---
title: "Lab 7: Does the Therapy Work?"
author: "Your Name Here"
date: "`r Sys.Date()`"
format: docx
editor_options:
  chunk_output_type: console
  markdown:
    wrap: 72
---

```{r setup, message = FALSE, warning = FALSE}
library(tidyverse)
library(rio)
library(here)
library(emmeans)

cbt <- import(here("data", "cbt_data_f25.csv"))
```

# Lab 7 — Does the Therapy Work?

**Due Tuesday, October 6, 11:59 pm.** Render to Word and submit both the
`.qmd` and the Word document.

Ninety adults with elevated depression scores were **randomly assigned**
to **Individual CBT**, **Group CBT**, or a **Waitlist Control**.
Depression was measured with the BDI before (`bdi_pre`) and after
(`bdi_post`) eight weeks. Higher = more symptoms. Five people did not
complete the post-assessment.

Write your answers under each **Your Answer:** line, in complete
sentences.

------------------------------------------------------------------------

## Exercise 1 — Import and inspect (3 points)

a)  How many participants are in each group?
b)  How many are missing a `bdi_post` score? Which group(s) are they in?
c)  What is your analysis N — the number of people who actually
    contribute to a model of `bdi_post`?

```{r}
# Your code here

```

**Your Answer:**

------------------------------------------------------------------------

## Exercise 2 — Did randomization work? (3 points)

Before trusting any treatment effect, check that the groups started out
similar. Compare the three groups on **`bdi_pre`**, and on one
demographic variable of your choice (`age` or `sex`).

```{r}
# Your code here

```

a)  Report the pre-treatment means by group.
b)  Do the groups look comparable at baseline? What would it have meant
    for your conclusions if they had *not*?

**Your Answer:**

------------------------------------------------------------------------

## Exercise 3 — Describe and visualize (3 points)

Make a table of `bdi_post` (n, mean, SD) by group, and a plot that shows
the group differences. Label your axes and give the plot a title.

```{r}
# Your code here

```

**Your Answer:** (one or two sentences describing what the plot shows)

------------------------------------------------------------------------

## Exercise 4 — Fit the model (4 points)

Fit a linear model predicting `bdi_post` from `group`, and print the
summary.

```{r}
# Your code here

```

a)  Which group is the reference? How do you know?
b)  What does the **intercept** mean, in the units of this study?
c)  What does **each** of the two other coefficients mean?
d)  Report the omnibus test: *F*, both degrees of freedom, and *p*.

**Your Answer:**

------------------------------------------------------------------------

## Exercise 5 — Choose the reference group on purpose (4 points)

R chose the reference alphabetically. That is not the question the trial
was designed to answer: the control group is the natural baseline.

Re-fit the model with **Waitlist Control** as the reference.

```{r}
# Hint: fct_relevel() inside mutate()

```

a)  What is the new intercept, and what does it mean?
b)  What do the two coefficients now tell you?
c)  Which numbers from Exercise 4 changed, and which stayed exactly the
    same? Why?

**Your Answer:**

------------------------------------------------------------------------

## Exercise 6 — Which pairs actually differ? (3 points)

The coefficient table compares each treatment to the control, but never
compares the two treatments to each other. Get all three pairwise
comparisons with a correction for multiple testing.

```{r}
# Your code here

```

a)  Report the three comparisons and their adjusted p-values.
b)  Is Individual CBT significantly better than Group CBT?
c)  Why not just run three t-tests instead?

**Your Answer:**

------------------------------------------------------------------------

## Exercise 7 — Effect size (3 points)

a)  Compute Cohen's *d* for **Individual CBT vs. Waitlist Control**.
b)  Report R² for the full model.
c)  Explain what each number tells a reader. Which one would you put in
    an abstract?

```{r}
# Your code here

```

**Your Answer:**

------------------------------------------------------------------------

## Exercise 8 — Write it up (3 points)

Write **one paragraph** reporting these results as they would appear in
the Results section of a paper. Include, in this order: the omnibus
test, the group descriptives, the pairwise comparisons that matter, and
an effect size.

**Your Answer:**

------------------------------------------------------------------------

## Exercise 9 — Judgment calls (2 points)

a)  Five people are missing post-treatment scores, and four of them were
    in the Individual CBT group — the group with the best outcome. Why
    might that matter for how you read the result? What is the one
    sentence you would add to the paper about it?
b)  Participants were **randomly assigned** to condition. Does that let
    you say the therapy *caused* the reduction in depression? Compare
    your answer to Lab 6, where you could not make a causal claim.

**Your Answer:**

------------------------------------------------------------------------

## Bonus (+1 point)

Everything above used `bdi_post` alone, ignoring where people started.
Fit a model that predicts `bdi_post` from **both** `group` and
`bdi_pre`:

```{r}
# Your code here

```

What happens to the treatment coefficients, and why might a clinical
researcher prefer this model? (One or two sentences — we do this
properly in Week 8.)

**Your Answer:**

------------------------------------------------------------------------

**Total: 28 points (+1 bonus)**

*Remember to render to Word before submitting.*