What’s New in Design-Expert version 7 Pat Whitcomb September 13, 2005

1. What’s New inDesign-Expert version 7Pat WhitcombSeptember 13, 2005

2. What’s New • General improvements • Design evaluation • Diagnostics • Updated graphics • Better help • Miscellaneous Cool New Stuff • Factorial design and analysis • Response surface design • Mixture design and analysis • Combined design and analysis

3. Design Evaluation • User specifies what order terms to ignore. • Can evaluate by design or response. • New options for more flexibility. • User specifies D/s ratios for power calculation. • User specifies what to report. • User specified options for standard error plots. • Annotation added to design evaluation report.

4. Design Evaluation Specify Order of Terms to Ignore Focus attention on what is most important.

5. Design Evaluation Evaluate by Design or Response Useful when a response has missing data.

6. Design Evaluation New Options for More Flexibility • User specifies D/s ratios for power calculation. • User specifies what to report. • User specified options for standard error plots.

7. Design EvaluationAnnotated Design Evaluation Report

8. Diagnostics • Diagnostics Tool has two sets of buttons: • “Diagnostics” and “Influence”. • New names and limits. • Internally studentized residual = studentized residual v6. • Externally studentized residual = outlier t v6. • The externally studentized residual has exact limits. • New – DFFITS • New – DFBETAS

9. DiagnosticsDiagnostics Tool has Two Sets of Buttons ei = residuali

10. DiagnosticsExact Limits t(a/n, n-p'-1) p' is the number of model terms including the interceptn is the total number of runs

11. Diagnostics DFFITS DFFITS measures the influence the ithobservation has on the predicted value.(See Myers, Raymond: “Classical andModern Regression with Applications”,1986, Duxbury Press, page 284.) It isthe studentized difference between thepredicted value with observation i andthe predicted value without observation i. DFFITS is the externally studentized residual magnified by high leverage points and shrunk by low leverage points. It is a sensitive test for influence and points outside the limits are not necessarily bad just influential. These runs associated with points outside the limits should be investigated to for potential problems. DFFITS is very sensitive and it is not surprising to have a point or two falling outside the limits, especially for small designs.

12. Diagnostics DFBETAS DFBETAS measures the influence the ith observation has on each regression coefficient. (See Myers, Raymond: “Classical and Modern Regression with Applications”, 1986, Duxbury Press, page 284.) The DFBETASj,i is the number of standard errors that the jth coefficient changes if the ith observation is removed.

13. Updated Graphics • New color by option. • Full color contour and 3D plots. • Design points and their projection lines added to 3D plots. • Grid lines on contour plots. • Cross hairs read coordinates on plots. • Magnification on contour plots. • User specified detail on contour “Flags”. • Choice of “LSD Bars”, “Confidence Bands” or “None” on one factor and interaction plots.

14. New Color by Option

15. Full Color Contour and 3D Plots

16. Design Points on 3D Plots

17. Grid lines on contour plots

18. Cross Hairs

19. Magnification on Contour Plots

20. Specify Detail on Contour “Flags”

21. “LSD Bars” & “Confidence Bands”

22. Better Help • Improved help • Screen tips • Movies (mini tutorials)

23. Miscellaneous Cool New Stuff • “Graph Columns” now has its own node. • Highlight points in the design layout or on a diagnostic graph for easy identification. • Right click and response cell and ignore it. • Improved design summary. • Numerical optimization results now carried over to graphical optimization and point prediction. • Export graph to enhanced metafile (*.emf).

24. Graph Columns Node

25. Highlight Points

26. Ignore Response Cells

27. Improved Design Summary • New in version 7: • Means and standard deviations for factors and responses. • The ratio of maximum to minimum added for responses.

28. Numerical optimization results carried over to graphical optimization and point prediction.

29. What’s New • General improvements • Design evaluation • Diagnostics • Updated graphics • Better help • Miscellaneous Cool New Stuff • Factorial design and analysis • Response surface design • Mixture design and analysis • Combined design and analysis

30. Two-Level Factorial Designs • 2k-p factorials for up to 512 runs (256 in v6) and 21 factors (15 in v6). • Design screen now shows resolution and updates with blocking choices. • Generators are hidden by default. • User can specify base factors for generators. • Block names are entered during build. • Minimum run equireplicated resolution V designs for6 to 31 factors. • Minimum run equireplicated resolution IV designs for 5 to 50 factors.

31. 2k-p Factorial DesignsMore Choices Need to “check” box to see factor generators

32. 2k-p Factorial DesignsSpecify Base Factors for Generators

33. MR5 Designs Motivation Regular fractions (2k-p fractional factorials) of 2k designs often contain considerably more runs than necessary to estimate the [1+k+k(k-1)/2] effects in the 2FI model. • For example, the smallest regular resolution V design for k=7 uses 64 runs (27-1) to estimate 29 coefficients. • Our balanced minimum run resolution V design for k=7 has 30 runs, a savings of 34 runs. “Small, Efficient, Equireplicated Resolution V Fractions of 2k designs and their Application to Central Composite Designs”, Gary Oehlert and Pat Whitcomb, 46th Annual Fall Technical Conference, Friday, October 18, 2002. Available as PDF at: http://www.statease.com/pubs/small5.pdf

34. MR5 DesignsConstruction • Designs have equireplication, so each column contains the same number of +1s and −1s. • Used the columnwise-pairwise of Li and Wu (1997) with the D-optimality criterion to find designs. • Overall our CP-type designs have better properties than the algebraically derived irregular fractions. • Efficiencies tend to be higher. • Correlations among the effects tend be lower.

