The Effect Screening platform uses the principle of effect sparsity (Box and Meyer, 1986). This principle asserts that relatively few of the effects that you study in a screening design are active. Most are inactive, meaning that their true effects are zero and that their estimates are random error.
Gives parameter estimates corresponding to factors that are scaled to have a mean of zero and a range of two. See Scaled Estimates and the Coding of Continuous Terms.
Identifies parameter estimates that deviate from normality, helping you determine which effects are active. See Normal Plot Report.
Computes posterior probabilities for all model terms using a Bayesian approach. See Bayes Plot Report.
Plots the absolute values of the orthogonalized and standardized parameter estimates, relating these to the sum of their absolute values. See Pareto Plot Report.
1.

Open the Drug.jmp sample data table.

2.

Select Analyze > Fit Model.

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Change the Emphasis to Minimal Report.

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Click Run.

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From the red triangle menu next to Response y, select Effect Screening > Scaled Estimates.

The report (Scaled Estimates Report) indicates that the continuous factor, x, is centered by its mean and scaled by its halfrange.
The model fits three parallel lines, one for each Drug group. The x values range from 3 to 21. The Scaled Estimate for x, 8.8846543, is half the difference between the predicted value for x = 21 and the predicted value for x = 3 for any one of the Drug groups. You can verify this fact by selecting Save Columns > Prediction Formula from the report’s red triangle menu. Then add rows to obtain predicted values for each of the Drug groups at x = 21 and x = 3.
So, over the range of x values in this particular data set, the impact of x is to vary the response over a range of about 17.8 units. Note that the parameter estimate for x based on the raw data is 0.9871838; it does not permit direct interpretation in terms of the response.
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.)
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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.

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 pvalue of 0.15 or less. All versions of the report give Term, Estimate, and either tRatio and Prob>t or Pseudo tRatio and Pseudo pValue.
Gives the pvalue for the test. If a transformation is applied, this option gives the pvalue 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 tRatio is the parameter estimate divided by Lenth’s PSE. If the relative standard errors vary, it is calculated as shown in Pseudo tRatios.
Appears when there are no degrees of freedom for error. The pvalue 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.
Effect Screening Report for Equal Variance and Uncorrelated Estimates 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 pvalues are given for these t ratios. Rows corresponding to the three estimates with pvalues of 0.15 or less are highlighted.
In the Odor.jmp sample data table, run the Model script and click Run. To create the report shown in Effect Screening Report for Unequal Variances and Correlated Estimates, 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 tTest 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 corresponding to the three estimates with pvalues of 0.15 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 (Effect Screening Report for Unequal Variances and Correlated Estimates). 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 premultiplying the original estimates with this matrix and dividing the result by 2.
Below the Normal Plot report title, select either a normal plot or a halfnormal plot (Daniel 1959). Both plots are predicated on the principle of effect sparsity, namely, the idea that relatively few effects are active. Those effects that are inactive represent random noise. Their estimates can be assumed to have a normal distribution with mean 0 and variance σ2, where σ2 represents the residual error variance. It follows that, on a normal probability plot, estimates representing inactive effects fall close to a line with slope σ.
If no transformation is required, the vertical coordinate of the normal plot represents the value of the estimate and the horizontal coordinate represents its normal quantile. Points that represent inactive effects should follow a line with slope of σ. Lenth’s PSE is used to estimate σ and a blue line with this slope is shown on the plot.
If a transformation to orthogonality has been applied, the vertical axis represents the Normalized Estimates. These are the Orthog tRatio values found in the Parameter Estimate Population report. (The Orthog tRatio values are the Orthog Coded estimates divided by the Coded Scale Lenth PSE.)
Because the estimates are normalized by an estimate of σ, the points corresponding to inactive effects should fall along a line of slope 1. A red line with slope 1 is shown on the plot, as well as a blue line with slope equal to the tTest Scale Lenth PSE.
In all cases, estimates that deviate from normality at the 0.15 level, based on the pvalues in the Parameter Estimate Population report, are labeled on the plot.
Normal Plot shows the Normal Plot report for the Bicycle.jmp sample data table. No transformation is needed for this model, so the plot shows the raw estimates plotted against their normal quantiles. A line with slope equal to Lenth’s PSE is shown on the plot. The plot suggests that Gear, Dynamo, and Seat are active factors.
1.

Open the Bicycle.jmp sample data table.

2.

Select Analyze > Fit Model.

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5.

Click Run.

6.

From the red triangle menu next to Response Y, select Effect Screening > Normal Plot.

The Bayes Plot report gives another approach to determining which effects are active. This report helps you compute posterior probabilities using a Bayesian approach. This method, due to Box and Meyer (1986), assumes that the estimates are a mixture from two distributions. The majority of the estimates, corresponding to inactive effects, are assumed to be pure random normal noise with variance σ2. The remaining estimates, the active ones, are assumed to come from a contaminating distribution that has a variance K times larger than σ2.
Gives the parameter estimate. The Bayes plot is constructed with respect to estimates that have estimated standard deviation equal to 1. If the estimates are not correlated, the tRatio is used. If the estimates are correlated, the Orthog tRatio is used.
The value of the contamination coefficient, representing the ratio of the contaminating distribution variance to the error variance. K is commonly set to 10, which is the default value.
The specifications window, showing default settings for a Bayes Plot for the Bicycle.jmp sample data table, is shown in Bayes Plot Specifications. Clicking Go in this window updates the report to show Posterior probabilities for each of the terms and a bar chart (Bayes Plot Report).
1.

Open the Bicycle.jmp sample data table.

2.

Select Analyze > Fit Model.

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Click Run.

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From the red triangle menu next to Response Y, select Effect Screening > Bayes Plot.

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Click Go to calculate the posterior probabilities.

The Pareto Plot report presents a Pareto chart of the absolute values of the estimates. Pareto Plot shows a Pareto Plot report for the Bicycle.jmp sample data table.
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If the original estimates have unequal variances and are not correlated, the t ratios are plotted.
