.95, 1.0) )

     0%      5%     25%     50%     75%     95%    100% 
 4.7500  8.8645 12.1600 15.3750 19.9750 27.6380 40.4300

Quantiles are commonly represented on a box and whiskers plot. This can be produced in ggplot2 using geom_boxlot() (Figure 8)

# Box and whiskers plot for the Cpgmg variable in the wolf data frame
ggplot(data=wolf.sub,                      # Define the data to plot
       aes(x=NULL, 
           y=Cpgmg)) + 
  geom_boxplot() +                         # Draw a box and whiskers plot
  labs(y='Cortisol [pg/mg]') +             # Add y-axis title
  theme_bw()                               # Set the background to white

Figure 8: A very simple box and whiskers plot that provides a concise summary of the data. Box and whisker plots are especially useful when comparing several groups (see below)

The box and whiskers plot displays:

the median as the central bar in the box
the 25% quantile as the lower end of the box
the 75% quantile as the upper end of the box
outliers as individual points
whiskers extend to 1.5 times the inter-quartile range

Box and whisker plots show less information than a histogram but they can be used to easily plot the distributions from several variables. For example, we can compare the distributions from the two populations in the wolf.sub data frame (one population associated with heavy hunting pressure, the other with light hunting pressure, Figure 9).

# Box and whiskers plot for the Cpgmg variable from
# populations with light and heavy hunting
ggplot(data=wolf.sub,                      # Define the data to plot
       aes(x=Hunting, 
           y=Cpgmg)) +   
  geom_boxplot() +                         # Draw a box and whiskers plot
  labs(y='Cortisol [pg/mg]') +             # Add y-axis title
  theme_bw()                               # Set the background to white

Figure 9: An example of using a boxplot to visualise the distribution of data across several groups.

Draw a box and whiskers plot across two variables (Hunting and Sex, Figure 10)

# Box and whiskers plot for the Cpgmg variable from
# populations with light and heavy hunting
# and colours representing the sex
ggplot(data=wolf.sub,                      # Define the data to plot
       aes(x=Hunting, 
           y=Cpgmg, 
           fill=Sex)) +                    # Different fill colours
  geom_boxplot() +                         # Draw a box and whiskers plot
  labs(y='Cortisol [pg/mg]') +             # Add y-axis title
  theme_bw()                               # Set the background to white

Figure 10: An example of a box plot that uses colour to represent a third variable (in this case the sex of a wolf)

Box and whisker plots can be produced without ggplot2 using R’s base plotting with the boxplot() command. Here is an example for you to try.

# R's base function for a box and whisker plot

# Box and whiskers plot for the Cpgmg variable from 
# populations with light and heavy hunting
boxplot(Cpgmg~Hunting, 
        data=wolf.sub, 
        ylab='Cortisol [pg/mg]', 
        xlab='Population')

Error bars

Error bars can be added to a plot using geom_errorbar() from ggplot2.

Here is an example that plots the mean and standard deviation of the Cpgmg variable for populations under Heavy and Light hunting pressure.

Step 1

Create a new data frame to contain this information, using NA’s in places where we will add data.

# Create a data frame to contain mean and standard deviation of cortisol
# for populations under Heavy and Light hunting pressure
d <- data.frame(Hunting=c('Heavy', 'Light'), 
               mean=NA, 
               sd=NA)

d   # Display this largely empty data frame

  Hunting mean sd
1   Heavy   NA NA
2   Light   NA NA

Step 2

Calculate the mean and standard deviations for Heavy and Light hunting and add them into the data frame

# Calculate mean and sd cortisol for Hunting='Heavy'
ind <- wolf.sub$Hunting=='Heavy'
d$mean[1] <- mean(wolf.sub$Cpgmg[ind], na.rm=T)
d$sd[1] <- sd(wolf.sub$Cpgmg[ind], na.rm=T)

# Calculate mean and sd cortisol for Hunting='Light'
ind <- wolf.sub$Hunting=='Light'
d$mean[2] <- mean(wolf.sub$Cpgmg[ind], na.rm=T)
d$sd[2] <- sd(wolf.sub$Cpgmg[ind], na.rm=T)

d   # Display the completed data frame

  Hunting     mean       sd
1   Heavy 17.07495 5.543389
2   Light 15.56222 7.298785

