Expected Counts in Two Way Tables
Isabella Lopez
7 min read
Study Guide Overview
This study guide covers chi-squared (χ²) tests for two-way tables, focusing on the test for homogeneity and the test for independence. It explains how to calculate expected counts using the formula (Row Total * Column Total) / Table Total. The guide also differentiates between analyzing across populations (homogeneity) and within a single population (independence).
#Chi-Squared Tests for Two-Way Tables
Hey there, future AP Stats superstar! 👋 Let's break down chi-squared (χ²) tests for two-way tables. These tests are super common, so nailing them is key. Remember, we're using these to see if there's a relationship between categorical variables. Let's dive in!
#What's a Two-Way Table?
Think of a two-way table as a grid that shows how two categorical variables are related. For example, car type (SUV vs. sports car) and gender (male vs. female). Here's a visual:
Two-way tables help us organize and analyze categorical data to see if there's a relationship between the variables.
#Types of Chi-Squared Tests for Two-Way Tables
Okay, here's where it gets a bit tricky. We have two main types of χ² tests for two-way tables, and it's crucial to know which one to use. Don't worry, I've got your back!
#Chi-Squared Test for Homogeneity
- What it does: Compares the distribution of a categorical variable across two or more independent groups or populations. 🍞
- Goal: To see if the proportions of categories are the same in all groups.
- When to use it: When you're comparing different populations to see if they have different distributions for a categorical variable.
- Example: Comparing the proportion of people who prefer coffee vs. tea in different age groups.
Homogeneity = Same-ness. Think of it as testing if different populations are homogeneous (similar) in their distribution of a categorical variable.
#Chi-Squared Test for Independence
- **What...
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