The sums of squares step in the ANOVA calculations does what? calculates the sum

Question

The sums of squares step in the ANOVA calculations does what?

calculates the sum of the squared values for each datapoint in the groups

separates the two sources of variation in the data: within groups and among groups

combines the variation from all data sources for quantification purposes

sums the datapoints for each group and then takes the square of each group sum to evaluate the groups

calculates the sum of the squared values for each datapoint in the groups

separates the two sources of variation in the data: within groups and among groups

combines the variation from all data sources for quantification purposes

sums the datapoints for each group and then takes the square of each group sum to evaluate the groups

Explanation / Answer

Ans:

Option b is correct.

separates the two sources of variation in the data: within groups and among groups.

Explanation:

We calculate sum of squares for within groups and between(among) groups.

The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean. There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance.

Between Group Variation

The variation due to the interaction between the samples is denoted SS(B) for Sum of Squares Between groups.

Within Group Variation

The variation due to differences within individual samples, denoted SS(W) for Sum of Squares Within groups.

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