I am not even sure if it is appropriate to call this scenario a partially nested design, but I settled for it for lack of a better term.

My design is similar to the following in terms of its overall structure: Suppose we are interested in the effects of (i) caffeine intake (IV 1) and (ii) room temperature (iv 2) on how well people do on a test (DV).

Life would be easy, of course, if this was a 2x2 Factorial design where all 4 possible combinations of the two IVs were available (e.g., +Caffeine/Cold room, -Caffeine/Cold room, +Caffeine/Warm room, -Caffeine/Warm room). But for a reason which does not apply well to this toy example, I could not fully cross the two IVs I am working with. So I have +Caffeine/Cold room, -Caffeine/Cold room, and +Caffeine/Warm room, but not the final combination of -Caffeine/Warm room. So not all combinations are present. If you are in the cold room, you may be either +caffeine or -caffeine, but if you are in the warm room, this necessarily means you are also +caffeine. Similarly, if you are +caffeine, you can be either in a cold room or a warm room, but -caffeine necessarily means you are in a cold room, because this is the only pairing that contains that.

Now, the descriptions of nested designs say that we have a nested design if ALL levels of a factor are fully contained within another factor. This is obviously not the case here, which is why I chose to call it a "partially nested design."

But I would appreciate if someone told me about the right terminology.

Also, what design would be appropriate here? If I had all 4 combinations, I'd use a 2x2 factorial ANOVA. But for the current design, I am puzzled as to what would be the correct choice.

  • $\begingroup$ What is the goal of the experiment? This is still an (uncomplete) anova design, what to be done depends on which contrasts you want to test. Please tell us! $\endgroup$ Commented Oct 25, 2021 at 15:38
  • $\begingroup$ This experiment wants to test the effects of room temperature (cold vs. warm room) and caffeine intake (caffeine vs. no caffeine) on test performance (as measured by a score on a test people take in a room). As you say, this design is "incomplete" in the sense that not all combinations of this 2x2 design are present. I am asking how the data would be analyzed under these circumstances. Only 3 of the 4 theoretically possible conditions are available here. $\endgroup$
    – Freya
    Commented Oct 25, 2021 at 16:38


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