When utilizing anova, what does the between group sum of squares measure?

a. the sum of the squared deviations between each group mean and every other group mean

b. the sum of the squared deviations between each group mean and the mean across all groups

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

d. the sum of the squared deviations between each individual observation and the mean across all groups

b. The sum of the squared deviations between each group mean and the mean across all groups

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Solution to the problem

If we assume that we have groups and on each group from we have individuals on each group we can define the following formulas of variation:  

And we have this property

As we can see the sum of squares between represent the sum of squared deviations between each group mean and the mean across all groups.

So then the best option is:

b. The sum of the squared deviations between each group mean and the mean across all groups

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.