We begin by looking at a simple 2*2 factorial with 5 replications in a CRD (completely randomized design). Let the following table denote mean yields, Yij MAIN EFFECT OF P, MAIN EFFECT OF N What we see is that the difference between low P and high P is a difference in mean yield of 40 – 31 = 9 in our sample. Is there a nonzero difference in the population? INTERACTION OF P AND N We see that this difference, 9, is not consistent over the levels of N. When N is low (n” ) a change in P produces an increase 6 in yield. When N is high, the increase in P (from p” to p# ) produces an increase in yield of 12. The effect of P depends on the level of N in our sample. Another way to say this is that N and P interact in the sample. Is this interaction large enough to declare a nonzero interaction in the population?