Statistics in Society
Warm-up
Two headlines from the same study, side by side: "Study: teens who eat breakfast score 20% higher" / "Study finds no proof breakfast improves grades." Both cite the same correlation. Discuss: how can one dataset feed opposite stories?
Grade 9 statistics is society-facing: sampling, bias, correlation-vs-causation, and misleading graphs — the defence kit for a world that argues with data.
Explore
Bias autopsy stations: (1) sampling methods ranked for "what do students at our school think of the cafeteria?" — survey the lunch line (biased toward buyers), first-period class (one grade), random 40 from the roster (defensible) — selection bias named and felt; (2) question-wording lab: "Do you agree the cafeteria needs improvement?" vs "How satisfied are you with the cafeteria?" — leading questions bend answers; (3) the graph crimes gallery: truncated axes, cherry-picked windows, area-inflated pictograms — each crime re-plotted honestly.
Then correlation-vs-causation with the classic: ice-cream sales correlate with drownings (lurking variable: summer). Pairs invent their own lurking-variable triples and trade.
Formalize
Formalize the vocabulary of statistical skepticism:
The three questions to ask ANY statistic: Who was asked (sample and how chosen)? What exactly was asked (wording, options)? Compared to what (base rates, axes, time windows)? A statistic that survives all three has earned provisional trust — the standard is survival, not perfection.
Practice
Practice: design an unbiased sampling plan for a school question; rewrite two leading questions neutrally; autopsy two graph crimes (re-plot one honestly); one correlation-causation analysis with a proposed lurking variable and — the hard part — a study design that could distinguish them.
Exit ticket: "Nine of ten dentists recommend Brand X" — write the two questions you'd ask before believing it. (Who chose the dentists? Recommend over WHAT — anything, or competitors?)
Exit ticket
Practice: design an unbiased sampling plan for a school question; rewrite two leading questions neutrally; autopsy two graph crimes (re-plot one honestly); one correlation-causation analysis with a proposed lurking variable and — the hard part — a study design that could distinguish them.
Exit ticket: "Nine of ten dentists recommend Brand X" — write the two questions you'd ask before believing it. (Who chose the dentists? Recommend over WHAT — anything, or competitors?)
The task: determine the school's music preferences for the dance (900 students).
Step 1: Draft plan A — poll the music club. Attack: self-selected enthusiasts; genre tastes skew instantly. Selection bias.
Step 2: Draft plan B — Instagram poll on the dance account. Attack: reaches followers only (those already engaged), response bias toward the outspoken.
Step 3: Draft plan C — random 60 names from the full roster, surveyed directly, anonymous. Defensible: every student equally likely; anonymity curbs social-pressure answers.
Step 4: The cost-honesty step: plan C is slower and needs chasing absentees. Real statistics trades convenience against credibility CONSCIOUSLY — and says which it chose.
Step 5: The wording pass on the instrument itself: "What music do you actually want to hear?" with genre checkboxes + write-in beats "You like pop, right?" by exactly the width of the lesson.
The exhibit: a bar chart titled "Our app CRUSHES the competition!" — Brand A bar towers at triple Brand B's height. Axis starts at 4.0 stars; A scores 4.6, B scores 4.2.
Step 1: Read the NUMBERS, not the picture: 4.6 vs 4.2 — a 0.4-star gap, about 10%.
Step 2: Name the crime: axis truncation at 4.0 makes the bars display only the slivers above 4.0 (0.6 vs 0.2) — a 3× VISUAL ratio manufactured from a 1.1× actual one.
Step 3: Re-plot honestly from zero: two nearly-equal bars. The drama evaporates.
Step 4: The nuance that keeps it fair: truncation isn't always criminal — plotting body temperatures 36–41°C from zero would hide fevers. The test: does the truncation REVEAL meaningful variation or MANUFACTURE fake ratios? Intent shows in whether the bars invite ratio-reading ("triple!").
Step 5: The defence reflex: every bar chart — find the axis floor FIRST, then look at the bars. Two seconds; permanent immunity.
The finding: students with more evening screen time report worse sleep (a solid negative correlation in the class's own anonymous survey).
Step 1: The causal candidates, all listed before judging: (a) screens harm sleep (light, stimulation); (b) poor sleepers reach for screens (reverse causation — can't sleep, so scroll); (c) a lurking variable drives both (stress: worried students both scroll more and sleep worse).
Step 2: What the correlation alone supports: NONE exclusively — it's consistent with all three. This is the honest checkpoint most headlines skip.
Step 3: Design the discriminating study: an experiment — randomly assign half of volunteers to no-screens-after-9 for two weeks, compare sleep changes between groups. Randomization breaks (b) and (c): stress and prior sleep habits land evenly in both groups.
Step 4: The realism audit: will teens comply? Self-reported sleep is noisy — measurement error discussed, not hidden.
Step 5: The takeaway hierarchy, posted: anecdote < correlation < controlled experiment — each rung earns stronger verbs. "Linked to" is rung two; "causes" must climb to rung three or stay unsaid.