Title: Week 16 — Readings & Resources · Chi-Square Tests for Categorical Data
Course: Introduction to Statistics (18-Week Generic Edition)

Course: Introduction to Statistics (18-week generic edition) Objective covered: Objective 9 — use chi-square procedures to test claims about categorical data: goodness-of-fit and independence. Your primary reading is Chapter 16 (in this module — it carries the critical-value mini table). Everything below is the optional, go-deeper layer.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded, and nothing costs money.

The load is deliberately light: 4 short readings + 4 short videos, grouped by the four big ideas of the week. Read or watch one item per group and you're well prepared; do all of them and you'll be very comfortable. Total time is roughly 75–85 minutes if you do everything, far less if you pick one per group.

Order that matches the chapter and lecture: ① observed vs. expected & the goodness-of-fit test → ② the chi-square distribution, df & critical values → ③ the test of independence → ④ choosing the right chi-square (and saying the conclusion carefully).

A habit for this week: whenever a resource states a critical value or a df, spot-check it against the mini table in Chapter 16 (df = k − 1 for goodness-of-fit; (r − 1)(c − 1) for independence). If a claimed value and the table disagree, trust the table.

① Observed vs. Expected & the Goodness-of-Fit Test

Maps to Chapter 16, Sections 1–3 and Lecture Segments 2–3. The whole move: what the claim predicts, what you counted, and one number — χ² = Σ (O − E)² ⁄ E — for the drift between them.

Reading — Chi-Square Goodness of Fit Test: Formula, Guide & Examples (Scribbr) 🔗 https://www.scribbr.com/statistics/chi-square-goodness-of-fit/ Why it's assigned: the cleanest step-by-step of the whole test — hypotheses, expected counts, the formula, and a worked example laid out exactly in our seven-step order. ⏱ ~10 min

Video — Pearson's chi square test (goodness of fit) (Khan Academy) (video, ~12 min, captioned) 🔗 https://www.youtube.com/watch?v=2QeDRsxSF9M Why it earns the click: a full goodness-of-fit test computed on screen, cell by cell — watch the contributions pile into the statistic and the critical-value comparison settle the verdict.

② The Chi-Square Distribution, df & Critical Values

Maps to Chapter 16, Sections 3–4 and Lecture Segment 3. χ² has no universal scale — "big" is defined only by the df-matched critical value (or a p-value).

Video — An Introduction to the Chi-Square Distribution (jbstatistics) (video, ~6 min, captioned) 🔗 https://www.youtube.com/watch?v=hcDb12fsbBU Why it earns the click: a calm, precise look at the distribution itself — why it's right-skewed, why it can't go negative, and what changing the degrees of freedom does to the curve our critical values come from.

③ The Test of Independence

Maps to Chapter 16, Section 6 and Lecture Segment 6. Week 4's two-way table, on trial: expected = row × column ⁄ total, df = (r − 1)(c − 1) — and associated never means caused.

Reading — Chi-Square Test of Independence: Formula, Guide & Examples (Scribbr) 🔗 https://www.scribbr.com/statistics/chi-square-test-of-independence/ Why it's assigned: mirrors our pet-and-housing machinery on a fresh study (a city recycling program), with the expected-count table built in the open and the hypotheses worded the careful way. ⏱ ~10 min

Reading — Chi-Square Test of Independence: Definition, Formula, and Example (Statistics By Jim) 🔗 https://statisticsbyjim.com/hypothesis-testing/chi-square-test-independence-example/ Why it's assigned: a genuinely fun worked example (which TV-uniform color is dangerous?) that lands this week's guardrail — a significant association can have a lurking third variable behind it. ⏱ ~8 min

Video — Contingency table chi-square test (Khan Academy) (video, ~18 min, captioned) 🔗 https://www.youtube.com/watch?v=hpWdDmgsIRE Why it earns the click: builds a full expected-count table from row and column totals and runs the independence test end to end — the exact technology-assist workflow of our data lab, shown slowly.

④ Choosing the Right Chi-Square (and Saying It Carefully)

Maps to Chapter 16, Section 7 and Lecture Segments 4 & 7. One variable vs. a claim → goodness-of-fit; two variables, linked? → independence — and "fail to reject" is never "proven."

Reading — Chi-Square (Χ²) Tests: Types, Formula & Examples (Scribbr) 🔗 https://www.scribbr.com/statistics/chi-square-tests/ Why it's assigned: a compact map of the chi-square family — when each test applies, what its hypotheses say, and how to report the result — ideal for the "which test?" items on the quiz and final. ⏱ ~7 min

Video — Chi-Square Tests: Crash Course Statistics #29 (CrashCourse) (video, ~12 min, captioned) 🔗 https://www.youtube.com/watch?v=7_cs1YlZoug Why it earns the click: the liveliest tour of goodness-of-fit and independence side by side, with real examples and the careful-conclusion language this course grades.

Optional one-stop reference (free online text)

If you'd like one optional reference to skim, OpenStax Introductory Statistics 2e keeps its full text free to read online. Chapter 11 (The Chi-Square Distribution) covers this week end to end — the distribution, goodness-of-fit, and the test of independence. 🔗 https://openstax.org/books/introductory-statistics-2e/pages/11-introduction Why it's here: a reputable, currently-available reference you can return to during final-exam review — entirely optional this week.

Pick-one quick path (≈30 min total)

In a hurry? You've read Chapter 16 — then do exactly these three and you'll be ready for the quiz: 1. Read Chi-Square Goodness of Fit Test (group ①). 2. Watch Crash Course #29 — Chi-Square Tests (group ④). 3. Read Chi-Square (Χ²) Tests: Types, Formula & Examples (group ④).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the OpenStax reference above in the meantime.