Analysing and Visualising Repeated Measures Data

Scientists working in exercise physiology often design experiments containing repeated measurements on different athletes or participants over the course of time.

One example, in a sport science setting, is the monitoring of a team-sport athlete’s response to training and competition loads. The countermovement jump (CMJ) is used to monitor an athlete’s neuromuscular status. A CMJ will often be performed by an athlete prior to training or match and monitored over the course of a week, tournament or season.

To show how repeated measures data can be analysed and visualised in R, I have created a (hypothetical) example of different athletes performing two trials of a CMJ at two different times of the day and monitored over a three day period. I have chosen Peak Velocity as my dependent variable purely for display purposes only. A useful variable to monitor the neuromuscular status of Australian Rules athletes appears to be Flight Time:Contraction Time.

Athletes = c("Gus", "Hudson", "Bobby", "Tom", "Jessie")
# CMJ performed at two different time points
TimeOfDay = c("AM", "PM")
# Set the start date of data collection
StartDate = as.Date("2016-02-01")
# Set the seed, to reuse the same set of random variables
set.seed(60)
# Create a data.frame containing dummy raw CMJ data
CMJRawData = data.frame(Name = rep((Athletes), each = 4),
Day = rep((weekdays(StartDate + 0:2)), each = 20),
Trial = as.numeric(rep(1:2, each = 1)),
TimeOfDay = rep((TimeOfDay), each = 2),
PeakVelocity = runif(60, 1.5, 2.8))

Plots can be created in R using the base packages however, I prefer to use ggplot2 due to it’s easy to follow syntax and ability to create complex figures in a visually pleasing manner. This package will need to be installed into R prior to loading.

# Load the required ggplot2 package
require(ggplot2)
# Create a basic box and whisker plot to visualise Peak Velocity
ggplot(data = CMJRawData, aes(x = Day, y = PeakVelocity)) +
 geom_boxplot(aes(fill = TimeOfDay))

The above plot is OK however, I personally prefer a cleaner plotting background plus emphasised ticks and correct axis labels. The code below creates a much more visually pleasing plot that can be used for presentation or scientific purposes.

# Create a neater looking plot with correct scientific notation
ggplot(data = CMJRawData, aes(x = Day, y = PeakVelocity)) +
geom_boxplot(aes(fill = TimeOfDay)) +
ylab(expression(Peak ~ Velocity ~ (m.s^-1))) +
scale_y_continuous(expand = c(0, 0), limits = c(0, 4)) +
theme_classic() +
theme(legend.title = element_blank(),
legend.text = element_text(size = 13),
strip.text.x = element_text(size = 15, face = "bold"),
axis.title.x = element_blank(),
axis.text.x = element_blank(),
axis.line.x = element_blank(),
axis.ticks.x = element_blank(),
axis.title.y = element_text(color="black", size = 15, vjust=1.5),
axis.line.y = element_line(colour = "black"),
legend.position = "bottom") +
facet_wrap(~ Day, scales="free_x")

I found the above plot much easier to read. The labels or ticks can be highlighted by including face = “bold” where appropriate. The y-axis scale can also be adjusted to zoom in on the figure and lose the white space by simply configuring the line:

scale_y_continuous(expand = c(0, 0), limits = c(0, 4))

To obtain summary statistics for a repeated measures dataset, install the package “psych” into R and run the following code. Other statistics, including the SE, can also be obtained by substituting “se” for “sd” in the line of code below.

# Load the required package
require(psych)
# Obtain the Mean and SD for Peak Velocity, over each day and time of day
PeakVelocity = ddply(CMJRawData, c("Day", "TimeOfDay"), summarise,
Mean = mean(PeakVelocity),
SD = sd(PeakVelocity))

Of interest to many scientists and practitioners is the individual response to training. This can be calculated and plotted using the code below, to track athletes over time. Note: I have calculated a mean Peak Velocity measure from the two trials at each time of day.

# Calculate the Mean and SD for Peak Velocity, for each athlete, over each day and time of day
PeakVelocityIR = ddply(CMJRawData, c("Day", "TimeOfDay", "Name"), summarise,
Mean = mean(PeakVelocity),
SD = sd(PeakVelocity))
# Plot individual responses across time for each day
ggplot(data = PeakVelocityIR, aes(x = TimeOfDay, y = Mean, colour = Name, group = Name)) +
geom_point() +
geom_line() +
ylab(expression(Mean ~ Peak ~ Velocity ~ (m.s^-1))) +
xlab("\nTime of Day") +
scale_y_continuous(expand = c(0, 0), limits = c(1.5, 2.75)) +
theme_classic() +
theme(legend.text = element_text(size = 13),
strip.text.x = element_text(size = 15, face = "bold"),
axis.title.y = element_text(color="black", size = 15, vjust=1.5),
axis.title.x = element_text(color="black", size = 15),
axis.line.y = element_line(colour = "black")) +
facet_wrap(~ Day, scales="free_x") 

Individual responses can also be displayed with a mean or group average overlay. This is displayed below.

# Create a new column, called name, for plotting
PeakVelocity$Name = c("Average")
# Plot the individual responses plus means
ggplot(PeakVelocity, aes(x = TimeOfDay, y = Mean, group = Name)) +
geom_point(colour = "black", size = 4) +
geom_line(colour = "black") +
geom_point(data = PeakVelocityIR, aes(x = TimeOfDay, y = Mean,
group = Name, colour = Name)) +
geom_line(data = PeakVelocityIR, aes(x = TimeOfDay, y = Mean,
group = Name, colour = Name)) +
ylab(expression(Mean ~ Peak ~ Velocity ~ (m.s^-1))) +
xlab("\nTime of Day") +
scale_y_continuous(expand = c(0, 0), limits = c(1.5, 2.75)) +
theme_classic() +
theme(legend.text = element_text(size = 13),
strip.text.x = element_text(size = 15, face = "bold"),
axis.title.y = element_text(color="black", size = 15, vjust=1.5),
axis.title.x = element_text(color="black", size = 15),
axis.line.y = element_line(colour = "black")) +
facet_wrap(~ Day, scales="free_x")

The above is only a sample of how repeated measures data can be visualised. What methods do you use to display repeated measures data? How do you clearly communicate individual responses?