How do I randomly assign participants in a factorial experiment?


This is done essentially the same way as in an RCT, except instead of assigning people to 2 or 3 conditions, you need to assign people to many more conditions. One way to approach random assignment in a factorial experiment is to produce many sets of permutations of the integers from 1 to C where C is the number of conditions, and use these numbers to assign subjects to conditions in a permuted block fashion. For example, suppose you were conducting a 23 factorial experiment, which of course has 8 experimental conditions, and you want to assign 160 subjects. You could use software to conduct random sampling of the integers 1 through 8 without replacement, and repeat this 20 times. You now have 20 lists of the numbers 1 through 8 randomly assorted, in other words, 160 random numbers. Then you can use these numbers to assign each of the 160 subjects. This approach will ensure that the experimental conditions fill up approximately evenly.

There are other approaches to random assignment in factorial optimization trials. We recommend the excellent article by Gallis et al. (2019).


Gallis, J. A., Bennett, G. G., Steinberg, D. M., Askew, S., & Turner, E. L. (2019). Randomization procedures for multicomponent behavioral intervention factorial trials in the multiphase optimization strategy framework: challenges and recommendations. Translational Behavioral Medicine, 9(6), 1047-1056.

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Further Learning

Whether you are looking for additional support as you prepare a grant proposal involving MOST or practical information helpful in managing your optimization trial, this section provides resources for a deeper dive into intervention optimization.

REDCap with Most

The goal of this manual is to show how one might setup a REDCap project to support a research study with multiple conditions, such as factorial experiments common in the Multiphase Optimization Strategy (MOST) framework.

Informal introduction to factorial experimental designs

The purpose of this page is to clarify some concepts, notation, and terminology related to factorial experimental designs, and to compare and contrast factorial experiments to randomized controlled trials (RCTs). A more in-depth introduction can...


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