Step 3

Create the plot using the data in data frame d (Figure 11)

# Create the plot
ggplot(data=d,                  # Define data to plot
       aes(x=Hunting,
           y=mean,
           ymin=mean-sd,        # Bottom edge of errorbar
           ymax=mean+sd)) +     # Top edge of errorbar
  geom_point(size=4) +          # Draw means as points
  geom_errorbar(width=0.2) +    # Add errorbars (+/- 1 sd)
  labs(x='Hunting Pressure',    # Add axis titles
       y='Cortisol [pg/mg]') +
  theme_bw()                               # Set the background to white

Figure 11: An example of a plot with errorbars. In this case the errorbars represent the spread of the data using the standard deviation as the measure of spread.

Scatterplots

Two quantitative variables can be compared using a scatterplot. Figure 12 is an example of a scatterplot for total time asleep versus time in REM sleep (data from the msleep data set)

# Plot REM sleep (hours per day) against total sleep (hours per day)
ggplot(data=msleep,                        # Define data to plot
       aes(x=sleep_total, 
           y=sleep_rem)) +
  geom_point(na.rm=TRUE) +                 # Draw points 
  labs(x='Total sleep (hr/day)',           # Set axis titles
       y='REM sleep (hr/day)') +
  theme_bw()                               # Set the background to white

Figure 12: A scatterplot can be a good way to visualise the relationship between two quantitative variables

Adding a smoothed line

Sketching a line through your data point can help your eye visualise the relationship between two continuous variables.

Using ggplot2 a smoothed line can be added to a plot using geom_smooth(). Figure 13 the loess smoothing method.

# Adding a smoothed line to the plot using geom_smooth()

ggplot(data=msleep,                            
       aes(x=sleep_total, 
           y=sleep_rem)) +
  geom_point(na.rm=T) +                          
  geom_smooth(method='loess',           # Draw a smoothed line through the points
              formula=y~x,
              na.rm=T) +  
  labs(x='Total sleep (hr/day)',                
       y='REM sleep (hr/day)') +
  theme_bw()                            # Set the background to white

Figure 13: An example that adds a smoothed line over the top of a scatterplot.

Note: when drawing a smoothed line, it is import to also visualise the raw data (i.e. the data points). The smooth line helps your eye interpret the data.

Bubble plots

Bubble plots allow three variables to be displayed on one graph. The third variable is the size of a symbol.

Bubble plots were popularised in Hans Rosling’s TED talk

Video Tutorial

Hans Rosling using bubble plots (20 mins)

A simple bubble plot can be created using ggplot2 and the size= argument to modify the size of the symbols being plotted.

Figure 14 adds information about the body mass of animals (bodywt) to the scatterplot of sleep_total versus sleep_rem.

# A bubble plot where size of the symbol represents body weight (on a log scale)

# Plot REM sleep (hours per day) against total sleep (hours per day)
ggplot(data=msleep,                               # Define data to plot
       aes(x=sleep_total, 
           y=sleep_rem, 
           size=bodywt)) +                        # Define size of symbol
  geom_point(na.rm=TRUE) +                        # Draw points (remove NA's)
  scale_size_continuous(name='Body Weight (kg)',  # Define size scale
                        trans='log10') +          # Log10 transform body weight
  labs(x='Total sleep (hr/day)',                  # Set axis titles
       y='REM sleep (hr/day)') +
  theme_bw()                               # Set the background to white

Figure 14: An example of a bubble plot, using the size of a point to commnicate a third quantitative variable.

Multiple scatterplots

Multiple scatterplots can be used to visualise correlations within the data set.

Figure 15 displays the sleep data for mammals in the msleep data frame (data are in columns 6, 7, 8 and 9 corresponding to variables sleep_total, sleep_rem, sleep_cycle and awake) using the pairs() function

pairs(msleep[ ,c(6:9)])     # Display a grid of scatterplots

Figure 15: Using the `pairs()` function to display scatterplots for all pairwise combinations of variables in a data frame (note the variables must be quantitative)

Figure 15 displays a grid of scatterplots. The top row of plots has the sleep_total variable on the y-axis and each of the other variables (sleep_rem, sleep_cycle and awake) on the x-axis. You can see that sleep_total and awake are perfectly correlated (a negative correlation) because these two variables must sum to 24 hours. The plots below the diagonal repeat the plots above the diagonal but with x and y axes swapped.

