Week 10 · Applied Statistics · HEG Genève

Does topping preference depend on the neighbourhood?

The last chapter of the textbook, and the first that handles categories and more than two groups: the chi-square test for independence on a contingency table, the goodness-of-fit test against a claimed distribution, the F test for two variances, and one-way ANOVA for comparing several means at once.

🏫 In class: 3 h · lesson ~1 h, then exercises ~2 h 📖 Saylor ch. 11 ▶ The Lecture button shows the slide outline

By the end of Week 10 you will be able to

Compute expected counts and the chi-square statistic for a contingency table, and test independence.
Run a goodness-of-fit test against a claimed distribution.
Compare two variances with an F test.
Run a one-way ANOVA and read its table.
Choose among the semester's tests for a given business question — the "which test?" reflex.

Resources

✓Saylor §11.1 — Chi-square tests for independence ↗

✓Saylor §11.2 — Chi-square goodness-of-fit tests ↗

✓Saylor §11.3 — F-tests for equality of two variances ↗

✓Saylor §11.4 — F-tests in one-way ANOVA ↗

Homework for this week is written with the week itself, on the Week 1–2 pattern: a fresh dataset, hints and worked solutions.

Tools for this week

Exam cards c24–c27

← Course page

Section 10.1 · The hook

Toppings by neighbourhood

Planned · Hook

Estimate whether the 3×2 table shows dependence

Slider: "how confident are you that topping choice depends on neighbourhood?" Lock it.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.2 · Independence

Observed vs expected

Planned · χ² independence

The chi-square test on a contingency table (§11.1)

Widget: a 3×2 table of orders; click any cell for its expected count (row × column ÷ total); the chi-square statistic builds cell by cell; df = (r−1)(c−1). Exam card c24.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.3 · Goodness of fit

Are orders even across the week?

Planned · χ² fit

Observed vs a claimed distribution (§11.2)

Widget: seven weekday counts against "all days equal"; then against "Friday and Saturday double". Exam card c25.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.4 · Two variances

Is Rive really riskier than Pâquis?

Planned · F

F = s₁²/s₂² (§11.3)

Widget: the two neighbourhoods from Week 2, at last tested. Exam card c26.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.5 · ANOVA

Four branches, one question

Planned · ANOVA

Between vs within variance, the F ratio, the table (§11.4)

Widget: four branches × six days; between-group and within-group sums of squares as stacked bars; F and its p-value. The case is built so F is clearly significant while a naïve pairwise look would over-claim. Exam card c27.
Classify (8 rows): which test? — every procedure of the semester on eight pizzeria questions.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.6 · Checkpoint

Prove it to yourself

Planned · Quiz

Self-check quiz & where this goes next

Ten questions: expected counts, df, a chi-square decision, goodness of fit, an F for variances, an ANOVA table reading, and three "which test?" items.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 10.7 · Workshop

The pizzeria file · instalment ten

Planned · Exercise

Workbook fields

w10_table — a contingency table your pizzeria could collect, and the hypothesis it would test.
w10_which — for three questions you actually have about your pizzeria, name the test and why.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Course page →

Part 2 · Exercises

8 exercises, worked together

Planned · ~120 min

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

Exercise 1 · Expected counts 15 min
row × column ÷ total, cell by cell
Exercise 2 · The chi-square statistic 18 min
Σ(O − E)²/E, and df = (r−1)(c−1)
Exercise 3 · Decide 10 min
against the critical value — and what it means for the menu
Exercise 4 · Goodness of fit 15 min
weekday orders against “all days equal”
Exercise 5 · A second claim 12 min
the same counts against “Friday and Saturday double”
Exercise 6 · F for two variances 15 min
Pâquis vs Rive, at last tested
Exercise 7 · One-way ANOVA 20 min
four branches: between, within, F, and the table
Exercise 8 · Which test? 15 min
twelve pizzeria questions, twelve procedures

Status → outline only. Nothing here is interactive or counted yet.

Course page →