Two-Way Tables

Learn two-way tables, joint probability.

Lesson 1 of 32 parts Practice Flashcards

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Two-Way Tables

Objective: Explain two-way tables, apply the stated method, and check its conditions.

A two-way table records joint counts of two categorical variables. Row and column totals are marginal counts; the grand total includes every unit once. Use a cell for a joint event and a margin for a specified group total. A cell count and a marginal total describe different groups.

Formulas

Marginal count = sum over the other categorical variable

Worked examples

Try itA synthetic two-way table lists 42 bus riders in Group A and 49 bus riders in Group B. Find the bus-rider column total.Show answer

Step 1: A marginal total adds over the other grouping variable. Step 2: Add 42+49. Step 3: The total is 91 bus riders.

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Two-Way Tables

Objective: Explain two-way tables, apply the stated method, and check its conditions.

Formulas

Marginal count = sum over the other categorical variable

Worked examples

Try itA synthetic two-way table lists 42 bus riders in Group A and 49 bus riders in Group B. Find the bus-rider column total.Show answer

Step 1: A marginal total adds over the other grouping variable. Step 2: Add 42+49. Step 3: The total is 91 bus riders.

Joint Probability

Objective: Explain joint probability, apply the stated method, and check its conditions.

A joint probability measures simultaneous membership in two events. For equally weighted observations, divide the corresponding two-way-table cell count by the grand total. Do not use a row or column total unless the question is conditional instead. Joint probability uses the full reference population or sample total.

Formulas

P(A∩B)=joint count / grand total

Worked examples

Try itA synthetic table has 42 cases in the cell “A and B” out of 91 total cases. Find P(A∩B).Show answer

Step 1: A joint probability uses the full table total. Step 2: Use 42/91. Step 3: The joint probability is 6/13.

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