We can start to see patterns in the data. For example, sleep_total has a positive correlation with sleep_rem, whereas sleep_cycle has no clear relationship with sleep_rem.

Styling a ggplot

Logarithmic axes

A linear scale is sally the default scale for the axes of a plot, but a linear scale does not always communicate the data very clearly.

Below we plot a species’ total time asleep as a function of its brain weight. Most of the variation in brain weight is less than 1 kg, but there are a couple of species with large brain weights.

# Plot total time asleep as a function of brain weight
ggplot(data=msleep,                        # Define data to plot
       aes(x=brainwt, 
           y=sleep_total)) +
  geom_point(na.rm=T) +                    # Draw points
  labs(x='Brain weight (kg)',              # Set axis titles
       y='Total sleep (hr/day)') +
  theme_bw()                               # Set the background to white

The plot would be clearer if we plotted the x-axis on a scale of orders of magnitude (i.e. on a scale which looks like 1 g, 10 g, 100 g, 1 kg, 10 kg). This kind of scale is a logarithmic scale.

Use scale_x_log10() to convert the x-axis to a logarithmic scale.

# Plot total time asleep as a function of brain weight 
# using logarithmic x-axis

ggplot(data=msleep,                            
       aes(x=brainwt, 
           y=sleep_total)) +
  geom_point(na.rm=T) +                        
  labs(x='Brain weight (kg)',               
       y='Total sleep (hr/day)') +
  scale_x_log10()  +                       # Set x-axis to log scale
  theme_bw()                               # Set the background to white

Symbols

The symbol used to plot a point can be changed by setting the shape=, size= and colour= arguments of geom_point(). Below is an example of a scatter plot using solid squares (shape=15), with a size four times the default (size=4) and coloured dark orange (colour='darkorange'). The list of shape codes are at the end of this tutorial. More details on styling lines and points can be found at https://ggplot2.tidyverse.org/articles/ggplot2-specs.html.

# Plot total time asleep as a function of brain weight 
# usng logarithmic x-axis

ggplot(data=msleep,                            
       aes(x=brainwt, 
           y=sleep_total)) +
  # Set symbols to be dark orange, filled squares, 
  # with a size 4 times larger than the default size
  geom_point(na.rm=T, 
             shape=15, 
             size=4, 
             colour='darkorange') +                        
  labs(x='Brain weight (kg)',               
       y='Total sleep (hr/day)') +
  scale_x_log10()  +    
  theme_bw()

Axis titles and fonts

We’ve seen that labs() can be used to define the title of each axis. However, the size and font of these titles are set by changing the theme.

Below is an example where the axis labels and axis titles are set to a size of 18 points and have a serif font family (e.g. Times), set using family='serif'. Axis titles are in a bold face using face='bold'.

# Plot total time asleep as a function of brain weight 
# using logarithmic x-axis and changing font of axis text

ggplot(data=msleep,                            
       aes(x=brainwt, 
           y=sleep_total)) +
  geom_point(na.rm=T) +                        
  labs(x='Brain weight (kg)',               
       y='Total sleep (hr/day)') +
  scale_x_log10() +   
  theme_bw()  +
  theme(
    # Font size of axis labels and font family
    axis.text = element_text(size=18,
                             family="serif"),
    # Font of axis title, change size, font family and font face
    axis.title = element_text(size=18, 
                              family="serif", 
                              face='bold'))

A consistent style can be easily applied to lots of ggplot graphs by defining a custom theme and then applying that theme to every ggplot command. Below is an example of R code that will produce the same plot as above, but the customized style can also be applied to other ggplot graphics.

