# Calculating power for balanced incomplete block design

My experiment has a factorial 2x2 design: 2 factors are manipulated at levels 'high' and 'low'. We thus get 4 conditions:

• Condition 1: Factor A high, Factor B high
• Condition 2: Factor A high, Factor B low
• Condition 3: Factor A low, Factor B high
• Condition 4: Factor A low, Factor B low

Overall, I am interested in the differential effects of Factor A and B on the DV.

Now, I want to randomly allocate participants to participate in 2 out of 4 conditions: so they can get Condition 1+2, Condition 1+3, 1+4, 2+3 etc.

However, before I start my data collection, I want to determine the required sample size for this study with a power analysis. I first wanted to treat it as 6 separate conditions with each a within-subjects factor, but this does not really add up since the different IVs are spread across participants.

Could anyone advise me on how to do a power calculation for this sort of experimental design?

(Also a side-question: is there a formal name for this type of experimental design?)

• For your aside question, I think you are looking for "latin square". – B.Liu Mar 15 at 16:37
• Thanks! Useful! :) – Sari Nijssen Mar 16 at 9:23
• I've searched a bit more and it looks like the design is calld a 'balanced incomplete block design' which is a variant of a latin square - I think – Sari Nijssen Mar 19 at 13:01