--- title: "Lab 5: Two Tests, One Line" author: "Your Name Here" date: "`r Sys.Date()`" format: docx editor: visual editor_options: chunk_output_type: console --- ## Scenario and Goal The graduate school wants to know how students can study more effectively for their stats quiz. The researchers ran a study with **120 graduate students**: - Each student was **randomly assigned** to one of two study strategies: **Rereading** their notes, or **Retrieval Practice** (quizzing themselves without looking). - The researchers also **measured** (but did *not* assign) how long each student studied, how much they slept the night before, and their test anxiety. - Everyone then took the same quiz. Your goal is to answer **two research questions** with the tests from this week, then look at both of them a new way. By the end, you should notice something surprising about how these "different" tests relate to each other. ## Variables - `student_id`: Unique student ID - `condition`: Study strategy (**randomly assigned**): `"Rereading"` or `"Retrieval Practice"` - `study_minutes`: Minutes spent studying (measured) - `sleep_hours`: Hours of sleep the night before the quiz (measured) - `test_anxiety`: Test anxiety score, 10–50 (measured; higher = more anxious) - `exam_score`: Quiz score, 0–100 ------------------------------------------------------------------------ ## Exercises ### Exercise 1: Import, Inspect, and Think About Design Load all of your libraries and import the data in the chunk below. I should not see any lines that say `install.packages()`. Make sure your code is reproducible: I will run it on my own computer. ```{r ex1} # Load the libraries (tidyverse, rio, here) # Import study_strategies.csv from your data folder # Get an overview of your data (e.g., glimpse()) ``` **Question 1:** How many students are in the dataset? How many are in each `condition`? **Your Answer:** **Question 2:** Which variable is part of an **experiment**, and which variables are **observational**? For each type, can a significant result support a **causal** claim? Explain using what you learned in the Week 4 lecture. **Your Answer:** ------------------------------------------------------------------------ ### Exercise 2: Describe Create a summary table of `exam_score` (mean, SD, and n) **for each condition**. Then calculate the mean and SD of `study_minutes` for the whole sample. ```{r ex2} # Grouped summary of exam_score by condition # Mean and SD of study_minutes ``` **Question 3:** Which study strategy had the higher average quiz score, and by how many points? **Write this difference down; you will need it later.** **Your Answer:** ------------------------------------------------------------------------ ### Exercise 3: Research Question 1 (Comparing Groups) > **"Does the study strategy affect quiz scores?"** 1. Make a **boxplot** of `exam_score` by `condition`, with the individual points added (`geom_jitter()`), axis labels, and a title. 2. Run an **independent-samples t-test** with `var.equal = TRUE`. This tells R to assume both groups have about the same spread (variance), which gives the classic *Student's* t-test. It's also the version that matches the model you'll meet in Exercise 6. ``` r t.test(outcome ~ predictor, data = your_data, var.equal = TRUE) ``` ```{r ex3} # Boxplot # t-test ``` **Question 4:** Report the result in APA style: *t*(df) = \_\_\_, *p* = \_\_\_. Include the two group means. **Your Answer:** **Question 5:** In plain language, what does this p-value tell you? What does it **not** tell you? (Think back to the Inference Machine activity.) **Your Answer:** ------------------------------------------------------------------------ ### Exercise 4: Research Question 2 (Association) > **"Is the amount of time spent studying related to quiz scores?"** 1. Make a **scatterplot** with `study_minutes` on the x-axis and `exam_score` on the y-axis. Add a line of best fit (`geom_smooth(method = "lm", se = FALSE)`), axis labels, and a title. 