In the amphipod example, imagine that female amphipods of each genotype have about the same MPI activity, while male amphipods with the SS genotype had much lower MPI activity than male FF or FS amphipods (they don't, but imagine they do for a moment). The interaction test tells you whether the effects of one factor depend on the other factor. Null hypothesesĪ two-way anova with replication tests three null hypotheses: that the means of observations grouped by one factor are the same that the means of observations grouped by the other factor are the same and that there is no interaction between the two factors. This is most commonly done without replication (one plot per block), but it can be done with replication as well. Each treatment is applied to one or more plot within the larger block, and the positions of the treatments are assigned at random. 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. This often occurs in agriculture, where you may want to test different treatments on small plots within larger blocks of land. Randomized blocks: Another experimental design that is analyzed by a two-way anova is randomized blocks. If the goal is to determine whether a particular exercise program affects running speed, there would be little point in testing whether individuals differed from each other in their average running speed only the change in running speed over time would be of interest. In a repeated measures design, one of main effects is usually uninteresting and the test of its null hypothesis may not be reported. Repeated measures experiments are often done without replication, although they could be done with replication. Sometimes the repeated measures are repeated at different places rather than different times, such as the hip abduction angle measured on the right and left hip of individuals. Because individuals would start with different running speeds, it is better to analyze using a two-way anova, with "individual" as one of the factors, rather than lumping everyone together and analyzing with a one-way anova. For example, you might measure running speed before, one week into, and three weeks into a program of exercise. This usually involves measurements taken at different time points.
Repeated measures: One experimental design that people analyze with a two-way anova is repeated measures, where an observation has been made on the same individual more than once.
You can also do two-way anova without replication (only one observation for each combination of the nominal variables), but this is less informative (you can't test the interaction term) and requires you to assume that there is no interaction. For our amphipods, a two-way anova with replication means there are more than one male and more than one female of each genotype. Unlike a nested anova, each grouping extends across the other grouping: each genotype contains some males and some females, and each sex contains all three genotypes.Ī two-way anova is usually done with replication (more than one observation for each combination of the nominal variables). Because I didn't know whether sex also affected MPI activity, I separated the amphipods by sex. The nominal variables (often called "factors" or "main effects") are found in all possible combinations.įor example, here's some data I collected on the enzyme activity of mannose-6-phosphate isomerase (MPI) and MPI genotypes in the amphipod crustacean Platorchestia platensis. You use a two-way anova (also known as a factorial anova, with two factors) when you have one measurement variable and two nominal variables. It tests three null hypotheses: that the means of the measurement variable are equal for different values of the first nominal variable that the means are equal for different values of the second nominal variable and that there is no interaction (the effects of one nominal variable don't depend on the value of the other nominal variable). Use two-way anova 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.
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