Education Technology

Statistics: Contingency Tables and Chi-Square

by Texas Instruments


  • 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.


  • 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.