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This method computes the TotalSumOfSquares which is a measure of the total variation of the data from the overall population mean.
TotalSumOfSquares consists of two parts: SumOfSquaresF, a measure of variation attributed to the factor, and SumOfSquaresRF, a measure of variation attributed to random fluctuation. In other words,
TotalSumOfSquares = SumOfSquaresF + SumOfSquaresRF
The method computes the two mean square quantities MeanSquareErrorF and MeanSquareErrorRF from SumOfSquaresF and SumOfSquaresRF by dividing SumOfSquaresF and SumOfSquaresRF by their own degrees of freedom. The larger MeanSquareErrorF is relative to MeanSquareErrorRF, the more significant effect the factor has on the experimental outcome.
In particular, if the null hypothesis is true, then the ratio
f, f=MeanSquareErrorF / MeanSquareErrorRF
is taken from an F distribution with k–1 and n–k degrees of freedom, from which you can calculate probabilities. Given a particular f, Significance is the probability that you get a value larger than f when sampling from this distribution.