# **************************************************
# Defining a customized style

# Define a custom style where font size and font face are specified
custom_style <- theme(
    # Font size of axis labels and font family
    axis.text = element_text(size=18,
                             family="serif"),
    # Font of axis title, change size, font family and font face
    axis.title = element_text(size=18, 
                              family="serif", 
                              face='bold')) 



# Now produce the plot and add the customized style
ggplot(data=msleep,                            
       aes(x=brainwt, 
           y=sleep_total)) +
  geom_point(na.rm=T) +                        
  labs(x='Brain weight (kg)',               
       y='Total sleep (hr/day)') +
  scale_x_log10() +   
  theme_bw()  +
  custom_style                      # Apply custom style to the plot

We can use the scales package to format the labels on the x-axis into publication quality (i.e. from 1e-03 to 10^-3).

# Plot total time asleep as a function of brain weight 
# make x-axis labels nicely formatted

ggplot(data=msleep,                            
       aes(x=brainwt, 
           y=sleep_total)) +
  geom_point(na.rm=T) +                        
  labs(x='Brain weight (kg)',               
       y='Total sleep (hr/day)') +
  scale_x_log10(  
    # Set x-axis tick mark positions 
    breaks = scales::trans_breaks("log10", function(x) 10^x),   
    # Set x-axis labels to be nicely formatted 
    labels = scales::trans_format("log10", scales::math_format(10^.x))) +   
  theme_bw() +
  custom_style

Colour scales

We can use colour scales to represent additional information.

Discrete colour scales

A great resource for picking informative colour scales that are discrete is http://colorbrewer2.org.

We can add information about the different feeding types (variable vore with levels herbi, omni, carni and insecti) to the plot of total sleep time versus REM sleep time, by using a discrete colour scale with the symbols.

First we’ll define labels that will be used in the plot’s legend.

# Plot feeding types using different colours

# Define labels for the bars
labs <- c('herbi'='Herbivore',
         'carni'='Carnivore',
         'omni'='Omnivore',
         'insecti'='Insectivore')

Then we’ll set the colour scale to the feeding type by colour=vore in the aesthetics. Finally, the colour palette and labels can be set using scale_colour_discrete().

# Plot REM sleep (hours per day) against total sleep (hours per day)
# Use different coloured points for different feeding types

# Define a custom style where font size and font face are specified
# for axis and legend text
custom_style <- theme(
    # Font size of axis labels and font family
    axis.text = element_text(size=18),
    # Font of axis title, change size, font family and font face
    axis.title = element_text(size=18, 
                              face='bold'), 
    legend.text = element_text(size=16),
    legend.title = element_text(size=16)) 


# Now produce the ggplot graphics with the custom style
ggplot(data=msleep,                               # Define data to plot
       aes(x=sleep_total, 
           y=sleep_rem, 
           colour=vore)) +                        # Symbol colour given by variable vore
  geom_point(na.rm=TRUE, size=2) +                      
  scale_colour_discrete(name = 'Feeding Type',    # Name the colour scale 
                        labels=labs) +            # Set labels for the legend
  labs(x='Total sleep (hr/day)',              
       y='REM sleep (hr/day)') +
  theme_bw() +
  custom_style                                    # Use custom style defined earlier

The above plot uses the default colour palette. To use colorbrewer palettes we can use scale_colour_brewer().

# Plot REM sleep (hours per day) against total sleep (hours per day)
# Use different coloured points for different feeding types
# Use www.colorbrewer2.org colour palette
ggplot(data=msleep,                               # Define data to plot
       aes(x=sleep_total, 
           y=sleep_rem, 
           colour=vore)) +                        # Symbol colour given by variable vore
  geom_point(na.rm=TRUE, size=2) +                      
  scale_colour_brewer(name = 'Feeding Type',      # Name the colour scale
                      labels=labs,                # Set labels for the legend
                      palette = 'Dark2') +        # Use colorbrewer palette Dark2
  labs(x='Total sleep (hr/day)',              
       y='REM sleep (hr/day)') +
  theme_bw()  +
  custom_style

Continuous colour scales

The viridis colour palettes are good colours to use for continuous scales.

Below we add information about body weight to the plot of total sleep time versus REM sleep. We do this using symbol colour on a continuous scale. This becomes a coloured version of the bubble plot.

We use scale_colour_viridis_c() to add a continuous colour scale using a viridis palette.

