Home / DOE / Create Designs / Factor Names and Coding
Factor Names and Coding¶
The Enter Factor Names and Coding page appears while you build a 2-level factorial, CCD, Box-Behnken or Plackett-Burman design, in the Design Wizard, and again from QXL DOE New > Modify Design > Input Name, Low/High, and Type on a design that already exists.
Enter Factor Names and Coding takes one row per factor. What the grid holds depends on the design type:
| Design type | The grid |
|---|---|
| 2-level factorial, Plackett-Burman | Name, Low (or Name), High (or Name) and Categorical |
| CCD, Box-Behnken | Name, Low and High. No Categorical column and no categorical hint line, so every factor is quantitative |
The rest of this section describes the first case. The two value columns carry both readings in their headings because they hold different things depending on the factor:
| Factor | What goes in the two value cells |
|---|---|
| quantitative, Categorical clear | the low value in one and the high value in the other |
| categorical, Categorical ticked | one level name in each cell, so the factor has exactly two levels |
The page states the rule on screen as well, in two hint lines: For Quantitative Inputs enter the low and high values (e.g. low=10 high=20) and For Categorical Inputs enter the name of each level (e.g. Red,Blue). That last example means Red in one cell and Blue in the other. Nothing splits a cell on commas, so typing Red,Blue into one cell gives one level whose name is Red,Blue.
A factor with three or more levels cannot be described here, since there are only two cells. Those designs use their own factor page, with a # Levels column and one Level n column per level.
The coded name is not the same as the name¶
Every factor keeps two names. The coded name is assigned by position, A for the first factor, B for the second and so on, and it is what the design matrix, the alias table and the interaction names use. The name you type is what the reports and charts label. Renaming a factor never changes its coded name, so an interaction stays AB whatever you call A and B.
Quantitative and categorical factors¶
A factor is either Quantitative or Categorical, and the choice changes what the software can do with it.
A Quantitative factor takes numeric values on a scale, so the model can interpolate between the settings you ran and predict at a value you did not run. It is coded to a common scale before the regression, and it can carry an axis on a surface or contour chart.
A Categorical factor takes named levels with no scale between them. It is never coded to a numeric range; instead each non-reference level gets its own coefficient. There is nothing between two levels to predict at, so a chart that needs to evaluate the model between settings either refuses a categorical factor on that axis or draws it as separate levels rather than as a line. Which of the two depends on the chart, and each chart page says.
The Categorical column is not on every design's factor page. The builder shows it, and the categorical hint line under the grid, only for the 2-level factorial and Plackett-Burman designs. For CCD and Box-Behnken the same page carries Name, Low and High only, with no Categorical column and no categorical hint line, so every factor in those designs is quantitative. The quantitative hint line, For Quantitative Inputs enter the low and high values (e.g. low=10 high=20), is shown on every version of the page, including those two. The Design Wizard and Modify Design > Input Name, Low/High, and Type gate the column the same way.
The 3-level and N-level factorial designs use a different factor page, a grid headed Factor name, # Levels, Categorical and one Level n column per level. That is where a factor with three or more levels is described. The # Levels column is shown on the N-level factorial page only: on the 3-level factorial page it is hidden, and every factor has exactly three levels, which cannot be changed. Taguchi designs use a third layout again, described on Taguchi Designs.
Coding¶
New designs are created autocoded. To change it, use QXL DOE New > Modify Design > Change Coding (Autocode/Standardize), which offers three choices on a page headed Change design coding:
| Choice | What the design's numbers become |
|---|---|
| Autocode | scaled so the factorial low maps to -1 and the factorial high maps to +1 |
| Standardize | scaled to a mean of 0 and a standard deviation of 1 |
| Do not code the design | left in the units you entered |
Standardize is greyed out when any factor in the design is categorical, and a design that was stored as standardized comes up showing Autocode selected instead once a categorical factor is present.
Every quantitative factor is put on a common scale before the regression runs. One expression does it, whichever coding is in force, using a centre \(m_c\) and a scale \(s_c\) that the coding chooses:
A categorical factor is never coded this way. Its coded value is \(1\), and the level it sits at selects which coefficient is used instead.
An interaction's coded value is the product of the coded values of the factors in it.
Only rows whose point type is factorial or edge centroid set the scale. Centre points, both kinds of axial point, and any extra runs added with Add/Remove Runs are all excluded. That applies to the minimum and maximum behind Autocode and equally to the mean and sample standard deviation behind Standardize.
Two consequences are worth knowing. Centre points and replicated centre runs do not move the centre or the scale. And an extra run entered outside the factorial range does not widen the minimum or the maximum, so it codes outside the usual range with nothing on the sheet to explain why.
A factor needs at least two distinct values among those rows. With only one the scale would be zero, and the coding stops instead, for Autocode as well as for Standardize.
For a central composite design under Autocode this has a visible consequence: the corners code to \(\pm 1\) as usual, and axial points beyond the corners code to values outside \(\pm 1\), at \(\pm \alpha_{\text{axial}}\). Under Standardize the same rows set a mean and a standard deviation instead, so neither the corners nor the axial points land on those values exactly.
The standard deviation model reuses the coding of the response model. It does not recompute a centre and scale from its own subset of rows, so the two models are on the same coded scale and their coefficients are comparable.
Full details: Design Coding.
Messages you can hit on this page¶
The page checks each row as you leave it, and stops you with one of these. The three that name a factor use the name you typed in the Name cell.
| Message | What caused it |
|---|---|
| Values must be numeric. | the Categorical box is clear, so the cell must hold a number, and what you typed is not one |
| Low and High value for Factor name are the same. | a quantitative factor was given the same value twice, so it has no range to code against |
| All levels in Factor name are the same. | a categorical factor was given the same level name in both cells |
One more message exists but cannot be reached from this page. Low and/or High value is not set for output name. guards against a missing value, and says "output" where it means the factor. Both callers parse the two cells and assign them before the guard runs, so a blank or non-numeric cell produces Values must be numeric. first and the guard never fires.
Separate messages come from coding the design later, when a model is loaded or a regression is run rather than while you fill this page in. Those name the factor by its position, not by its name, and they are listed on Design Coding.