DOE Code and Uncoded levels of factor

[#1]

Hi:

I have a question regarding DOE with code and uncoded levels of factors.

Assuming that we have three factors. Each factor is continuous not a category variable. Should we use the real value of each level, i.e. 150, 250, 350, or coded values, i.e. -1,0,1? What are the reasons behind the selection? Other factors contain the levels that have big differences in magnitude, i.e. 2.4e-16, 2.4e-17, 2.4e-18 and 24e6, 28.8e6.

Sincerely,

TK

[#2]

You enter the real values to specify the factor range when you design your experiment. The ranges are assumed to be reasonably wide - enough to produce a large effect. These levels appear in the columns of the design matrix, D, that you run. The regression analysis commonly codes the factor levels before making the model matrix, X, which expands the columns in the D matrix (what you did) into the estimation columns (what you want to know). Coding benefits the analysis in several ways:

• The parameter estimates are comparable.They are independent of the associated scale (units).
• The parameter estimates are interpretable. The intercept when estimated with real values is the response when all your factors are zero. What does that mean? With coding, the intercept is the mean response at the origin (center) of your design. The other parameters still represent the change in the response for 1 unit change in the factor, but in the coded space, 1 unit change is half the range. Double the estimate and that is the change in the response over the full range of the factor.
• The parameter estimates are uncorrelated or minimally correlated. This preserves power for the significance tests.

[#3]

Thank you Mark for helping explain this concept. There is a new column "Uncoded Estimates" in the regression model table. Can you show how these Uncoded Estimates are determined? They do not seem to be used in the Parameter Expression window that shows the full regression model equation.

[#4]

Where do you see the Uncoded Estimates column? How did you make it appear?

You should be able to match these estimates by first deleting the Coding column property and running the model again. Here is an illustration based on the Stretch Data in the sample data folder. Here are the coded estimates produced by default:

Here are the estimates after removing the Coding column property:

(Note that the factors were still centered but not scaled.)