How is the column between-groups variance estimate found in a 2 x 2 design?

The correct choice highlights that the column between-groups variance estimate in a 2 x 2 design is determined by the differences in means between the two groups. In a 2 x 2 factorial design, there are typically four groups based on two independent variables, and you are often interested in how these groups differ from one another.

To compute the between-groups variance, you calculate the mean for each group and then find the overall mean. The variance is then computed based on how much each group mean deviates from the overall mean, squared, and weighted by the number of observations in each group. This method effectively captures the variability attributable to the treatment effects or differences when comparing group means. It highlights the impact of the independent variables on the dependent variable by elaborating on how much these group means differ from the overall mean, providing insight into the factor's effects.

In contrast, examining total group means does not isolate the differences effectively. Averaging the variances of all groups does not directly measure how much the group means differ from one another, and using the combined variance of all cells does not specifically address the mean differences that define the between-groups variance estimate. Thus, option B accurately represents the method for finding the column between-groups variance