Question

5 multiple choice 1 point what does the within - group sum of squares measure? the sum of the squared deviations between each individual observation and its group mean the sum of the squared deviations between each group mean and every other group mean the sum of the squared deviations between each individual observation and the mean across all groups the sum of the squared deviations between each group mean and the mean across all groups

Explanation:

To determine the correct answer, we analyze the concept of within - group sum of squares:

1. Recall the definition of within - group sum of squares: It quantifies the variation that exists within each group. This variation is calculated as the sum of the squared differences between each individual data point (observation) in a group and the mean of that specific group.
2. Analyze the other options:

• The option "The sum of the squared deviations between each group mean and every other group mean" describes a measure related to the differences between group means, not within - group variation.
• The option "The sum of the squared deviations between each individual observation and the mean across all groups" is related to the total variation (including both within - group and between - group) around the overall mean, not within - group.
• The option "The sum of the squared deviations between each group mean and the mean across all groups" is the between - group sum of squares, which measures the variation between the group means and the overall mean.

Answer:

A. The sum of the squared deviations between each individual observation and its group mean