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Pure Error Sum of Squares

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Whenever an experimental design is replicated two or more times, the error (residual) sum of squares for the design can be broken down into two parts:

One part is the Pure Error sum of squares measuring the variance of the Replicates. Thus, pure error represents random variation in the response variable because it is based on differences between different observations on the same response for the same treatment combination.

The remaining part then is the Lack-of-Fit sum of squares, measuring the effect of terms not included in the model.

The Lack of fit and Pure error sums of squares are used to test the fit of the model, called the Lack-of-fit test.

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