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Answer :
The statement is false; the correct term for the statistic that quantifies the variability of group means around the grand mean is 'mean square between groups', not 'mean square within'.
The statement that the statistic which quantifies the variability of the group means around the grand mean is called the mean square within is false. The correct term for this statistic is the 'mean square between groups' or MSbetween, which measures the variance between the different groups. In contrast, the 'mean square within groups' or MSwithin pertains to the variation within groups caused by random chance or natural variability, not the differences between the various group means.
The MSbetween quantifies how much the group means deviate from the grand mean, which is the mean of all group means. Conversely, the MSwithin calculates how much the individual scores within each group deviate from their respective group means.
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