Analysis of two factor factorial experiment under CRD

Two-way ANOVA can be used when you have one measurement variable and two nominal variables, and each value of one nominal variable is found in combination with each value of the other nominal variable. It tests three null hypotheses.

• The means of observations grouped by one factor are the same.
• The means of observations grouped by the other factors are the same.
• There is no interaction between the two factors. The interaction test tells you whether the effects of one factor depend on the other factors.

When the interaction term is significant, the usual advice is that you should not test the effects of the individual factors.

One experimental design that people analyze with a two-way ANOVA is repeated measures. In this design, the observation has been made on the same individual more than once. This usually involves measurements taken at different time points or at different places. Repeated measures experiments are often done without replication, although they could be done with replication.

Another experimental design that is analyzed by a two-way ANOVA is randomized blocks. This often occurs in agriculture, where you may want to test different treatments on small plots within larger blocks of land. Because the larger blocks may differ in some way that may affect the measurement variable, the data are analyzed with a two-way ANOVA, with the block as one of the nominal variables. Each treatment is applied to one or more plots within the larger block, and the positions of the treatments are assigned at random.

Here, the example used shows the enzyme activity of mannose-6-phosphate isomerase and MPI genotypes in the amphipod crustacean. Amphipods were separated by gender to know gender also affected enzyme activity.