Changing the value of a for a central composite design
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The position of the axial points in a central composite design is denoted by alpha (a). The value of a, along with the number of center points, determines whether a design can be orthogonally blocked and is rotatable. Orthogonally blocked designs allow for model terms and block effects to be estimated independently and minimize the variation in the regression coefficients. Rotatable designs provide the desirable property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction.

Minitab's default designs achieve rotatability and orthogonal blocking when both properties can be achieved simultaneously. When the design is blocked and you cannot achieve both properties simultaneously, the default designs use a such that the design is orthogonally blocked. When there are no blocks, the default designs use a such that the design is rotatable.

The default value for a for each central composite design in Summary of central composite designs.