Week 4 — association

Quiz 2 scope: Weeks 1–8 per IITM May 2026 foundation courses. Source baseline: IITM BS admissions important-dates calendar · May 2026 cycle. Times on assessments are operational conventions — verify hall ticket.

Week map

Classify → Represent → Execute → Trap-check

• Recognize: Ask: What does contingency table show?
• Procedure: Cell is joint count for row category AND column category. Margins sum rows/columns.
• Variations / traps: Watch for: Causation from correlation.

Formula chain (compressed)

contingency table → marginal totals → association vs causation → correlation r.

1. Contingency — rows × cols counts — two categorical vars
2. Marginal — row/col sums — univariate distributions
3. Scatterplot — (x,y) points — two numerical vars
4. Correlation — r ∈ [−1,1] — linear association strength
5. Causation trap — assoc ≠ cause — confounders / direction

Deep study

Statistics I · Week 4 — Association and correlation

Week map

Contingency table notation

• Contingency table → cross-classified counts → rows = one variable, columns = another.
• Cell → count in one row category AND one column category.
• Marginal total → row or column sum → not joint.
• Joint → specific pair; marginal → one variable alone.

Scatterplot language

• Direction → positive (upward), negative (downward), none.
• Form → linear, curved, clusters.
• Strength → tight cloud vs scattered.
• Outliers → points off main pattern.

Correlation $r$

• $r$ → Pearson correlation coefficient → measures linear association.
• Range $-1 \le r \le 1$.
• $r \approx 1$ → tight increasing line.
• $r \approx -1$ → tight decreasing line.
• $r \approx 0$ → weak linear pattern (curved pattern may still exist).

• Sign of $r$ matches slope of best-fit line.
• $r$ unchanged if you add constant to all $x$ or scale $x$ by positive constant (linear transform).

Association vs causation

• Direct cause
• Confounding third variable
• Coincidence

Pattern families

Easy — Read contingency cell

• Identify joint count.
• Compute marginal from table.
• Percent of total in one cell: cell/n.

Medium — Describe scatter

• State direction, form, strength in words.
• Match sign of $r$ to scatter direction.
• Spot outlier effect on $r$.

Hard — Interpret $r$ and limits

• Near ±1 vs near 0 interpretation.
• Strong nonlinear pattern with $r$ near 0.
• Do not infer causation from $r$.
• Categorical coded as numbers — $r$ may mislead.

Worked mini-examples

Traps

• Causation from correlation.
• $r$ for categorical disguised as numbers (zip codes).
• Confusing strength with steep slope.
• Ignoring outliers dominating $r$.
• Contingency cell vs marginal confusion.

Diagnostic (try yourself)

1. In a 2×3 contingency table, what does a single cell count represent?
2. Describe in words a scatterplot that is negative, linear, and weak.
3. If $r = 0.15$ between study hours and exam score, is linear association strong or weak? Does high score cause more hours?
4. Table: exercise (Low/High) × health (Poor/Good). Low-Poor cell = 40, total $n=200$. What percent of all cases are Low and Poor?
5. A U-shaped scatter has $r \approx 0$. Can $y$ still depend on $x$? Explain briefly.

ChatGPT prep archive

• Chatty reference archive

Archived import for extra depth — complements the notes above, not official IITM material.

Core concepts

• Contingency table: counts for two categorical variables cross-classified.
• Scatterplot: numerical vs numerical; direction, form, strength.
• Correlation r: linear association −1 to 1; not for nonlinear or categorical.
• Association ≠ causation: confounders may explain pattern.

Notation & vocabulary

Pattern families

Easy — Read contingency cell

Medium — Describe scatter

Hard — r interpretation

Drill these on the pattern atlas — filter to week 4.

Traps

• Causation from correlation.
• r for categorical coded numbers.
• Outlier dominating r.
• Confusing strength with slope steepness.

Retrieval prompts

1. What does contingency table show?
2. Correlation measures what kind of association?
3. Why association not causation?

Practice loop

1. Read Deep study (if present) or core concepts once.
2. Recite the formula chain without looking.
3. Open one easy pattern on the interactive atlas for week 4.
4. Attempt without solutions; mark studied after an honest try.
5. Say one trap aloud before closing the tab.

Related

• Full weeks 1–8 prep guide
• Pattern atlas note
• Formula chain desk