Skip to content

Courses Modules Datasets Resources Educator

Sign in Create account

Courses Modules Datasets Resources Educator

Sign in Sign up

Courses Modules Datasets Resources Educator

Official Data Lab

Public data sources for examples, charts, and R practice.

Last updated: Checking...

Module progress

25%

Path

R lab readyLive

Loading

Preparing your learning workspace

STATLABAcademyStatistics through data and R practice

All STATLAB Academy lessons, quizzes, datasets, and notes are original or properly licensed. Textbooks may be used only as curriculum references.

Courses Modules Datasets Resources Educator Dashboard Log in Sign up

STATLAB Academy | Learn Statistics with R and Real-World Data

Lesson 11 of 16

Evaluating Independence with Contingency Tables

Home/Modules/Module 5/Evaluating Independence with Contingency Tables

Compare conditional and marginal probabilities descriptively without introducing formal inference.

Download lesson PDF

40 minutes69% path

Learning objectivesBy the end of this lesson, students will be able to:

1Define the events and probability quantities used in evaluating independence with contingency tables.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Compare conditional and marginal probabilities descriptively without introducing formal inference.

Explanation 1

Conditional comparison: Compare P(A given B) with P(A).

Explanation 2

Product comparison: Compare P(A and B) with P(A)P(B).

Explanation 3

Practical difference: A difference that may matter operationally even without exact equality.

Terminology

Concept map

Conditional comparison

Compare P(A given B) with P(A).

Volunteer rate among one program versus overall.

Product comparison

Compare P(A and B) with P(A)P(B).

Joint share versus product of margins.

Practical difference

A difference that may matter operationally even without exact equality.

A six-point engagement gap.

Notation and formulas

Descriptive independence

Key relationship

P(A and B) = P(A)P(B)

Define every event before substituting values, then validate the result and denominator.

Step 1Calculate marginals and joint probability.
Step 2Compare the values.
Step 3Describe association without a p-value or causal claim.

Interactive Mission

contingency independence checker

Row 1, column 1Row 1, column 2Row 2, column 1Row 2, column 2

Conditional minus marginal

0.08

0.64 - 0.56

A nonzero difference describes association in this table. This is not a formal hypothesis test and does not establish causation.

Worked example

Program engagement

Scenario

Volunteer rates vary across program types in a synthetic alumni file.

Exact equality is uncommon in finite data; describe scale and context.

R connection

R note: Contingency-Table Probabilities

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

Contingency-Table Probabilities

Calculate marginal, joint, row-conditional, and column-conditional probabilities from counts.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Create counts and totals.

Calculate joint probability.

Label the conditional denominator.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Do not introduce formal hypothesis testing or p-values in this lesson.

Reflection

Pause and write

Where could an unclear event definition or assumption change the conclusion in evaluating independence with contingency tables?

Name the event, denominator, probability interpretation, and one operational limitation.

Assistant

Ask your probability coach

Help me reason through Evaluating Independence with Contingency Tables by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

Exit check

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 11 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

Sign in before submitting to receive scored feedback and save progress.Sign in Create account

Question 1: Choose one

easyCalculate and responsibly interpret probability for a defined event.

A conditional probability differs from its marginal probability. What is the safest conclusion?

The events appear associatedThe table is invalidA p-value is required immediatelyOne event causes the other

Resource

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

Resource

Module 5 learning material

Download an original worksheet or guide for this lesson.

Previous Next lesson