Derived categorical factors are categorical factors whose levels are paired to the levels of another design factor. The levels of a derived categorical factor can be paired to those of another categorical factor or to those of a numerical factor. Since this type of factors directly dependent on other design factors, derived categorical do not contribute to the calculation or power of the DOE design.
A possible use case for deriving categorical factors levels from another categorical factor is when you want the same level to be used across multiple stages of your experiment. For example, you might want to prepare a set of mixtures that use different diluents (setting diluent as a factor), followed by an incubation step, before adding more liquids onto the mixtures using, for each run, the same diluent in this second mixing step as the one used in the first mixing step (Figure 1).
Figure 1. Using derived categorical factors for pairing of categorical factor levels across different stages of your workflow.
A common use case for deriving a categorical factors levels from a numerical factors levels is when dealing with buffers and pH. Often you will be interested in investigating the effect pH has on your biological system. pH is a continuous numerical factor, however, in reality, different pH reagents must be prepared as distinct liquids to use in mixtures.
These distinct pH reagents are thought of as categorical liquids, however the interesting property you want to study is the numerical pH. When you get to your data analysis, you might want to be able to model pH as a continuous numerical factor rather than as categorical choice of liquids whose pH are at specific set points. By doing so, you are able to fit models that allow you to predict optimal pH values that sit between those that were physically tested.
In Synthace, you are able to pair the numerical pH values to categorical liquids, such that when pH 6 is chosen in the DOE design, the categorical liquid “Buffer pH6.0” is used in your mixture (Figure 2).
Figure 2. Deriving categorical factor levels from numeric factor levels. A common use case is pairing numerical pH values to categorical liquid choices (dotted red lines). pH is the factor of interest that will be used in the design and analysis, and needs to be paired to the categorical liquid prepared at the correct and matching pH. This will allow you to analyse pH as a numerical factor when modelling, so you can better identify the optimal pH (dashed black line).
To learn how to derive a categorical factor from another categorical factor, click here.
To learn how to derive a categorical factor from a numerical factor, click here.