The Sorted Estimates option produces a version of the Parameter Estimates report that is useful in screening situations. If the design is not saturated, the Sorted Estimates report gives the information found in the Parameter Estimates report, but with the terms, other than the Intercept, sorted in decreasing order of significance (second report in Figure 3.21). If the design is saturated, then Pseudo t tests are provided. These are based on Lenth’s pseudo standard error (Lenth 1989). See Lenth’s PSE.
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Select Analyze > Fit Model.
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Make sure that 2 appears in the Degree box near the bottom of the window.
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Click Run.
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Select Estimates > Sorted Estimates from the red triangle menu.
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Figure 3.21 Sorted Parameter Estimates
Note the following differences between the Parameter Estimates report and the Sorted Parameter Estimates report (both shown in Figure 3.21):
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The effects are sorted by the absolute value of the t ratio, showing the most significant effects at the top.
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A bar chart shows the t ratio with vertical lines showing critical values for the 0.05 significance level.
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Screening experiments often involve fully saturated models, where there are not enough degrees of freedom to estimate error. In these cases, the Sorted Estimates report (Figure 3.21) gives relative standard errors and constructs t ratios and p-values using Lenth’s pseudo standard error (PSE). These quantities are labeled with Pseudo in their names. See Lenth’s PSE and Pseudo t-Ratios. A note explains the change and shows the PSE.
The parameter estimates are presented in sorted order, with smallest p-values listed first.
A t ratio for the estimate, computed using pseudo standard error. The value of Lenth PSE is shown in a note at the bottom of the report.
A p-value computed using an error degrees of freedom value (DFE) of m/3, where m is the number of parameters other than the intercept. The value of DFE is shown in a note at the bottom of the report.
Lenth’s pseudo standard error (PSE) is an estimate of residual error due to Lenth (1989). It is based on the principle of effect sparsity: in a screening experiment, relatively few effects are active. The inactive effects represent random noise and form the basis for Lenth’s estimate.
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When relative standard errors are equal, Lenth’s PSE is shown in a note at the bottom of the report. The Pseudo t-Ratio is calculated as follows:
When relative standard errors are not equal, the TScale Lenth PSE is computed. This value is the PSE of the estimates divided by their relative standard errors. The Pseudo t-Ratio is calculated as follows:
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Select Analyze > Fit Model.
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Click Run.
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From the red triangle menu next to Response Y, select Estimates > Sorted Estimates.
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Note that Lenth’s PSE and the degrees of freedom used are given at the bottom of the report. The report indicates that, based on their Pseudo p-Values, the effects Ct, Ct*T, T*Cn, T, and Cn are highly significant.