# A bubble plot where size of the symbol represents body weight (on a log scale)
# and symbol colour represents body weight (on a log scale) 

# Plot REM sleep (hours per day) against total sleep (hours per day)
ggplot(data=msleep,                               # Define data to plot
       aes(x=sleep_total, 
           y=sleep_rem, 
           colour=bodywt)) +                      # Use colour scale for body weight
  geom_point(na.rm=TRUE, size=2) +
  # Use viridis default palette
  scale_color_viridis_c(name='Body Weight (kg)',  
                        trans='log10', 
                        # Set x-axis labels to be nicely formatted 
                        labels = scales::trans_format("log10",scales::math_format(10^.x))) +
  labs(x='Total sleep (hr/day)',                                        
       y='REM sleep (hr/day)')  +
  theme_bw()  +
  custom_style

Making figures accessible to all

Make your visualisation have a big impact on people by making them accessible to as many people as possible.

When producing visualisations be aware that different people will see your visualisations differently. Some examples of reasons for perceptual differences are:

Viewing a black & white print out of your visualisation
Colour blindness: https://www.nature.com/articles/d41586-021-02696-z
People with low vision often magnify images. Magnified images can appear pixelated and hard to understand if they are too low resolution.

Google have come up with some nice visualisation design principles: https://medium.com/google-design/redefining-data-visualization-at-google-9bdcf2e447c6

Saving a plot as an image file

Using RStudio

If you are using RStudio you can use its GUI to save graphical output to a file. Here is a short video tutorial on this:

Video Tutorial

Saving R graphics to a file using RStudio (3 mins)

Using ggplot2

To save a plot to a file you can use the ggsave() command. Here is the code to save the coloured bubble plot (above).

# Save the figure to a file
ggsave(filename = 'coloured_plot.png',      # Set filename    
       width=8,                             # Set width (inches)
       height=5)                            # Set height (inches)

More visualisation ideas

We give some examples of more advanced data visualisation techniques that use packages such as ggplot2. We will present the visualisations but not the R code.

Violin plots

Violin plots are similar to boxplots, but the boxes are replaced by violin shapes that represent the distribution of the data. Below is the violin plot version of the boxplot above for cortisol in populations 1 & 2 (this violin plot was produced using package ggplot2). The boxplot version is also shown in grey inside each violin.

# Create a violin plot and overlay a box and whiskers plot


# Define axis label and title font size to be 18 
format <- theme(axis.title = element_text(size=18), 
               axis.text = element_text(size=18)) 

ggplot(data=wolf.sub,           # Define data to plot
       aes(x=Hunting, 
           y=Cpgmg)) + 
  geom_violin(fill='green4') +  # Draw violin plot in green
  geom_boxplot(colour='black',  # Draw box and whiskers plot 
               fill='grey', 
               width=0.1) + 
  theme_bw() +                  # Set background to white
  format +                      # Set the look of the plot
  labs(x='Population',          # Set axis titles
       y='Cortisol (pg per mg)')

Heatmaps

A heatmap represents three variables as a coloured matrix: two qualitative variables on the x and y axes and a third variable as a colour. They are commonly used in biology (e.g. gene expression data). You can create these plots using the function heatmap().

Below is a heatmap showing the monthly rainfalls at Malin Head from 2013 - 2016 (produced using ggplot2).

## Heatmap code
library(tidyr)
library(ggplot2)
# Import rainfall data
rainfall <- read.table('MALIN_HEAD.TXT', header=T, sep='\t')

# Create an array of the months in chronological order
monthList <- c('Jan','Feb','Mar','Apr','May','Jun',
              'Jul','Aug','Sep','Oct','Nov','Dec')

# Put rainfall data in long format
rainfall_long <- pivot_longer(data=rainfall, 
                             names_to = 'Month', 
                             values_to = 'rain', 
                             cols = any_of(monthList))

# Define the order of the months
rainfall_long$Month <- ordered(rainfall_long$Month, 
                              levels=monthList)

# Create the heatmap plot
ggplot(data=rainfall_long, 
       aes(x=Year,
           y=Month, 
           fill=rain)) + 
  geom_tile(colour='white') +
  scale_fill_gradient(low = "white", 
                      high = "steelblue") +
  labs(x="Year", 
       y="Month", 
       fill = "Rainfall (mm)", 
       title="Monthly Rainfall at Malin Head") +
  theme_bw() +
  theme(legend.title = element_text(size = 10),
        legend.text = element_text(size = 12),
        plot.title = element_text(size=16),
        axis.title=element_text(size=14, face="bold"),
        axis.text = element_text(size=14),
        axis.text.x = element_text(angle = 90, hjust = 1))

Correlation plot

Correlations can be calculated using the cor() function (see above). Heatmaps style visualisations are a great way to visualise correlations.

