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	Design Evaluation

Design Evaluation Results Window

The Design Evaluation Results window shows the detailed results of the design evaluation. It is accessed by clicking the Detailed Results link in the control panel's Design Evaluation area.

All available information and tables are presented next. To view or hide any of these results in the spreadsheet, use the check boxes in the Available Report Items panel.

• The Power Study table shows the calculated power/effect values for each term that you selected to include in the evaluation.

• • The Degrees of Freedom is the number of coefficients that represent the effect of each term in the model. For qualitative factors, this is the number of levels - 1 for each term. For quantitative factors, it is always 1.

  • The last column will vary depending on whether you selected to solve for power or effect.

  • • The Power for Effect Value is the calculated power for each term (i.e., the probability of detecting the specified amount of effect for each term). The column header displays the total effect, which is equal to the effect per standard deviation multiplied by the standard deviation (also shown in the header).

    • The Effect for Power Value is the calculated total effect for the each term (i.e., the largest difference between the response means obtained at each factor level). The column header displays the power value that was used to calculate the effect.

• The Alias Structure shows which effects are aliased with each other. It takes into account only the terms you've selected to include in the evaluation. Together with your engineering knowledge, you can use this table to help determine whether any important interaction information will be lost due to aliasing. If there are no aliased effects, the sentence "All selected terms are alias free" will appear. This table is not available for one factor designs.

• The D-Optimal Information table shows the following values.

• • The Determinate of X'X is the determinant calculated for the information matrix. This value is used to compare the design to other designs and determine which is closer to being orthogonal. Larger determinant values mean you can get more information about the factors you are studying compared to a design with the same model but a smaller determinant.

  • The D-Efficiency is used to measure the orthogonality of a design. A value close to 1 means the design is close to being orthogonal. A value of 1 means the design is orthogonal.

  • The Trace of X'X^-1 is the calculated trace of the variance-covariance matrix (i.e., the sum of all its diagonal elements). Like the determinate of X'X, this value is used to compare different designs. Smaller trace values mean less uncertainty for the estimated model coefficients.

• The Regressor table displays the regressors that were used to calculate the X'X and X'X^-1 matrices described next.

• X'X is the information matrix of the design. It is used to calculate the first and second values in the D-Optimal Information table.

• X'X^-1 is the normalized variance-covariance matrix of the design. It is multiplied by the estimated variance of the error to obtain the variance-covariance matrix of the estimated model parameters.

The ReliaWiki resource portal has more information on design evaluation at: http://www.ReliaWiki.org/index.php/Design_Evaluation_and_Power_Study.