Module 6 — Statistical Investigation Project
A Rigorous Statistical Investigation (RSI) integrating every Module 6 concept: scatterplots, correlation, regression, sets, probability, tree diagrams, sample spaces, data classification, pictographs, and two-way frequency tables — with a group collaboration component and discussion forum.
Student Learning Outcomes
- SLO 1: Classify variables as categorical or quantitative and identify individuals in a dataset.
- SLO 2: Construct and interpret scatterplots to describe direction, form, and strength.
- SLO 3: Calculate and interpret the correlation coefficient and distinguish association from causation.
- SLO 4: Fit a simple linear regression model, interpret slope and intercept, and evaluate residuals.
- SLO 5: Use set operations (union, intersection, complement) to describe events in a sample space.
- SLO 6: Compute probabilities using the addition rule, multiplication rule, and tree diagrams.
- SLO 7: Construct and interpret two-way frequency tables with marginal, joint, and conditional probabilities.
- SLO 8: Create pictographs and assess whether they communicate data proportionally.
- SLO 9: Communicate statistical findings with defensible language and identify limitations.
The Dataset: Study Habits & Exam Performance
A dataset from 12 students in an introductory statistics course. Each recorded weekly study hours, practice problems completed, whether they attended a review session, and their final exam score (out of 100).
Interactive Scatterplot Explorer
Select variables to plot. The scatterplot updates live. Use this to explore relationships before completing Task 2.
Interactive Correlation Calculator
See the step-by-step correlation calculation. Select two variables.
Interactive Regression Line
Adjust the sliders to fit a line, then compare with the actual best-fit line.
Interactive Probability Tree
Build a probability tree for a randomly selected student, branching on review attendance and scoring 75+.
Interactive Two-Way Frequency Table
Fill in the frequency table from the dataset. The calculator checks your work and computes probabilities.
Interactive Self-Checks
A scatterplot shows points rising from lower-left to upper-right with minor scatter. What direction, form, and strength?
If r = 0.98 between study hours and exam scores, does this prove that increasing study hours causes exam scores to rise?
You compute a regression line \(\hat{y} = 46.4 + 4.1x\). What does the slope of 4.1 mean in context?
In a sample of 12, 6 scored 75+ (set A) and 6 attended review (set B). If 5 students are in both, what is P(A ∪ B)?
A tree shows P(Review) = 0.5 and P(75+ | Review) = 0.83. What is P(Review ∩ 75+)?
P(75+ | Attended) = 0.83 and P(75+ | Did Not Attend) = 0.17. Are "Attended" and "Scored 75+" independent?
Project Tasks
Variable Classification & Individuals 9 pts
RSI phase: Research question setup.
- Identify the individuals (observational units) in this dataset.
- For each variable (Study Hours, Practice Problems, Attended Review, Exam Score), classify it as categorical or quantitative and explain why.
- For quantitative variables, identify the units of measurement.
- State whether this is an observational study or an experiment. Justify and explain what this means for causal claims.
Scatterplot & Description 12 pts
RSI phase: Exploratory analysis. Use the interactive scatterplot explorer above to explore, then create your own by hand or with software.
- Create a scatterplot of Study Hours (x) vs Exam Score (y). Label both axes with units.
- Describe using direction, form, and strength.
- Identify any outliers. If none, state so.
- Create a second scatterplot of Practice Problems vs Exam Score. Compare the two — which is stronger, and why?
Correlation Coefficient 12 pts
RSI phase: Statistical measurement. Use the correlation calculator above to check your work.
- Calculate the correlation coefficient \(r\) between Study Hours and Exam Score. Show your work.
- Interpret \(r\) in context: direction and strength.
- Calculate \(r\) between Practice Problems and Exam Score. Compare.
- A classmate claims: "Since r is high, studying more causes higher exam scores." Explain why this is not justified. Name at least two confounding variables.
Simple Linear Regression 15 pts
RSI phase: Model building. Use the regression fitter above to explore.
- Fit a regression line for predicting Exam Score from Study Hours. Calculate slope and intercept.
- Write the equation: \(\hat{y} = b_0 + b_1 x\).
- Interpret the slope in context.
- Interpret the intercept. Is it meaningful? Why or why not?
- Predict the exam score for 9 hours/week. Is this extrapolation?
- Compute residuals for all 12 students. Create a residual plot. Does the linear model appear appropriate?
Sets, Sample Spaces & Probability 12 pts
RSI phase: Probabilistic reasoning.
Define: A = {scored 75+}, B = {attended review}, C = {fewer than 25 practice problems}.
- List the elements of: A, B, C, A ∪ B, A ∩ B, Ac, and B ∩ Cc.
