Statistics: Contingency Tables and Chi-Square

Objectives

• Students will be able to interpret whether values represented in a two-way table represent independent events by using conditional probabilities.
• Students will be able to derive a chi-square for two categorical variables from a single population.
• Students will be able to determine if a chi-square indicates an association between two categorical variables.

Vocabulary

• association
• chi-square
• conditional probability
• independent

About the Lesson

This lesson involves deriving and interpreting the chi-square as an indication of whether two variables in a population are independent or associated.
As a result, students will:

• Derive the chi-square based on observed values from a two-way table.
• Analyze chi-squares calculated from samples drawn from a population in which the categorical variables are independent, and observe the distribution of such chi-squares.
• Use a simulated chi-square distribution to decide whether the original chi-square indicates an association between the variables.