Analysis of Variance (ANOVA) is used to analyze the differences between two or more groups in a dataset. It allows us to determine if there are significant variations among the means of different groups, beyond what can be attributed to random chance.

ANOVA helps researchers understand the effect of categorical independent variables on a continuous dependent variable.

## INTUITION

In ANOVA, we compare the variation between groups (often referred to as “group variance” or “treatment variance”) with the variation within groups (referred to as “error variance” or “residual variance”).

If the variation between groups is significantly larger than the variation within groups, it suggests that the means of the groups are different.

To illustrate this principle, let’s consider an analogy using a classroom scenario. Imagine you are a teacher evaluating the performance of three different study groups (Group A, Group B, and Group C) in a math test. You want to determine if there are significant differences in the mean scores of the groups.

In this analogy:

- The variation between groups represents the differences in average performance across the study groups.

- The variation within groups represents the differences in individual scores within each study group.

If the variation between groups is large compared to the variation within groups, it suggests that the average performance of the groups is different. This can be visualized as the groups having distinct peaks on a histogram of the test scores. For example, Group A may have higher scores on average, while Group B and Group C may have lower scores on average.

On the other hand, if the variation between groups is similar to or smaller than the variation within groups, it suggests that the average performance of the groups is similar. This can be visualized as the groups having overlapping or similar peaks on the histogram. In this case, it would be difficult to conclude that there…