- Compute: P(A), P(B), P(C), P(A ∩ B), P(A ∪ B), and P(A | B).
- Verify the addition rule. Show the numbers.
- Are A and B independent? Check whether P(A | B) = P(A).
Tree Diagram & Conditional Probability 9 pts
RSI phase: Probabilistic reasoning. Use the interactive tree above.
- Construct a tree diagram: first branch "Attended Review" (Yes/No), second branch "Scored 75+" (Yes/No). Label each branch with its probability.
- Compute: P(75+ | Attended), P(75+ | Did Not Attend), P(75+) using law of total probability.
- Write a one-paragraph interpretation. What caveats apply?
Two-Way Frequency Table 12 pts
RSI phase: Statistical communication. Use the interactive table above to check your work.
- Construct a two-way frequency table with "Attended Review" as rows and "Scored 75+" as columns. Include all marginal totals.
- Compute marginal, joint, and conditional probabilities.
- Convert to a relative frequency table.
- Explain what the conditional probabilities tell you. Compare to your tree diagram results.
Pictograph Design & Critique 9 pts
RSI phase: Communication & visualization ethics.
- Create a pictograph showing average exam score for review attendees vs non-attendees. Use icons where each represents 10 points.
- Critique your pictograph: does the visual area accurately represent proportions? Could differently-sized icons mislead?
- Find one example of a misleading pictograph or bar chart. Describe what makes it misleading and how you would fix it.
Screen Recording: Walkthrough of a Key Finding 10 pts
RSI phase: Statistical communication. Assesses SLO 9.
- As a group, choose one finding from your project that you find most interesting or surprising. This could be the correlation strength, the regression prediction, the conditional probability from the tree diagram, or the independence check.
- Record a 3–5 minute screen recording where one or more group members explain the finding. Share your screen showing the interactive QuantegyAI page, your scatterplot, regression output, tree diagram, or two-way table while you talk through:
- What the data shows
- What the statistic means in context
- One caveat or limitation of the analysis
- Upload the recording to YouTube (unlisted), Google Drive, or Canvas Studio and paste the link in your submission.
Tip: You can use free tools like Loom, OBS Studio, or your computer's built-in screen recorder (QuickTime on Mac, Snipping Tool / Xbox Game Bar on Windows). Speak naturally — this is about explaining statistics in your own words, not a polished production.
Group Project Component 30 pts
Group Roles
Assign one role per member. If 4 members, split Data Analyst into two (one for regression, one for probability).
Completes Tasks 1 & 2: Variable classification, study type, scatterplot creation and description. Identifies individuals, classifies variables, produces both labeled scatterplots with written descriptions of direction, form, and strength.
Completes Tasks 3 & 4: Correlation calculation and regression modeling. Computes both correlations, fits the regression line, interprets slope/intercept, makes predictions, performs residual analysis. Responsible for the causal-boundary discussion.
Completes Tasks 5 & 6: Set operations, probability calculations, tree diagram. Lists all set elements, computes all probabilities, verifies the addition rule, checks independence, builds the tree diagram.
Completes Tasks 7 & 8: Two-way frequency table, pictograph, and final report assembly. Constructs the frequency table, creates the pictograph, finds a misleading graph example, and compiles all members' work into a unified report.
Group Submission Form
Group Collaboration Guidelines
- Meet early. Schedule your first meeting at least one week before the deadline.
- Shared document. Use Google Docs or similar so all members can contribute in real time.
- Individual contributions. Each member's work must be clearly labeled with name and role. The Communication Reporter compiles the final document.
- Cross-checking. The Data Analyst verifies the Researcher's scatterplot descriptions. The Probability Builder verifies the Analyst's calculations. The Reporter verifies the Builder's tree diagram.
- Conflict resolution. If a member is not contributing, contact your instructor before the deadline.
- Peer evaluation. Each member submits a brief peer evaluation (50 words per teammate) assessing contribution quality.
Interactive Group Activities
Work through these collaborative challenges together. Each activity saves your group's progress in your browser.
Discussion Component 20 pts · Required
Discussion: "Correlation Does Not Imply Causation — But What Does It Imply?"
You found a strong positive correlation between study hours and exam scores. Attending a review session is associated with higher scores. Your regression model can predict exam scores from study hours.
But can you conclude that studying more causes higher scores?
In a 200–300 word discussion post, address all three prompts:
- The causal boundary: What is the difference between "studying more is associated with higher scores" and "studying more causes higher scores"? Use at least two confounding variables to explain the distinction.
- The design question: What study design would you need to make a causal claim? Describe what such a study would look like. What ethical or practical concerns might arise?