35. MR5 DesignsProvide Considerable Savings

36. MR4 DesignsMitigate the use of Resolution III Designs The minimum number of runs for resolution IV designs is only two times the number of factors (runs = 2k). This can offer quite a savings when compared to a regular resolution IV 2k-p fraction. • 32 runs are required for 9 through 16 factors to obtain a resolution IV regular fraction. • The minimum-run resolution IV designs require 18 to 32 runs, depending on the number of factors. • A savings of (32 – 18) 14 runs for 9 factors. • No savings for 16 factors. “Screening Process Factors In The Presence of Interactions”, Mark Anderson and Pat Whitcomb, presented at AQC 2004 Toronto. May 2004. Available as PDF at: http://www.statease.com/pubs/aqc2004.pdf.

37. MR4 DesignsSuggest using “MR4+2” Designs Problems: • If even 1 run lost, design becomes resolution III – main effects become badly aliased. • Reduction in runs causes power loss – may miss significant effects. • Evaluate power before doing experiment. Solution: • To reduce chance of resolution loss and increase power, consider adding some padding: • New Whitcomb & Oehlert “MR4+2” designs

38. MR4 DesignsProvide Considerable Savings * No savings

39. Two-Level Factorial Analysis • Effects Tool bar for model section tools. • Colored positive and negative effects and Shapiro-Wilk test statistic add to probability plots. • Select model terms by “boxing” them. • Pareto chart of t-effects. • Select aliased terms for model with right click. • Better initial estimates of effects in irregular factions by using “Design Model”. • Recalculate and clear buttons.

40. Two-Level Factorial AnalysisEffects Tool Bar • New – Effects Tool on the factorial effects screen makes all the options obvious. • New – Pareto Chart • New – Clear Selection button • New – Recalculate button (discuss later in respect to irregular fractions)

41. Two-Level Factorial AnalysisColored Positive and Negative Effects

42. Two-Level Factorial AnalysisSelect Model Terms by “Boxing” Them.

43. Two-Level Factorial AnalysisPareto Chart to Select Effects The Pareto chart is useful for showing the relative size of effects, especially to non-statisticians. Problem: If the 2k-p factorial design is not orthogonal and balanced the effects have differing standard errors, so the size of an effect may not reflect its statistical significance. Solution: Plotting the t-values of the effects addresses the standard error problems for non-orthogonal and/or unbalanced designs. Problem: The largest effects always look large, but what is statistically significant? Solution: Put the t-value and the Bonferroni corrected t-value on the Pareto chart as guidelines.

44. Pareto Chart C 11.27 8.45 AC A t-Value of |Effect| 5.63 Bonferroni Limit 5.06751 2.82 t-Value Limit 2.77645 0.00 1 2 3 4 5 6 7 Rank Two-Level Factorial AnalysisPareto Chart to Select Effects

45. Two-Level Factorial AnalysisSelect Aliased terms via Right Click

46. Two-Level Factorial AnalysisBetter Effect Estimates in Irregular Factions • Design-Expert version 6 Design-Expert version 7

47. Two-Level Factorial AnalysisBetter Effect Estimates in Irregular Factions ANOVA for Selected Factorial ModelAnalysis of variance table [Partial sum of squares] Sum ofMeanFSourceSquaresDFSquareValueProb > F Model 38135.17 4 9533.79 130.22 < 0.0001A10561.33110561.33144.25< 0.0001B8.1718.170.110.7482C11285.33111285.33154.14< 0.0001AC14701.50114701.50200.80< 0.0001 Residual 512.50 7 73.21 Cor Total 38647.67 11

48. Two-Level Factorial AnalysisBetter Effect Estimates in Irregular Factions Main effects only model: [Intercept] = Intercept - 0.333*CD - 0.333*ABC - 0.333*ABD [A] = A - 0.333*BC - 0.333*BD - 0.333*ACD [B] = B - 0.333*AC - 0.333*AD - 0.333*BCD [C] = C - 0.5*AB [D] = D - 0.5*AB Main effects & 2fi model: [Intercept] = Intercept - 0.5*ABC - 0.5*ABD [A] = A - ACD [B] = B - BCD [C] = C [D] = D [AB] = AB [AC] = AC - BCD [AD] = AD - BCD [BC] = BC - ACD [BD] = BD - ACD [CD] = CD - 0.5*ABC - 0.5*ABD

49. Two-Level Factorial AnalysisBetter Effect Estimates in Irregular Factions • Design-Expert version 6 calculates the initial effects using sequential SS via hierarchy. • Design-Expert version 7 calculates the initial effects using partial SS for the “Base model for the design”. • The recalculate button (next slide) calculates the chosen (model) effects using partial SS and then remaining effects using sequential SS via hierarchy.

50. Two-Level Factorial AnalysisBetter Effect Estimates in Irregular Fractions • Irregular fractions – Use the “Recalculate” key when selecting effects.