What are the correct sources of variance in an unequal n ANOVA?

In an unequal n ANOVA, the correct sources of variance are defined as between, within, and total. The "between" variance refers to the variability among the group means, capturing how different the means of each group are from the overall mean. The "within" variance pertains to the variability within each group, indicating how much the individual scores in each group deviate from their respective group mean. Lastly, the "total" variance encompasses the overall variability present in the entire dataset, which can be partitioned into the between and within components.

Understanding these sources of variance is fundamental for interpreting the results of an ANOVA, as it allows researchers to assess how much of the total variability can be attributed to the differences between groups versus the variability that exists within the groups themselves. The inclusion of residual variance or covariance is not necessary in this context when discussing the primary sources for an ANOVA, especially given that these terms serve distinct purposes in different analytical frameworks.