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Statistics I · Week 4 — Association

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Statistics I · Week 4 — Association

1098 words

5 min read

2026-08-16

Reading compass

Now · Week map

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.

Part of the Quiz 2 prep system · Weeks 1–8 index · Pattern atlas · Formula chains.

Week map

Two variables → table or scatter → pattern → correlation strength

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.

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

Open interactive formula desk · Week 4 tab.

Deep study

Statistics I · Week 4 — Association and correlation

Two variables together: tables for categorical pairs, scatterplots and $r$ for numerical pairs. Association is not causation.

Week map

Two variables → contingency table → marginal totals → scatterplot features → correlation

r

→ strength vs direction → limitations of

r

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.

Mini-table (transport × gender, counts):

	Bus	Train	Total
F	30	20	50
M	25	25	50
Total	55	45	100

Cell (F, Train) = 20. Marginal female total = 50.

Scatterplot language

For numerical

x

and

y

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

Mini-description: “positive, roughly linear, moderate strength, one high outlier.”

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).

Trap:

r

is not steepness of slope — standardized measure of linear fit strength/direction.

Properties (linear world):

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

Pattern may be due to:

Direct cause
Confounding third variable
Coincidence

Ice cream sales and drowning correlate — weather confounds both.

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

Example 1 — Cell percent.

From table above: percent female bus riders = 30/100 = 30% of all, or 30/50 = 60% of females.

Example 2 — Scatter words.

Points rise left to right tightly → positive, linear, strong.

Example 3 — $r$ sign.

r = -0.82

→ strong negative linear association.

Example 4 — Nonlinear trap.

Parabolic cloud around 0 →

r

might be near 0 though

y

clearly depends on

x

Example 5 — Outlier.

Most points tight positive line; one far low point pulls

r

down.

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)

In a 2×3 contingency table, what does a single cell count represent?
Describe in words a scatterplot that is negative, linear, and weak.
If $r = 0.15$ between study hours and exam score, is linear association strong or weak? Does high score cause more hours?
Table: exercise (Low/High) × health (Poor/Good). Low-Poor cell = 40, total $n=200$ . What percent of all cases are Low and Poor?
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

Tool	Variables
contingency	both categorical
scatter	both numerical
r	linear correlation

Pattern families

Easy — Read contingency cell

Cell is joint count for row category AND column category. Margins sum rows/columns.

Medium — Describe scatter

State positive/negative/none, linear/curved, weak/strong. Correlation sign matches slope direction for linear cloud.

Hard — r interpretation

Near ±1 tight linear; near 0 weak linear (nonlinear pattern may exist). r unchanged by scaling if linear.

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

What does contingency table show?
Correlation measures what kind of association?
Why association not causation?

Practice loop

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