In the context of ANOVA (Analysis of Variance), understanding between groups variance and within groups variance is essential for interpreting the results correctly.
Between Groups Variance refers to the variation in sample means among different groups. It measures how much the group means deviate from the overall mean of all groups combined. Essentially, if the means of the groups are very different from each other, between groups variance will be large.
Within Groups Variance, on the other hand, examines the variation within each group itself. It measures how much individual data points within each group vary around their group mean. If individual scores within a group are similar to each other, the within groups variance will be small.
The difference between the two can be summarized as follows: Between groups variance looks at the differences between the group averages, while within groups variance assesses the variability of scores within each group.
In ANOVA, we want the between groups variance to be larger than the within groups variance. This indicates that the group means are significantly different from each other, justifying the conclusion that the treatments or conditions have a real effect. When between groups variance is large relative to within groups variance, it suggests that any observed effect is statistically significant.