Cogito
AP Statistics · Chapter 7 · Lesson 2
Chi-Square for Two-Way Tables
Independence and homogeneity.
12 problems · about 22 minutes · VAR-8.E, DAT-3.O
What this lesson teaches
The student carries out chi-square tests on two-way tables and distinguishes the two designs.
- Expected counts are row total times column total over grand total.
- Degrees of freedom are (rows − 1)(columns − 1).
- Independence uses one sample; homogeneity compares several.
Warm Up
Straightforward practice. Get the method working first.
5 problemsA 2 by 5 table. What are the degrees of freedom?
Answer 4
Why 4.
What distinguishes independence from homogeneity?
Answer How the data was collected: one sample or several.
Why The sampling design.
A 2 by 2 table. Degrees of freedom?
Answer 1
Why (2−1)(2−1).
A 4 by 5 table. Degrees of freedom?
Answer 12
Why (4−1)(5−1).
Row total 40, column total 50, grand total 200. Expected count?
Answer 10
Why 2000 ÷ 200.
Build It Up
The same ideas with more to keep track of.
3 problemsOne sample classified by two variables. Which test? 1 independence, 2 homogeneity.
Answer 1
Why One sample, two variables.
Several separate samples compared on one variable. Which test? 1 or 2?
Answer 2
Why Comparing groups.
Does the arithmetic differ between the two tests? 1 yes, 0 no.
Answer 0
Why Only the design and wording differ.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each study by which chi-square test it needs.
Answer Independence: One survey recording two characteristics per person, A single sample cross-classified · Homogeneity: Three separate schools surveyed and compared, Separate random samples from two populations
Why Count how many samples were taken.
A 3 by 3 table. Degrees of freedom?
Answer 4
Why (3−1)(3−1).
The Expected Count: Row total 50, column total 60, grand total 200. What is the expected count?
Answer 15
Why 15.
The Degrees of Freedom: A 3 by 4 table. What are the degrees of freedom?
Answer 6
Why 6.