What’s the Difference Between Chi-Square Test and ANOVA?

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Chi-Square tests and ANOVA (“Analysis of Variance”) are two commonly used statistical tests.

Thus, it’s important to understand the difference between these two tests and how to know when you should use each.

This tutorial provides a simple explanation of the difference between the two tests, along with when to use each one.

Explanation of Chi-Square Tests

In statistics, there are two different types of Chi-Square tests:

1. – Used to determine whether or not a categorical variable follows a hypothesized distribution.

For example:

• We want to know if a die is fair, so we roll it 50 times and record the number of times it lands on each number.
• We want to know if an equal number of people come into a shop each day of the week, so we count the number of people who come in each day during a random week.

2. – Used to determine whether or not there is a significant association between two categorical variables.

For example:

• We want to know if gender is associated with political party preference so we survey 500 voters and record their gender and political party preference.
• We want to know if a person’s favorite color is associated with their favorite sport so we survey 100 people and ask them about their preferences for both.

Note that both of these tests are only appropriate to use when you’re working with categorical variables. These are variables that take on names or labels and can fit into categories.

Explanation of ANOVA

In statistics, an ANOVA is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups.

For example:

• We want to know if three different studying techniques lead to different mean exam scores.
• We want to know if four different types of fertilizer lead to different mean crop yields.

Note that it’s appropriate to use an ANOVA when there is at least one categorical variable and one continuous dependent variable.

When to Use Chi-Square Tests vs. ANOVA

As a basic rule of thumb:

• Use Chi-Square Tests when every variable you’re working with is categorical.
• Use ANOVA when you have at least one categorical variable and one continuous dependent variable.

Use the following practice problems to improve your understanding of when to use Chi-Square Tests vs. ANOVA:

Practice Problem 1

Suppose a researcher want to know if education level and marital status are associated so she collects data about these two variables on a simple random sample of 50 people.

To test this, she should use a Chi-Square Test of Independence because she is working with two categorical variables – “education level” and “marital status.”

Practice Problem 2

Suppose an economist wants to determine if the proportion of residents who support a certain law differ between the three cities.

To test this, he should use a Chi-Square Goodness of Fit Test because he is only analyzing the distribution of one categorical variable.

Practice Problem 3

Suppose a basketball trainer wants to know if three different training techniques lead to different mean jump height among his players.

To test this, he should use a one-way ANOVA because he is analyzing one categorical variable (training technique) and one continuous dependent variable (jump height).

Practice Problem 4: 

Suppose a botanist wants to know if two different amounts of sunlight exposure and three different watering frequencies lead to different mean plant growth.

To test this, she should use a two-way ANOVA because she is analyzing two categorical variables (sunlight exposure and watering frequency) and one continuous dependent variable (plant growth).

The following tutorials provide an introduction to the different types of Chi-Square Tests:

The following tutorials provide an introduction to the different types of ANOVA tests:

The following tutorials explain the difference between other statistical tests: