---
title: 'Lab 9: Model Selection'
author: "Your Name Here"
date: "`r Sys.Date()`"
output:
  word_document: default
  html_document: default
---

**Objective:** This lab is designed to develop the crucial skill of translating a behavioral science research question into an appropriate statistical model, and vice-versa. Instead of relying on a fixed decision tree, we will practice linking the *substance* of a question and the *structure* of the data to the choice of an analytic method. The goal is to foster statistical reasoning, where the model serves the scientific inquiry.

**Instructions:** This lab has two parts. For each scenario, provide the requested information, focusing on clear and concise justifications. Please submit your completed lab as a single document.

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## **Part 1: From Research Question to Statistical Model**

For each of the following scenarios, you are given a description of a research goal, similar to what might be in an intro.

1.  Identify the most appropriate statistical model from the options we have covered so far (**T-test (i.e., Independent, Dependent, Single Sample)**, **One-Way ANOVA**, or **Simple Linear Regression**).
2.  Write a brief (2-3 sentences) justification for your choice. Your justification must reference:
    -   The nature of the predictor variable (e.g., categorical with two levels, continuous).
    -   The nature of the outcome variable.
    -   What the key research question is asking for (e.g., a mean difference, a predictive relationship, a linear trend).

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### **Scenario A**

> "Previous research suggests that individuals with major depressive disorder (MDD) show deficits in cognitive control. However, it is unclear if this deficit is present in those with sub-threshold depressive symptoms. To address this, we recruited two independent groups of young adults: one group meeting formal criteria for MDD (n=50) and a control group with no history of psychiatric disorders (n=50). We hypothesized that the MDD group would show lower performance on the Stroop task, a measure of cognitive control, compared to the control group."

-   **1. Statistical Model:**
-   **2. Justification:**

### **Scenario B**

> "Sleep continuity is vital for well-being, yet its direct relationship with daily mood in non-clinical populations is not well-characterized. We conducted a study to examine whether the number of times a person wakes up during the night predicts their self-reported mood the following morning. We collected data from 100 university students, measuring their number of nocturnal awakenings via a wrist-worn device and their morning mood on a 100-point scale. We expect that a higher number of awakenings will be associated with a lower mood score."

-   **1. Statistical Model:**
-   **2. Justification:**

### **Scenario C**

> "Parental expressed emotion is a key factor in the home environment. We are interested in whether there are differences in academic achievement among adolescents from three distinct home environments, characterized by low, moderate, or high levels of expressed parental criticism. We categorized 150 adolescents into one of these three groups based on a structured family interview and obtained their grade point average (GPA) for the academic year."

-   **1. Statistical Model:**
-   **2. Justification:**

### **Scenario D**

> "A core symptom of social anxiety disorder is the avoidance of social situations. To test a new intervention, we conducted a randomized controlled trial where participants were assigned to either a 12-week mindfulness-based therapy group or a psychoeducation control group. At the end of the trial, we measured the number of social events each participant attended in the final week. We hypothesize that the mindfulness group will attend a greater number of social events on average than the control group."

-   **1. Statistical Model:**
-   **2. Justification:**

### **Scenario E**

> "It is well-established that age is related to cognitive function, but the specific trajectory is of interest. To explore this, we gathered a cross-sectional sample of 200 adults ranging from age 20 to 80. Each participant completed a standardized test of working memory. Our primary goal is to model the linear relationship between a person's age and their working memory score to understand the rate of change across the lifespan."

-   **1. Statistical Model:**
-   **2. Justification:**

### **Scenario F**

> "Chronic stress during adolescence can impact physiological regulation. We are interested in whether adolescents who report experiencing high, medium, or low levels of chronic life stress show differences in their morning cortisol levels, a key biomarker of the stress response system. We collected saliva samples from 90 adolescents who were categorized into one of the three stress groups based on a validated questionnaire."

-   **1. Statistical Model:**
-   **2. Justification:**

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## **Part 2: From Statistical Model to Research Question**

For each of the following scenarios, you are given the statistical output and a brief description of the variables.

1.  Infer and write out the specific research question that this analysis was likely designed to answer.
2.  Explain which parts of the output led you to your conclusion.

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### **Scenario G**

-   **Data Description:** A dataset includes `bdi_score` (Beck Depression Inventory score, continuous) and `sleep_hours` (average hours of sleep per night, continuous).
-   **Statistical Output:**

``` r
Call: lm(formula = bdi_score ~ sleep_hours, data = df)  Coefficients: (Intercept)  sleep_hours      35.50        -2.50
```

-   **1. Inferred Research Question:**
-   **2. Explanation:**

### **Scenario H**

-   **Data Description:** A dataset includes `anxiety_score` (a continuous measure of anxiety) and `treatment_group` (a categorical variable with two levels: "CBT" and "Waitlist").
-   **Statistical Output:**

``` r
Two Sample t-test data:  anxiety_score by treatment_group t = -4.5, df = 98, p-value < 0.001 alternative hypothesis: true difference in means is not equal to 0 mean in group CBT    mean in group Waitlist              15.2                      25.8
```

-   **1. Inferred Research Question:**
-   **2. Explanation:**

### **Scenario I**

-   **Data Description:** A dataset includes `perfectionism_score` (a continuous measure from a personality questionnaire) and `procrastination_index` (a continuous score based on a behavioral task).
-   **Statistical Output:**

``` r
Call: lm(formula = procrastination_index ~ perfectionism_score, data = df)  Coefficients:       (Intercept)  perfectionism_score             -5.22                 0.85
```

-   **1. Inferred Research Question:**
-   **2. Explanation:**

### **Scenario J**

-   **Data Description:** A dataset includes `adhd_symptoms` (a continuous symptom count) and `school_type` (a categorical variable: "Public," "Private," or "Charter").
-   **Statistical Output:**

``` r
One-way analysis of means data:  adhd_symptoms by school_type  F = 5.67, num df = 2, denom df = 147, p-value = 0.004
```

-   **1. Inferred Research Question:**
-   **2. Explanation:**

### **Scenario K**

-   **Data Description:** A dataset includes `pain_rating` (a patient's self-reported pain on a 0-10 scale) and `condition` (a categorical variable: "Acupuncture" or "Sham Procedure").
-   **Statistical Output:**

``` r
Two Sample t-test data:  pain_rating by condition t = 2.8, df = 78, p-value = 0.006 alternative hypothesis: true difference in means is not equal to 0 mean in group Acupuncture  mean in group Sham Procedure                     4.1                       6.2
```

-   **1. Inferred Research Question:**
-   **2. Explanation:**

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*End of Lab. Don't forget to Knit to a Word Doc! 🧶*
