Title: Week 4 Data Lab — Relationships Between Two Variables
Course: Introduction to Statistics (18-Week Generic Edition)

Course: Introduction to Statistics (18-week generic edition) Objective: Objective 3 — scatterplots; correlation r; two-way tables & conditional distributions · SLO A (reason quantitatively from data) Worth 50 points · Data labs group = 15% of the grade · Data Lab 4 · Due: end of Week 4 Format: a hands-on data lab — real research data, a spreadsheet scatterplot, your own =CORREL(), a species-by-island two-way table; then you catch the AI's mistakes when it interprets your work.

This is the course's signature weekly component. Every instructional week has a Data Lab: real, free, linked public data — nothing to buy, download from a store, or sign up for — worked in your spreadsheet, finished with an AI-critique step. Plan on 60–90 minutes.

Part 1 — The Big Picture

For three weeks the penguins have been a pile of single columns — you counted them, graphed one variable, summarized one variable. This week the dataset becomes what it really is: 344 individuals, each carrying several measurements at once. Do penguins with longer flippers weigh more? Is a penguin's species tied to which island it lives on? Those are two-variable questions — one for a scatterplot and r, one for a two-way table and conditional distributions — and they're exactly this week's two toolkits, pointed at real Antarctic field data.

And a deeper lesson is hiding in the cloud: the overall flipper–mass relationship mixes three different species. Part of what looks like "flippers go with mass" is really "Gentoos are big." That's this week's lurking variable idea, live in your own spreadsheet.

The data (same dataset as Weeks 1–3): between 2007 and 2009, researchers at Palmer Station, Antarctica measured 344 penguins from three species (Adélie, Chinstrap, Gentoo) across three islands — bill and flipper dimensions, body mass, and sex — released as the freely available palmerpenguins teaching dataset.

Part 2 — The Task

The guiding question: How strongly does flipper length travel with body mass — and is species associated with island — in the full 344-penguin dataset?

The dataset (both links are free, no login): - About the data — palmerpenguins documentation 🔗 https://allisonhorst.github.io/palmerpenguins/ - The data itself (CSV file, opens as plain text) 🔗 https://raw.githubusercontent.com/allisonhorst/palmerpenguins/main/inst/extdata/penguins.csv

Part 3 — Materials & Procedure

You need: a web browser and a spreadsheet — Google Sheets (free) or Excel. Nothing else.

Warm-up (5 min, no dataset needed). Below are 10 penguins from the dataset's three species. Before computing anything, look at the flipper and mass columns together and write down: (a) the direction you expect for flipper length vs. body mass, and (b) which species you'd guess sits at the top-right of that scatterplot.

The table below lists species, island, flipper length, and body mass for 10 penguins (this is also your fallback dataset for Step 9).

Penguin | Species | Island | Flipper (mm) | Body mass (g)
1 | Adelie | Torgersen | 181 | 3750
2 | Adelie | Biscoe | 187 | 3550
3 | Adelie | Dream | 190 | 3900
4 | Chinstrap | Dream | 195 | 3650
5 | Chinstrap | Dream | 198 | 3775
6 | Gentoo | Biscoe | 216 | 4900
7 | Gentoo | Biscoe | 219 | 5100
8 | Gentoo | Biscoe | 222 | 5350
9 | Adelie | Torgersen | 185 | 3600
10 | Gentoo | Biscoe | 230 | 5700

Now the real data:

1. Import the dataset (same routine as the earlier labs). Simplest route that works everywhere: open the CSV link above in your browser, select all (Ctrl/Cmd-A), copy, paste into cell A1 of a blank sheet, then Data ▸ Split text to columns if needed. (Excel: Data ▸ From Web with the CSV URL.) You should end with 8 columns — species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year — plus a header row.
2. Count your rows. In an empty cell, =COUNTA(A2:A400) — it should say 344. If not, re-import before continuing.
3. Build the scatterplot. Copy the flipper_length_mm column (E) into empty column J and body_mass_g (F) into column K — putting the pair side by side keeps the chart tool happy. Select J and K (with their headers) → Insert ▸ Chart → set the chart type to Scatter chart if it guessed something else. Flipper length is the explanatory variable (x); body mass is the response (y).
4. Read your cloud. Fill in Scaffold Table 1: direction, form, strength, outliers — then the one-sentence description, in context.
5. Compute r. In an empty cell: =CORREL(E2:E345, F2:F345). Record it to two decimals in Table 1. (Two penguins have NA for these measurements — spreadsheets skip non-numeric pairs automatically, so your r uses the 342 complete pairs. Note the swap test: =CORREL(F2:F345, E2:E345) returns the identical value.)
6. Build the two-way table. Select columns A and B (species and island) → Insert ▸ Pivot table (new sheet) → Rows: species · Columns: island · Values: COUNTA of species. Copy the counts (with the row/column totals) into Scaffold Table 2. Fallback that always works: =COUNTIFS(A2:A345,"Adelie",B2:B345,"Biscoe") and so on, one cell per combination.
7. Check the margins. Your row totals must add to 344, and so must your column totals. If they don't, hunt the typo now.
8. Compute the conditionals. Fill Scaffold Table 3: among Dream-island penguins, what percent are Chinstrap? Among Biscoe penguins, what percent are Gentoo? And the marginal: what percent of all 344 penguins live on Dream? (Divide, then say each denominator's group out loud — that's the week's discipline.)
9. See the lurking variable. Add a filter (Data ▸ Create a filter) and view the scatterplot columns for one species at a time (easiest: filter, then copy that species' J–K rows to a fresh area and chart them, or just eyeball the filtered values). Notice: within a single species, the flipper–mass cloud is looser than the overall cloud. Record the one species you inspected in Table 1's last row.