2. Run a **correlation test** with `cor.test()`. ```{r ex4} # Scatterplot with a line of best fit # Correlation test ``` **Question 6:** Report the result in APA style: *r*(df) = \_\_\_, *p* = \_\_\_. Describe the direction and strength of the relationship. Also, `cor.test()` reports a **t** value. Write that down too. **Your Answer:** **Question 7:** Can we conclude that studying longer **causes** higher scores? Why or why not? Name one possible confound. **Your Answer:** ------------------------------------------------------------------------ ### Exercise 5: Seeing the Group Difference as a Line In Exercise 4 the relationship was a **line**. Can a *group difference* be a line too? 1. Use `mutate()` to create a new variable, `retrieval`, that is `0` for Rereading and `1` for Retrieval Practice. (Hint: `if_else(condition == "Retrieval Practice", 1, 0)`.) 2. Make a **scatterplot** with `retrieval` on the x-axis and `exam_score` on the y-axis. Use `geom_jitter(width = 0.05)` so the points don't stack, and add `geom_smooth(method = "lm", se = FALSE)`. 3. Add `scale_x_continuous(breaks = c(0, 1))`, axis labels, and a title. ```{r ex5} # Create the 0/1 variable # Plot exam_score by retrieval with a line ``` **Question 8:** Look at your line. a. About where does the line cross **x = 0**? Which group's mean is that? b. About where does it cross **x = 1**? Which group's mean is that? c. How much does the line go **up** when x moves from 0 to 1? Compare this to your answer to Question 3. **Your Answer:** ------------------------------------------------------------------------ ### Exercise 6: Sneak Peek at Next Week 👁️👄👁️ ::: callout-important ## You haven't learned this yet, and that's the point! Next week we meet the **linear model**, `lm()`. This exercise is a *discovery* activity: you run the code, find a few numbers, and make a thoughtful guess about what's going on. **Exercises 6 and 7 are graded on completion and effort, not on being right.** ::: Run the code below (replace the blanks with your data name). `tidy()` from the **broom** package turns the model into a small, readable table. broom is installed with the tidyverse, so you don't need to install anything new. ```{r ex6} # Model 1: the same question as the t-test model_groups <- lm(exam_score ~ condition, data = ___) broom::tidy(model_groups) # Model 2: the same question as the correlation model_minutes <- lm(exam_score ~ study_minutes, data = ___) broom::tidy(model_minutes) ``` Each output has two rows. Find the row whose `term` is **not** `(Intercept)`, and read across it: `estimate`, `statistic` (this is the *t* value), and `p.value`. Fill in the table below with the numbers from your earlier tests and from the `lm()` output. | Research Question | Earlier test | Earlier **t** | Earlier **p** | `lm()` **estimate** | `lm()` **statistic** (t) | `lm()` **p.value** | |-----------|-----------|-----------|-----------|-----------|-----------|-----------| | Strategy → Score | t-test | | | | | | | Minutes → Score | correlation | | | | | | **Question 9:** Compare the columns. What is the **same**, and what (if anything) is different? (Look closely at the sign of *t* in the first row.) **Your Answer:** **Question 10:** For Model 1, compare the estimate in the `(Intercept)` row and the estimate in the `conditionRetrieval Practice` row to your answers to Questions 3 and 8. What do you think these two numbers represent? **Your Answer:** ------------------------------------------------------------------------ ### Exercise 7: Reflect and Predict *Graded on completion and effort. A thoughtful guess earns full credit.* **Question 11:** A t-test and a correlation are usually taught as two completely different tests. Based on this lab, what do they have in common? In 2–3 sentences, make a prediction: what do you think "**everything is a linear model**" means? **Your Answer:** **Question 12 (Bonus):** `scale()` converts a variable into z-scores (mean = 0, SD = 1). Run the model below. Compare the estimate for `scale(study_minutes)` with your correlation from Question 6. What do you notice? ```{r ex7-bonus} broom::tidy(lm(scale(exam_score) ~ scale(study_minutes), data = ___)) ``` **Your Answer:** ------------------------------------------------------------------------ *End of Lab 5. You just ran two "different" tests and found that they are both lines. Hold on to that idea for next week! Don't forget to Render!*