What does a one-way ANOVA test?

A one-way ANOVA (Analysis of Variance) is designed to compare the means of three or more independent groups to determine if there are statistically significant differences among them regarding a specific outcome. The core purpose of a one-way ANOVA is to assess whether the mean scores of a dependent variable—such as test scores, treatment outcomes, or any measured variable—differ depending on the levels of a single independent factor.

In this context, when the test assesses the means of one outcome across various groups, it is evaluating whether the differences observed in the means are greater than would be expected due to random chance. This method of analysis is particularly useful in situations where researchers want to examine the effect of one categorical independent variable (with two or more groups) on a continuous dependent variable.

Using a one-way ANOVA provides a robust statistical technique that controls for Type I error that would occur if multiple t-tests were conducted between the groups. It also offers an overall view of differences without losing the ability to identify specific group comparisons, often followed by post-hoc tests to evaluate these differences more closely.

In summary, the essence of a one-way ANOVA is centered on evaluating and comparing the means of one outcome variable across different groups, making the identification of significant