# 11: Chi-Square and Analysis of Variance (ANOVA)


A chi-squared test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true.

• 11.0: Prelude to The Chi-Square Distribution
You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.
• 11.1: Goodness-of-Fit Test
In this type of hypothesis test, you determine whether the data "fit" a particular distribution or not. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test (meaning the distribution for the hypothesis test is chi-square) to determine if there is a fit or not. The null and the alternative hypotheses for this test may be written in sentences or may be stated as equations or inequalities.
• 11.2: Tests Using Contingency tables
• 11.3: Prelude to F Distribution and One-Way ANOVA
Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example, an environmentalist is interested in knowing if the average amount of pollution varies in several bodies of water. A sociologist is interested in knowing if the amount of income a person earns varies according to his or her upbringing. A consumer looking for a new car might compare the average gas mileage of several models.
• 11.E: F Distribution and One-Way ANOVA (Optional Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.
• 11.E: The Chi-Square Distribution (Optional Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.