Week 4 — Moving Together Is Not Causing: A Short Relationship Report

Assignment 4 of the term — work four short problems about how two variables relate, explain what each result does and does not show, and tell someone new to statistics why a strong link is not proof of cause.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 2 you read the species-by-island table cell by cell; this week you read it two ways, as marginal and conditional distributions, and you add scatterplots and the correlation coefficient. This week's lecture tutorial, quiz, discussion, and Data Lab practise the same ideas from other angles; this assignment is where you put them together and explain them.

The task

The Palmer penguins field log is a real observational study: researchers recorded 344 penguins of three species on three islands and assigned nothing. For the 342 penguins with both measurements, flipper length runs from 172 mm to 231 mm, body mass runs from 2,700 g to 6,300 g, and the correlation between them is r = 0.8712. In the species-by-island table, Gentoo are 36.0% of all 344 penguins, and 124 of the 168 Biscoe penguins, about 73.8%, are Gentoo. You will also use a die and the calendar: a game scores each die face by its squared distance from the die's mean of 3.5, and pairing each month's position in the year with its number of days gives a correlation of about 0.27 for all twelve months and about −0.13 with February removed.

Work these four problems, showing your arithmetic:

1. The 342 penguins' flipper lengths run from 172 mm to 231 mm. There are 10 mm in a centimeter. How wide is that range of flipper lengths in centimeters?
2. A board game scores each die face by its squared distance from the die's mean of 3.5. What score does a roll of 6 earn?
3. For the 12 months of a common year, the correlation between month position and number of days is about 0.27; with February removed, it is about negative 0.13. By how much did removing February change the correlation?
4. Gentoo are 36.0% of all 344 penguins and 73.8% of the 168 Biscoe penguins. By how many percentage points does the Biscoe share exceed the overall share?

Beside each answer, add one brief interpretation: what that value shows about the relationship and one use or limit of it. For problem 1, say what happens to the penguin correlation of 0.8712 when flipper length is measured in centimeters. For problem 2, say why the six die scores form a perfect pattern but have a correlation of 0. For problem 3, say what the change tells you about how resistant r is. For problem 4, say whether species and island are associated, and whether marginal or conditional distributions show it.

Explain it to a non-expert

A friend who runs a community wildlife-tour business has never studied statistics. They read that "longer-flippered penguins are heavier" and want to tell tour guests that growing long flippers makes a penguin heavy. Write a 3–5 sentence message that says what the data do show, explains in everyday words why they cannot show cause and effect, and names one lurking variable that could explain the pattern. Explain any technical term in everyday words. More than one good lurking variable can be defended.

For a different, ungraded example, imagine a gym owner who notices that members who bring water bottles stay longer per visit. Model answer: "The two go together, but that doesn't mean the water bottle keeps people at the gym. Members who plan a long workout are more likely to bring water in the first place, so the plan to train hard could be driving both. To know whether water itself matters, you would need to hand out bottles at random and compare. For now, it's a pattern worth noticing, not a reason to sell bottles as a stay-longer trick."

Use that pattern for the penguins, with your own explanation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the tour operator before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about how two variables relate: scatterplots, the correlation coefficient r, marginal and conditional distributions, and association versus causation. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data: the Palmer penguins field log, an observational study of 344 penguins; for the 342 with both measurements, flipper length runs from 172 mm to 231 mm, body mass from 2,700 g to 6,300 g, and the correlation between them is r = 0.8712. Gentoo are 36.0% of all 344 penguins and about 73.8% (124 of 168) of the Biscoe penguins. A game scores each die face by its squared distance from the die's mean of 3.5. Month position and days in a common year have r of about 0.27 for all 12 months and about negative 0.13 without February.
PROBLEM P1: The 342 penguins' flipper lengths run from 172 mm to 231 mm. There are 10 mm in a centimeter. How wide is that range of flipper lengths in centimeters?
PROBLEM P2: A board game scores each die face by its squared distance from the die's mean of 3.5. What score does a roll of 6 earn?
PROBLEM P3: For the 12 months of a common year, the correlation between month position and number of days is about 0.27; with February removed, it is about negative 0.13. By how much did removing February change the correlation?
PROBLEM P4: Gentoo are 36.0% of all 344 penguins and 73.8% of the 168 Biscoe penguins. By how many percentage points does the Biscoe share exceed the overall share?
After the four answers, I must briefly interpret each one: what that value shows about the relationship and one use or limit of it; for P1, what happens to the penguin correlation of 0.8712 when flipper length is in centimeters; for P2, why the six die scores form a perfect pattern but have a correlation of 0; for P3, what the change shows about how resistant r is; for P4, whether species and island are associated and whether marginal or conditional distributions show it. I must then write a 3-5 sentence message to a wildlife-tour operator who is new to statistics, saying what the penguin data show, why they cannot show cause and effect, and naming one lurking variable. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct relationship computations (40 points), relationship and causation reasoning (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct width, score, change, or difference = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate account of what that value shows about the relationship plus a use or limit tied to the penguin, die, or calendar data = 2; exactly one of the two = 1; neither = 0. For P1, a claim that r changes with the units does not count. For P2, reading r = 0 as "no relationship" does not count. For P4, BOTH an accurate comparison of the conditional and marginal shares that names the association AND a final message that keeps association apart from causation with a named lurking variable = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to statistics, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to the tour operator AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised relationship report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised relationship report with all four answers, their brief interpretations, and your message to the tour operator — written, or recorded as audio or video with a transcript, or as a labelled sketch of the scatterplots with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 4 skills — describing a relationship with a scatterplot and the correlation coefficient, knowing what r can and cannot measure, reading marginal and conditional distributions to spot an association, and keeping association apart from causation — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to the tour operator. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised relationship report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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