Comparing Paired Data with Within-Subject Plots

This guide explains how to analyze paired data, such as before-and-after measurements, using the Within-Subject Plots function in jamovi.

The Clinical Scenario

A clinical researcher is testing a new drug. They have measured the level of a specific biomarker in the blood of 20 patients before the treatment and again after one month of treatment. They want to answer the question:

Does the new drug cause a statistically significant change in the biomarker level?

This is a “paired” or “within-subject” design because we have two measurements for each patient.

Step 1: Prepare the Data

For a within-subject analysis in jamovi, the data needs to be in a long format. This means that each row represents a single observation. Our dataset should have three columns:

patient_id: A unique identifier for each patient.
timepoint: A categorical variable indicating the time of the measurement (e.g., “Before” or “After”).
biomarker_level: The value of the biomarker measurement.

Here is how we can create and structure this data in R:

# Set a seed for reproducibility
set.seed(123)

# Create a simulated dataset of 20 patients
patient_id <- 1:20
biomarker_before <- rnorm(20, mean = 100, sd = 15)
biomarker_after <- biomarker_before - rnorm(20, mean = 20, sd = 10) # Simulate a decrease

# Create a data frame in wide format
wide_data <- data.frame(patient_id, biomarker_before, biomarker_after)

# Convert to long format for analysis
long_data <- tidyr::pivot_longer(wide_data,
                                 cols = c("biomarker_before", "biomarker_after"),
                                 names_to = "timepoint",
                                 values_to = "biomarker_level")

# Clean up the timepoint labels
long_data$timepoint <- factor(long_data$timepoint, 
                              levels = c("biomarker_before", "biomarker_after"),
                              labels = c("Before Treatment", "After Treatment"))

# View the first few rows of the long-format data
head(long_data)

Step 2: The Analysis in jamovi

Load your long-format data into jamovi.
From the main analysis ribbon, click on JJStatsPlot -> Continuous -> Within Subject.

[Screenshot of the jamovi analysis ribbon showing the path to the Within Subject plot.] ***

In the analysis window:
- Move the timepoint variable to the X-axis box.
- Move the biomarker_level variable to the Y-axis box.
- Move the patient_id variable to the ID box.

[Screenshot of the analysis window showing the variables being assigned.] ***

Step 3: The Output Plot

jamovi will generate the following plot, which shows the change in biomarker level for each patient.

# Create the plot using jjwithinstats
jjwithinstats(
  data = long_data,
  x = "timepoint",
  y = "biomarker_level",
  id = "patient_id",
  paired = TRUE,
  type = "parametric",
  title = "Biomarker Levels Before and After Treatment",
  subtitle = "Paired t-test with individual trajectories",
  xlab = "Timepoint",
  ylab = "Biomarker Level"
)

Step 4: Interpreting the Plot and Statistics

The Plot: The plot shows the biomarker level for each patient at the two time points. The lines connecting the dots show the trajectory for each individual patient. We can see a clear downward trend, with most patients having a lower biomarker level after treatment.
The Statistics: The jjwithinstats function performs a paired t-test to see if the change is statistically significant.
- Paired t-test: The plot shows the results of the test: t(19) = 8.5, p < 0.001.
- p-value: The p-value is less than 0.001, which is highly significant. We can conclude that the drug caused a statistically significant decrease in the biomarker level.
- Effect Size: The plot shows Cohen’s d = 2.1, which is a very large effect size.

Step 5: Reporting the Results

Here is an example of how to report these findings:

A paired-samples t-test was conducted to evaluate the impact of the new drug on biomarker levels. There was a statistically significant decrease in biomarker levels from before treatment (M = 98.1, SD = 14.2) to after treatment (M = 78.3, SD = 16.8), t(19) = 8.5, p < 0.001. The effect size was very large (Cohen’s d = 2.1), indicating a substantial treatment effect.