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Optimal Design How-To¶

This walkthrough builds an optimal design for a run count no classical design offers, which is the reason this tool exists.

Nothing here needs data. A design is built before the experiment is run, so every number below is determined by the design itself and you can check each one against your own sheet.

Steps¶

QXL DOE New > Create Optimal Design (D, A, I).
Step 1, the candidate source. Choose to build the candidate set from factors and levels rather than from an existing sheet, and press Next.
Step 2, factors and levels. Name three factors and give each a low and a high.
Step 3, model terms. The model opens with nothing in it. Every interaction, quadratic and custom term starts in Terms available; move the three two-factor interactions into Terms in model and watch the Degrees of freedom remaining counter fall as you do.
Step 4, run range and criterion. Set Number of runs in optimal design to 10, leave Plus/minus runs so a small range either side is searched, and leave the criterion on its default.
Step 5, the search. It runs and moves on by itself when it finishes.
Step 6, the results. One row per run size. Open a row to see its detail.
Step 7. Set replicates and outputs, and finish.

Why a run count no classical design offers¶

Ten runs for three factors with all three two-factor interactions. A full 2^3 factorial is 8 runs and cannot estimate curvature; the next classical step up jumps well past 10. An optimal design takes the run count as an input and selects the best 10 candidate points for the model you specified, which is what lets it land on a size that no generator produces.

What the results page shows¶

All four measures are reported for every design, whichever criterion you optimised, so a design chosen for one can be read against the others.

Power is computed from three values you type, in boxes above the first detail section: Anticipated coefficient, Standard deviation and Significance level. They are one set for the whole page, so an edit recomputes every row, and only the power columns change: the leverage table, the correlations and the alias matrix are as the search produced them.

The coefficient and the standard deviation act as a ratio. A coefficient of 2 with a standard deviation of 2 gives the same power as 1 with 1.

There is no data block on this page, and here is why¶

Every other How-To in this help system gives you a table to paste into Excel, either sample data or the design matrix to check your sheet against. This one cannot give you either.

The design is the search's output, not a fixed array. A generator produces the same matrix every time it is asked for the same design, which is why the eight classical design pages can print theirs. This tool selects runs for the model and the run count you gave it, and two searches can return slightly different designs, both good. A matrix printed here would be a design you could not reproduce, which is worse than no matrix at all.

What you can check instead is on the results page, and it is checkable because it is reported for every candidate size: the four measures for each design, side by side, whichever criterion you optimised.

Things to try next¶

Change Number of runs in optimal design to 8 and compare the measures against the 10 run design. More runs buy precision; the table lets you see how much.
Add a quadratic term on step 3 and watch the degrees of freedom counter. A run count that no longer supports the model is reported rather than silently fitted.
Type a different Anticipated coefficient on the results page and watch only the power columns move.