What is the Difference Between One Way Anova and Two Way Anova?

The main difference between one-way and two-way ANOVA lies in the number of independent variables being tested. Here are the key differences between the two:

• One-way ANOVA: This test involves comparing the means of three or more groups of an independent variable on a dependent variable. It is used to test the equality of three or more population means simultaneously using variance. For example, testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka) and race finish times in a marathon.
• Two-way ANOVA: This test involves comparing the means of three or more groups of two independent variables on a dependent variable. It is used to study the interrelationship between factors influencing a variable for effective decision-making. For example, testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka), runner age group (junior, senior, master's), and race finishing times in a marathon.

In summary, one-way ANOVA compares the effect of multiple levels of one factor, while two-way ANOVA compares the effect of multiple levels of two factors.

Comparative Table: One Way Anova vs Two Way Anova

The main difference between one-way ANOVA and two-way ANOVA lies in the number of independent variables being analyzed. Here is a summary of the differences:

For example:

• One-way ANOVA: Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka) and race finish times in a marathon.
• Two-way ANOVA: Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka), runner age group (junior, senior, master’s), and race finishing times in a marathon.

Both one-way and two-way ANOVA are designed to test for differences among three or more groups. If you are only testing for a difference between two groups, use a t-test instead.