Fallback (no import available): do everything with the 10-penguin warm-up table instead — chart its flipper/mass pairs, compute =CORREL() on the 10 pairs, and build the species × island counts by hand (a 3 × 3 table). State in your submission that you used the fallback.

Part 4 — The Scaffold (complete all three tables)

Table 1 captures your scatterplot reading and r.

Item | Your answer
Direction (positive / negative) | ______
Form (linear / curved / clusters) | ______
Strength (strong / moderate / weak) | ______
Outliers (yes/no — where?) | ______
r from =CORREL() (2 decimals) | ______
One-sentence description, in context | ______
Species you filtered in Step 9 + what changed | ______

Table 2 is your species × island two-way table (counts, with margins).

 | Biscoe | Dream | Torgersen | Row total
Adelie | ______ | ______ | ______ | ______
Chinstrap | ______ | ______ | ______ | ______
Gentoo | ______ | ______ | ______ | ______
Column total | ______ | ______ | ______ | 344

Table 3 holds your marginal and conditional percentages (name each denominator).

Question | Fraction | Percent
Among Dream penguins, % Chinstrap | __ / ____ | ______
Among Biscoe penguins, % Gentoo | __ / ____ | ______
Marginal: % of ALL penguins on Dream | ______ / 344 | ______

Part 5 — Analysis Questions

Answer in 1–3 sentences each:

1. Give your one-sentence description of the flipper–mass relationship (direction, form, strength, in context) and say what r adds that the sentence alone doesn't. Does your r agree with your eyes?
2. Using Table 3: are species and island associated? Point to two conditional percentages that differ (for instance, the Gentoo share of Biscoe vs. the Gentoo share of Dream) and say what no association would have looked like instead.
3. The overall cloud mixes three species, and one species is both the heaviest and the longest-flippered. Explain how species acts like a lurking variable behind the strong overall r — and what your Step 9 single-species view showed about the within-species relationship.
4. Error sources: two penguins have NA for flipper and mass, and your import could silently store numbers as text or grab the wrong ranges. How did your spreadsheet handle the NAs in =CORREL(), and name one import error that would distort r without any warning.
5. (Preview.) If you drew one penguin at random from all 344, what fraction of the time would it come from Dream (use Table 3's marginal)? Keep that number — next week we start calling it a probability.

Part 6 — AI-Critique Moment (required — the BYOAI step)

Now bring in your chatbot and be the analyst who checks its work.

1. Paste your completed Table 2 (the counts) and your r value into your chatbot and ask: "Using this table: what percent of Dream-island penguins are Chinstrap? And explain what my r value means about flippers and body mass."
2. Check everything it says against your own work: - Denominator check: did it divide by the Dream total, or wrongly by 344 (marginal) or by the Chinstrap total (wrong variable)? Redo the division yourself. - r-language check: did it call r "87% of penguins" or "mass rises 87%"? (r is not a percent of anything.) Did it claim longer flippers cause higher mass? (Observational data — no arrow earned.) - Table integrity: did it invent a nonzero count for a cell your table shows as 0 (there are no Gentoos on Dream), or mis-add a margin? Re-add one margin yourself.
3. Write 2–3 sentences reporting what the AI got right and at least one thing you had to correct, question, or verify. If it happened to get everything right, say how you verified each claim — that's the skill.

The habit all term: the tool drafts, you judge. Wrong denominators and "r as a percent" are this week's signature machine mistakes — catching them is the point.

Part 7 — What to Submit

One document or text entry containing: your warm-up predictions (a) and (b), your completed Tables 1–3, your Part 5 answers (1–5), and your Part 6 AI-critique paragraph. Due at the end of Week 4 · 50 points (rubric below the key).

Grading rubric — 50 points

The rubric below maps each part to its points; bands are full / partial / none.

Criterion | Full | Partial | None
Import + scatterplot — 344 rows confirmed; scatter chart built with flipper on x, mass on y (8) | 8 | 4–6 | 0–3
r + reading — Table 1 complete; r = 0.87 (2 dp) from a correct range; sentence has direction, form, strength in context (12) | 12 | 6–10 | 0–5
Two-way table — Table 2 counts correct with margins adding to 344; Table 3 conditionals/marginal computed with the right denominators (12) | 12 | 6–10 | 0–5
Analysis questions — Q1–Q5 hit the expected ideas, especially association-by-conditionals in Q2 and the lurking-variable logic in Q3 (12) | 12 | 6–10 | 0–5
AI-critique — specific catch or verification reported in 2–3 sentences (6) | 6 | 3–4 | 0–2