Home / DOE / Additional Information / Categorical Inputs
Categorical Inputs¶
A categorical input takes named levels rather than values on a scale. This page covers how one is entered, how it enters the model, and what it does to the reports.
Entering one¶
Tick Categorical on the factor row and the two value cells hold level names instead of a low and a high value. One name per cell, so a factor described on that page has exactly two levels. The columns are headed Low (or Name) and High (or Name) for exactly this reason.
Nothing splits a cell on commas. The page's own hint, for categorical inputs enter the name of each
level (e.g. Red,Blue), means Red in one cell and Blue in the other; typing Red,Blue into a single
cell creates one level called Red,Blue.
For three or more levels use a design whose factor page has a # Levels column and one Level n column per level, which is the 3-level and N-level factorial page.
The reference level¶
For a categorical factor one level is the reference. The other levels each get a coefficient measured against it, and the reference itself has none, which is why the regression table shows one fewer coefficient than the factor has levels. The reference level is not missing from the model: it is the baseline the others are expressed relative to.
So a factor with three levels contributes two coefficients, and a factor with five contributes four. The number of coefficients a categorical factor adds to the model is always one fewer than its number of levels.
Coding¶
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.
A categorical factor is never coded, under any of the three coding settings. Its values are carried through unchanged, and in the prediction equation its coded value is 1 while the level decides which coefficient is read.
In the reports¶
| Report | What a categorical factor looks like |
|---|---|
| Coefficient table | one row per non-reference level |
| ANOVA table | one row for the whole term, its sum of squares being the total of its columns' |
| Pareto chart | one bar per non-reference level, named term - level |
| Main effects and interaction plots | the points are joined with a dotted line, because there is nothing between two levels |
| Surface plot | it can carry an axis, and it is put on the series axis, drawn as one ribbon per level. At least one of the two axes must be quantitative |
| Contour plot | it cannot carry an axis. The contour dialog's two axis lists offer quantitative factors only, so a categorical factor is not selectable there |
| Cube plot | it can carry an axis when it has exactly two levels, and the corners are labelled with the level names. Any other number of levels is refused |
Distinct values are counted only up to three¶
When Quantum XL checks how many distinct values a factor has, it stops counting at three. So an internal count of 3 means three or more, not exactly three. This matters only if you are reading the number back: it is a check for enough variation, not a report of how many levels the factor has.
Interactions between categorical factors¶
An interaction involving categorical factors gets a coefficient for each combination of their levels, selected by a combined level index rather than by multiplying values. The details, including the worked example the software's own code carries, are on Prediction Equation.
Nesting¶
A categorical factor whose levels only mean something inside another factor's level is nested. Mark it with Is nested within factor: in the custom design factor editor. Nesting is checked before the other model rules and a violation is treated as critical, so a model that breaks it is rejected rather than warned about.