Lab 6: Comparing Means

Instructions

Here are the things that you will need for this lab:

When you are finished, click the Knit button to turn your work into an HTML document. You will submit both this .Rmd file and the 🧶knitted .html file.

Scenario and Goal

Welcome back! For this lab you’ll step into the role of a data analyst for a clinical psychology lab. Your team has just completed a pilot randomized controlled trial (RCT) for a new, brief CBT (Cognitive Behavioral Therapy) intervention designed to reduce symptoms of depression (group variable). You’ve been given the initial dataset and tasked with running the primary analyses to see if the intervention shows promise.

This dataset includes participant demographics (sex, age) and depression scores from before (bdi_pre) and after (bdi_post) the trial. As is common in clinical research, some participants dropped out before the final assessment, resulting in missing data.

Note

The BDI is a common measure to assess for symptoms of depression. It stands for the Beck Depression Inventory and higher scores indicate a higher level of depression.

Exercises

Task 1: Setup & Data Inspection (10 points)

Your first and most important task is always to understand and inspect your data before running any analyses.

Tasks:

  1. Create a new R Markdown file named Week6_Lab.Rmd.

  2. Load Libraries and Data

  3. Initial Inspection:

    • Use glimpse() to see the structure of your data.

    • Use summary() to get a quick overview of each variable. Pay close attention to the bdi_post variable. What do you notice?

  4. Visualization:

    • Generate a visualization of the distribution for bdi_pre and bdi_post

      • These can be two separate figures

  5. Summary Stats (2 tables):

    • Provide descriptive statistics (Means & SD) in a nice looking table for age, bdi_pre, bdi_post. Include a correlation table with those variables as well.

Task 2: Paired-Samples t-test - Did the Individual CBT Work?

For participants who received one-on-one therapy (group == "Individual CBT"), did their depression scores significantly decrease?

  1. Filter the data: Create a new data frame called individual_tx that contains only the participants from the Individual CBT group.

  2. Run the test: Conduct a paired-samples t-test on the bdi_pre and bdi_post scores within the individual_tx data.

  3. Interpret the results: Based on the results, was there a statistically significant change in BDI scores? Describe the direction and magnitude of the change.

Task 3: One-Sample t-test - Achieving Clinical Remission

A BDI score below 10 is often considered the cutoff for clinical remission. Did our individual CBT group, on average, get below this threshold?

  1. Run the test: Using the individual_tx data, conduct a one-sample t-test on the bdi_post scores, testing against a population mean (mu) of 10.

  2. APA Write-up: Report your results in a full APA-formatted sentence. You will need to calculate the mean and standard deviation for the bdi_post scores separately to include in your write-up.

Task 4: One-Way ANOVA

Now we’ll compare the final outcomes (bdi_post) across all three groups: Individual CBT, Group CBT, and the Waitlist Control.

  1. Run the ANOVA: Using the full cbt_data, conduct a one-way ANOVA to test for differences in bdi_post among the three group conditions.

  2. Interpret the ANOVA: Look at the summary() of your ANOVA object. Is the overall F-test significant? What does this tell us? Note the degrees of freedom—does the sample size make sense given the data?

  3. Run Post-Hoc Tests: A significant ANOVA requires a post-hoc test. Run a Tukey HSD test to see which specific groups differ.

  4. Write a conclusion: In 2-3 sentences, summarize the findings from the post-hoc test. Which treatment(s) were effective compared to the control group?

Task 5: Independent-Samples t-test - Exploring Sex as a Moderator

We were also interested to use exploratory analyses to further understand the impact of the treatment. For instance, did the therapy work equally well for males and females? Let’s investigate this.

Tasks:

  1. Calculate change scores: Create a new data frame called cbt_active_tx that contains only the two active therapy groups (Individual and Group CBT). Add a new column to it called bdi_change, calculated as bdi_pre - bdi_post.

  2. Run the test: In this cbt_active_tx data, conduct an independent-samples t-test to see if there is a significant difference in the bdi_change scores between participants identified as Male and Female.

  3. Visualize and Interpret: Create a ggplot boxplot to visualize the bdi_change scores by sex. Based on your test and your plot, is there any evidence that the treatment effect was different for males versus females in this pilot study?

End of Lab. Don’t forget to Knit! 🧶