http://www.ck12.org Chapter 10. Chi-Square
10.1 The Goodness-of-Fit Test
Learning Objectives
- Understand the difference between the Chi-Square distribution and the Student’s t-distribution.
- Identify the conditions which must be satisfied when using the Chi-Square test.
- Understand the features of experiments that allow Goodness-of-Fit tests to be used.
- Evaluate an hypothesis using the Goodness-of-Fit test.
Introduction
In previous lessons, we learned that there are several different tests that we can use to analyze data and test
hypotheses. The type of test that we choose depends on the data available and what question we are trying to
answer. For example:
- We analyze simple descriptive statistics such as themean, median, modeandstandard deviationto give us
an idea of the distribution and to remove outliers, if necessary; - We calculateprobabilitiesto determine the likelihood of something happening; and
- We useregression analysisto examine the relationship between two or more continuous variables.
But what test do we run if we are trying to examine patterns between distinct categories such as gender, political
candidates, locations or preferences? To analyze patterns like these we use theChi-Square test.
The Chi-Square test is a statistical test used to examine patterns in distinct or categorical variables, which we learned
about in the earlier chapter entitledPlanning and Conducting an Experiment or Study. This test is used in:
- Estimating how closely a sample matches the expected distribution (also known as theGoodness-of-Fit test)
and - Estimating if two random variables are independent of one another (also known as theTest of Independence-
see Chapter 9).
In this lesson we will learn more about theGoodness-of-Fit testand how to create and evaluate hypotheses using
this test.
The Chi-Square Distribution
The Chi-Square Goodness-of-Fit test is used to compare theobserved valuesof a categorical variable with the
expected valuesof that same variable. For example, we would use this test to analyze surveys that contained
categorical variables (for example, gender, city of origin, or locations that people preferred to visit on vacation) to
determine if there are in fact relationships between certain items.