ANOVA (Analysis of Variance) is a statistical method used to compare the means of three or more groups to determine if there are significant differences among them. It examines the variability within each group and across groups to assess statistical significance. ANOVA is a statistical test used to examine differences among the means of three or more groups. Unlike a t-test, which only compares two groups, ANOVA can handle multiple groups in a single analysis, making it an essential tool for experiments with more than two categories. For example, if a researcher wants to test the effects of three different study methods on student performance, ANOVA can help determine if there are significant performance differences among the groups.
We use an ANOVA Test because we might have one or more independent variables with three or more levels. If you only have two comparison levels total, a t-test would be used instead. Your dependent variable is continuous, allowing for means to be calculated within each group. The groups have equal variances, which can be tested as part of implementing an ANOVA. Each observation in your dataset is independent of the others.
There are two types of ANOVA Tests:
One-way ANOVA is used to compare the means of three or more groups based on a single independent variable. It shows if there is a significant difference among the group means. This method is used when there is only one independent variable (factor) with multiple levels or groups. It tests if there is a significant difference in the means of the dependent variable across the different levels of the independent variable. One-way or two-way refers to the number of independent variables in your Analysis of Variance test. One-way has one independent variable with two levels. For example, soda brands.
Two-way ANOVA is used when there are two independent variables, allowing researchers to explore individual and interactive effects. This method is used when there are two independent variables (factors), each with multiple levels or groups. It tests for main effects of each factor and possible interaction effects between the factors on the dependent variable. Two-way has two independent variables (it can have multiple levels). For example: soda brands and calories. Two-way tests can be with or without replication.
In this page, we will focus on One-Way ANOVA Test.
To put it simply, to preform an ANOVA Test, you calculate the variance between the groups/the variance within the groups. A more in depth explanation would be: