import { Search, GitBranch, AlertTriangle, Scale, Layers, BookOpen, } from "lucide-react"; import LessonShell, { ConceptCard, ExampleCard, TipCard, PracticeFromDataset, } from "../../../components/lessons/LessonShell"; import StudyDesignWidget from "../../../components/lessons/StudyDesignWidget"; import { EVAL_STATS_EASY, EVAL_STATS_MEDIUM, } from "../../../data/math/evaluating-statistical-claims"; interface LessonProps { onFinish?: () => void; } const SECTIONS = [ { title: "Observational vs Experimental", icon: Search }, { title: "Random Assignment", icon: GitBranch }, { title: "Confounding Variables", icon: AlertTriangle }, { title: "Causation vs Correlation", icon: Scale }, { title: "Identifying Bias", icon: Layers }, { title: "Practice & Quiz", icon: BookOpen }, ]; export default function EvalStatisticalClaimsLesson({ onFinish }: LessonProps) { return ( {/* Section 1 */}

Observational vs Experimental Studies

The type of study determines what conclusions you can draw.

Observational Study

Researcher observes without intervening. Can show association only.

Experiment

Researcher assigns treatments. Can show{" "} causation.

Observational: "Students who eat breakfast tend to have higher GPAs."

Experiment: "Randomly assign half the students to eat breakfast for a month, compare GPAs."

Only the experiment can claim breakfast causes higher GPAs.

{/* Section 2 */}

Random Assignment

Random sampling determines generalizability.{" "} Random assignment determines causation. These are different concepts!

Random Assignment YES Random Assignment NO
Random Sampling YES Generalize + Cause & Effect Generalize only
Random Sampling NO Cause & Effect (this group only) Neither

Random sampling → can generalize to population. Random assignment → can claim cause-and-effect. These are independent concepts.

{/* Section 3 */}

Confounding Variables

A confounding variable is related to BOTH the explanatory and response variables, making it impossible to determine the true cause of an observed relationship.

Ice cream sales and drowning rates both increase in summer.

Confounding variable:{" "} temperature / season

Hot weather causes both — ice cream doesn't cause drowning!

Study: coffee drinkers exercise more.

Confounding: Maybe more energetic people both drink coffee AND exercise.

Can't conclude coffee causes more exercise.

{/* Section 4 */}

Causation vs Correlation

Correlation means two variables move together.{" "} Causation means one actually causes the other. Correlation alone does NOT prove causation.

Three Requirements for Causation

1. Random assignment to treatment/control groups

2. Controlled experiment (same conditions except treatment)

3. Confounding variables ruled out

The SAT will try to trick you with answer choices that claim causation from observational studies. Always check: was there random assignment?

{/* Section 5 */}

Identifying Bias

Bias systematically distorts results. Know these types:

Selection Bias

Non-random sample excludes or over-represents groups

Response Bias

Leading questions or social desirability affects answers

Nonresponse Bias

People who don't respond differ from those who do

Voluntary Response

Only people with strong opinions participate

"Do you agree that the new park is a waste of money?"

Response bias — the question pushes toward "agree"

{/* Section 6 */}

Practice & Quiz

{EVAL_STATS_EASY.slice(0, 2).map((q) => ( ))} {EVAL_STATS_MEDIUM.slice(0, 1).map((q) => ( ))}
); }