Education Technology

Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Probability and Statistics


Chi-Squared Tests

Activity Overview

In this activity, students will look at a problem situation that involves categorical data and will determine which is the appropriate chi-square test to use: the chi-squared goodness of fit or the chi-squared two-way test.


  • Students will recognize that chi-squared tests are for counts of categorical data.
  • Students will identify the appropriate chi-squared test to use for a given situation: Goodness of Fit Test, Test of Independence, or Test of Homogeneity.
  • Students will learn how to calculate the degrees of freedom for each type of chi-squared test.
  • Students will interpret the results of a chi-square test.
  • Students will reason abstractly and quantitatively.


  • alpha
  • categorical data
  • chi-squared (X2 distribution)
  • degrees of freedom
  • expected counts
  • goodness-of-fit test
  • observed counts
  • p-value
  • test of homogeneity
  • test of independence

About the Lesson

This lesson involves investigating chi-squared tests and distributions. Students will compare different scenarios and determine which chi-square test is appropriate. They will look at chi-square test results and make the correct decision to reject or fail to reject the null hypothesis and write their conclusions in context.