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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

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درس 11 از 16

Evaluating Independence with Contingency Tables

خانه/ماژول‌ها/ماژول 5/Evaluating Independence with Contingency Tables

Compare conditional and marginal probabilities descriptively without introducing formal inference.

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40 دقیقه69% مسیر

هدف‌های یادگیریتا پایان این درس، دانشجویان می‌توانند:

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.

توضیح 1

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

توضیح 2

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

توضیح 3

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

اصطلاحات

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.

نمادگذاری و فرمول‌ها

Descriptive independence

رابطه اصلی

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

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

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

فعالیت تعاملی

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.

مثال حل‌شده

Program engagement

سناریو

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

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

ارتباط با R

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.

بازاندیشی

مکث و یادداشت

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.

دستیار

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.

ارزیابی پایانی

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%.

برای دریافت بازخورد امتیازدهی‌شده و ذخیره پیشرفت، وارد شوید.ورود ساخت حساب

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

منبع

Recommended reading

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

منبع

Module 5 learning material

Download an original worksheet or guide for this lesson.

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