- The communication question: If advising a student who wants to improve their exam score, how would you communicate findings honestly using correlation and prediction language without overstating causation? Write one sentence you would say to the student.
Requirements: 200–300 words · proper statistical terminology · reference at least one specific number from your analysis · post by due date · respond to at least one classmate (50+ words).
Write Your Discussion Post
Type your 200–300 word response below. When done, click Download to save your work as a text file for submission.
Your Tree Diagram Interpretation
After exploring the interactive tree above, write your one-paragraph interpretation of the conditional probabilities and what they mean.
Your Reflection (Task 8 Self-Critique)
Write your pictograph self-critique and misleading-graph analysis here.
Discussion Response Prompts
When responding to a classmate's post, consider:
- Did they identify a confounding variable you hadn't considered? How does it change the analysis?
- Is their proposed experimental design feasible? What practical obstacles might they face?
- Do you agree with their one-sentence advice to the student? How would you revise it?
- Did they use "association" and "causation" correctly throughout their post?
Submission Checklist
- Task 1: Variable classification with justifications (9 pts)
- Task 2: Two labeled scatterplots with written descriptions (12 pts)
- Task 3: Two correlation calculations with interpretation and causal-boundary discussion (12 pts)
- Task 4: Regression line equation, interpretations, prediction, residual analysis (15 pts)
- Task 5: Set listings and probability calculations with addition-rule verification (12 pts)
- Task 6: Tree diagram with labeled probabilities and conditional-probability interpretations (9 pts)
- Task 7: Two-way frequency table with all probabilities (12 pts)
- Task 8: Pictograph, self-critique, and misleading-graph example (9 pts)
- Group information form completed with all member names and roles
- Discussion post (200–300 words) posted in forum
- Response to at least one classmate (50+ words)
- All work uses neutral examples — no demographic-based claims
- All statistical language is defensible (association vs causation)
- Screen recording (3–5 min) uploaded with link in submission (10 pts)
Grading Rubric (100 points total)
| Criterion | Excellent | Proficient | Developing | Beginning |
|---|---|---|---|---|
| Variable Classification (9) | All correctly classified with units; study type identified with justification | Most correct, minor errors | Classification errors but some understanding | Missing or incorrect |
| Scatterplots (12) | Both drawn with labels; direction/form/strength accurate; outliers noted | Drawn, descriptions mostly accurate | One scatterplot or vague descriptions | Missing or unreadable |
| Correlation (12) | Both r values correct; interpretation precise; 2+ confounders named | Calculations correct, interpretation vague | Calculation errors but method shown | Missing or no causal discussion |
| Regression (15) | Correct slope/intercept, interpretations, prediction, residual plot | Correct equation, partial interpretations | Equation errors, minimal residuals | Missing or no residual analysis |
| Sets & Probability (12) | All sets listed, all probabilities correct, addition rule verified, independence checked | Most correct, minor set errors | Several errors but approach shown | Missing or incorrect |
| Tree Diagram (9) | Correctly constructed, all probabilities computed, thoughtful interpretation | Tree correct, minor errors | Tree incomplete or errors throughout | Missing |
| Two-Way Table (12) | Complete table with marginals, all probabilities correct, relative frequency, comparison to tree | Table complete, most probabilities correct | Table incomplete, several errors | Missing |
| Pictograph (9) | Accurate pictograph, thoughtful self-critique, valid misleading example | Pictograph correct, critique superficial | Pictograph errors, minimal critique | Missing |
| Group Collaboration (30) | All roles filled, work clearly labeled, cross-checking evident, cohesive report | Roles filled, some labeling, minor gaps | Uneven contribution, incomplete labeling | Missing or non-functional group |
| Discussion | 200-300 words, references data, correct terminology, causal distinction, classmate response | Mostly correct, minor issues | Short, vague, missing causal discussion | Missing or no response to classmate |
| Screen Recording (10) | 3-5 min, clear explanation of one finding, uses visuals, states a limitation, natural delivery | Explains finding with minor gaps, uses some visuals | Brief or unclear, minimal use of visuals | Missing or no statistical content |
How to Submit
Statistical Tasks 1–8 (90 pts): Submit a single PDF with all 8 tasks. Include the group information form on page 1. Label each task with the responsible member's name and role. One submission per group.
Group Collaboration (30 pts): Assessed based on role completion, labeling, cross-checking, and peer evaluations.
Screen Recording (10 pts): Upload your 3–5 minute screen recording to YouTube (unlisted), Google Drive, or Canvas Studio. Paste the link in your group submission.
Discussion (20 pts): Post your 200–300 word response in the Canvas discussion forum. Respond to at least one classmate (50+ words).
Due: October 2 · Total: 150 points