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I have recently began studying a course on Designed Experiments and am having some trouble understanding some of the terminology. I've looked at some other answers on the site and I think that I am understanding correctly, but would like some clarification (and potentially more detail if there is anything of note).

I have seen that "factors" refer to a structure that splits units into groups. I can also see that "treatments" are a description of what can be applied to experimental units and that "blocks" divide up the experimental units into groups of a similar structure.

My understanding from a previous answer is that factors can be split up into two categories - treatment factors and block factors. I believe that treatment factors are those that we are interested in investigating the impact of and block factors are those that are necessary for the setup of the experiment but are not of any interest in our experiment.

My question is whether or not this simplified understanding of blocks, factors, and treatments is an accurate model for me to use when trying to understand these concepts and if there is a better way to understand this.

EDIT: for clarity, I am studying a course called "Designed Experiments". The primary textbooks that the course is based on are "Design and Analysis of Experiments" by Douglas Montgomery and another book with the same title but by Clarke Kempson.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Feb 7, 2023 at 21:52
  • $\begingroup$ I think I’ve made the problem quite clear, but if there’s anything specific, let me know @Community $\endgroup$
    – FD_bfa
    Commented Feb 7, 2023 at 23:25

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I think your understanding is good as a start. I am no great fan of the Montgomery book (the other you mention I do not know), a useful supplement would be Box, Hunter & Hunter: Recommended books on experiment design?

One principle from there is "Block what you can, randomize what you cannot" that is, known sources of heterogeneity in experimental material is used to define blocks. See also What is a block in experimental design?

My understanding from a previous answer is that factors can be split up into two categories - treatment factors and block factors. I believe that treatment factors are those that we are interested in investigating the impact of and block factors are those that are necessary for the setup of the experiment but are not of any interest in our experiment.

Maybe one can subdivide further. In some experiments (for instance for product design) there is factors that can be controlled under experimental conditions, but not under future product use. These might be called noise factors, and are similar to blocks, but are actually of interest, because you want product properties to not be unduly influenced by them! See for instance Factors in Taguchi designs.

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  • $\begingroup$ Thank you for your answer. Could I ask why you don’t like the Montgomery book? $\endgroup$
    – FD_bfa
    Commented Feb 9, 2023 at 19:30
  • $\begingroup$ I think that book is to focused on specific designs and algorithms, and not sufficient on general applicable principles! $\endgroup$ Commented Feb 9, 2023 at 20:06
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    $\begingroup$ @FD_bfa, I, too, highly recommend Box, Hunter, Hunter, especially the "boys shoes" example for understanding blocks/treatments and think this is a good general answer. Understanding the differences between treatment structure and block structure is massive with respect to being able to design and analyze experiments. I really like Stephen Senn's work on this, for example: errorstatistics.com/2019/03/09/… $\endgroup$ Commented Feb 10, 2023 at 20:35

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