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Suppose I gather data from an experiment with 2 treatments: a_1 and a_2. There are 3 blocks b_1 through b_3.

Each subject experiences only one treatment (either a_1 or a_2, not both). Each block experiences both treatments. Each combination (subject, block, treatment) results in a continuous (time) observation.

Subject Block Treatment a_1 Treatment a_2
1 b_1 Value
1 b_2 Value
1 b_3 Value
2 b_1 Value
2 b_2 Value
2 b_3 Value

This table continues until all subjects (people) are covered.

I know this isn't RCBD because not all treatments are applied each time.

What is the name of this experimental design? I need to find a formula to help with sample size calculation (no data have been gathered yet, this is just in the brainstorming phase).

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In analysis of variance (ANOVA) speak, this is referred to as a mixed factorial ANOVA, which can be used to test between-subjects differences (here, treatment) as well within-subjects (i.e., repeated measures) differences (here, block). In your case with two factors, of which one has two levels (treatment) and one has three levels (block), one could refer to this as a 2x3 mixed design.

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  • $\begingroup$ Doesn't 2x2 mixed design refer to 2 treatments and 2 blocks? Here I have 3 blocks. $\endgroup$
    – StatsSorceress
    Commented Nov 25 at 19:07
  • $\begingroup$ @StatsSorceress, yes, you are correct. I edited my answer accordingly. $\endgroup$
    – Brandmaier
    Commented Nov 27 at 7:51

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