Week 4 — Moving Together Is Not Causing: A Short Relationship Report — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned to describe a scatterplot, to read the correlation coefficient r and its limits, to read a two-way table as marginal and conditional distributions, and to keep association apart from causation. In Week 2 you read the species-by-island table cell by cell; this week you read it two ways. In this assignment you work four short problems on real data, interpret each one, and explain to someone who has never studied statistics why a strong link is not proof of cause. This week's lecture tutorial, quiz, discussion, and Data Lab practise the same ideas from other angles.

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.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

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.

Deliverables

Submit a single relationship report containing:

• the four answers, each with the arithmetic shown and a brief interpretation of what that value shows about the relationship and one use or limit of it;
• your message to the tour operator, saying what the penguin data show, why they cannot show cause and effect, and naming one lurking variable; and
• a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of the scatterplots with a short note. Every form is graded by the same scoring criteria. 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.

How you'll be graded

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

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's numbers, is an integrity violation under the course policy.

Built with The Course Maker · samples.thecoursemaker.com