Sums of Squares

Sums of squares (SS) may be calculated in several ways, depending on the model. The method known as Partial SS is popular because it extracts a value based on removing each model parameter one at a time. Such a technique is essential for unbalanced data or for designs having factors with different numbers of levels. It generates sums which are independent of the model order.

Sums of squares also must be apportioned in accordance with the model structure. For example, blocking requires that the SS be apportioned to blocks as a random factor rather than as one of the fixed factors of the model. Similar apportionment must be made for Nested or Hierarchal designs. SS for components of a model do not necessarily sum to the total SS for a group. Balanced, 2-level unblocked designs may use any of the feasible methods.

Partial Sum of Squares is calculated by an iterative process, which is explained in Mason Gunter Hunter. This is also called Deleted Sum of Squares because the value of the SS for each parameter is calculated as the difference between the residual SS when the parameter is included or not. It is the only correct way to calculate SS for unbalanced arrays.

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