A Lenth PSE (pseudo standard error) table appears directly beneath the notes or option lists. (For a description of the PSE, see Lenth’s PSE.) The statistics that appear in the Lenth table depend on the variances and correlation of the parameter estimates.
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The option Using estimates standardized to have equal variances applies a normalizing transformation to standardize the variances. This option is selected by default when the variances are unequal.
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The option Using estimates orthogonalized to be uncorrelated applies a transformation to remove correlation. This option is selected by default when the estimates are correlated. The transformation that is applied is identical to the transformation that is used to calculate sequential sums of squares. The estimates measure the additional contribution of the variable after all previous variables have been entered into the model.
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The columns that appear in the table depend on the selections initially described in the notes or option lists. The report highlights any row corresponding to an estimate with a p-value of 0.20 or less. All versions of the report give Term, Estimate, and either t-Ratio and Prob>|t| or Pseudo t-Ratio and Pseudo p-Value.
Gives the p-value for the test. If a transformation is applied, this option gives the p-value for a test using the transformed data.
Appears when there are no degrees of freedom for error. If the relative standard errors of the parameters are equal, Pseudo t-Ratio is the parameter estimate divided by Lenth’s PSE. If the relative standard errors vary, it is calculated as shown in Pseudo t-Ratios.
Appears when there are no degrees of freedom for error. The p-value is derived using a t distribution. The degrees of freedom are m/3, rounded down to the nearest integer, where m is the number of parameters.
If Using estimates standardized to have equal variances is selected and the note indicating that the parameter estimates are not correlated appears, the report shows a column called Standardized Estimate. This column provides estimates of the parameters resulting from the transformation used to transform the estimates to have equal variances.
If both Using estimates standardized to have equal variances and Using estimates orthogonalized to be uncorrelated are selected, the report gives a column called Orthog Coded. The following information is provided:
Appears if there are degrees of freedom for error. Gives the t ratio for the transformed estimates.
Appears if there are no degrees of freedom for error. It is a t ratio computed by dividing the orthogonalized estimate, Orthog Coded, by Coded Scale Lenth PSE.
Figure 2.43 shows the Effect Screening report that you create by running the Fit Model script in the Bicycle.jmp sample data table. Note that you would select Effect Screening > Normal Plot in order to obtain this form of the report. The notes directly beneath the report title indicate that no transformation is required. Consequently, the Lenth PSE is displayed. Because there are no degrees of freedom for error, no estimate of residual error can be constructed. For this reason, Lenth’s PSE is used as an estimate of residual error to obtain pseudo t ratios. Pseudo p-values are given for these t ratios. Rows for non-intercept terms corresponding to the three estimates with p-values of 0.20 or less are highlighted.
In the Odor.jmp sample data table, run the Model script and click Run. To create the report shown in Figure 2.44, select Effect Screening > Normal Plot from the Response Y red triangle menu. You can also create the report by selecting the Bayes Plot or Pareto Plot options in the Response Y red triangle menu.
The report shows the t-Test Scale and Coded Scale Lenth PSEs. But, because there are degrees of freedom for error, the tests in the Parameter Estimate Population report do not use the Lenth PSEs. Rows for non-intercept terms corresponding to the three estimates with p-values of 0.20 or less are highlighted. A note at the bottom of the Parameter Estimate Population report indicates that orthogonalized estimates depend on their order of entry into the model.
The Correlations of Estimates report appears only if the estimates are correlated (Figure 2.44). The report provides the correlation matrix for the parameter estimates. This matrix is similar to the one that you obtain by selecting the Estimates > Correlation of Estimates red triangle option. However, to provide a more compact representation, the report does not show column headings. See Correlation of Estimates for details.
The “Transformation to make uncorrelated” report appears only if the estimates are correlated. The report gives the matrix used to transform the design matrix to produce uncorrelated parameter estimates. The transformed, or orthogonally coded, estimates are obtained by pre-multiplying the original estimates with this matrix and dividing the result by 2.