The package corrplot provides a nice way to produce a correlation plot. Below is an example showing the correlations in the msleep data set (compare this plot to the pairs() scatterplot above).

# Display a correlation plot using the corrplot package

library(corrplot)

# First calculate correlation coefficients to be visualised
cor_matrix <- cor(msleep[ ,c(6:9)], method='pearson',use='complete.obs')

# Now produce the plot
corrplot(cor_matrix, method='circle', type='upper', addCoef.col = "black")

Positive correlations are represented in blue, negative correlations in red. The colour scale is shown on the right hand side.

Lollipop plot

This is a mix of a bar plot and a scatter plot.

Below is a lollipop plot for the mean monthly rainfall at Malin Head.

Interactive (HTML) visualisation

Displaying data in a browser (like a webpage in a web browser) allows you to interact with the visualisation. It is a great way to explore data, and it is becoming and increasingly popular data visualisation approach.

Interactive visualisations are not a good way to produce figures for a report, because a report is generally a static document.

There are a range of packages that allow you to produce interactive visualisation that you can view in a browser. Some of these packages are:

googleVis: https://cran.r-project.org/web/packages/googleVis/vignettes/googleVis_examples.html
plotly: https://plot.ly/r/
leaflet: https://rstudio.github.io/leaflet/
rCharts: https://ramnathv.github.io/rCharts/

Example interactive plots: Click here to see some examples of interactive plots

This webpage can be viewed at https://DrJonYearsley.github.io/Resources/interactive_plots_WebVersion.html

Inspirational websites

Here are some webpages with examples of data visualisation using R

Summary of the topics covered

Accessing R’s built-in data sets
Descriptive statistics
Contingency tables
Basic graphics functions: scatterplots, box and whisker plots, histograms, bar plots, pie charts, Q-Q plots
Customising graphs: axis labels, symbols and colours
Saving a graph as an image file

Appendix: codes for plotting symbols

Below are the codes corresponding to different symbols.

In ggplot2 these codes are used with shape= option.

In R’s base plotting functions, these codes are used with pch= option.

pch=0,square
pch=1,circle
pch=2,triangle point up
pch=3,plus
pch=4,cross
pch=5,diamond
pch=6,triangle point down
pch=7,square cross
pch=8,star
pch=9,diamond plus
pch=10,circle plus
pch=11,triangles up and down
pch=12,square plus
pch=13,circle cross
pch=14,square and triangle down
pch=15, filled square blue
pch=16, filled circle blue
pch=17, filled triangle point up blue
pch=18, filled diamond blue
pch=19,solid circle blue
pch=20,bullet (smaller circle)
pch=21, filled circle red
pch=22, filled square red
pch=23, filled diamond red
pch=24, filled triangle point up red
pch=25, filled triangle point down red

Objectives

Introduction

Before you continue:

Overview of the data

Import data

Descriptive statistics

Central tendency

Spread

summary() of a data frame

Other descriptive statistics

Correlation

Qualitative data

Contingency Tables

Barplots

Pie charts

Quantitative data

Histograms

Q-Q plots

An example of a non-normal distribution

Box and whisker plots

Error bars

Step 1

Step 2

Step 3

Scatterplots

Adding a smoothed line

Bubble plots

Multiple scatterplots

Styling a ggplot

Logarithmic axes

Symbols

Axis titles and fonts

Colour scales

Discrete colour scales

Continuous colour scales

Making figures accessible to all

Saving a plot as an image file

Using RStudio

Using ggplot2

More visualisation ideas

Violin plots

Heatmaps

Correlation plot

Lollipop plot

Interactive (HTML) visualisation

Inspirational websites

Summary of the topics covered

Further Reading

Appendix: codes for plotting symbols

`summary()` of a data frame