In a 3 × 2 × 4 design, there are _____ factors and _____ treatment conditions (cells).

a. 3; 9

b. 24; 3

c. 3; 24

d. 9;3

In the factorial design a×b×c

• The number of variable is three, so the number of factors involved in this experiment is 3.
• Also, the design represents that there are a number of levels of the first factor, b number of levels of the second factor and c number of levels of the third factor hence total number of levels is a+b+c (which is also called treatment conditions).

Hence the given design is 3×2×4 means;

• Number of factors = 3
• Number of treatment conditions =9(3+2+4)

Hence, in a 3×2×4design, there are 3 factors and 9 treatment conditions (cells).