# 2x2 Anova with simple generated data

I have generated data to understand a (repeated measures) 2x2 Anova better, however the results leave me baffled. The data is really simple: I am assuming I have 30 subjects, I am assuming that there are two medical tests, one in body region A, and one in body region B. I have created now the data as follows:

• Test1, region A: normal vector with mean 0.5 and standardeviation of 0.2
• Test1, region B: normal vector with mean -0.5 and standardeviation of 0.2

• Test2, region A: normal vector with mean -0.5 and standardeviation of 0.2

• Test2, region B: normal vector with mean 0.5 and standardeviation of 0.2

This is quite observations we really have: Test1 shows excitation of some substance in region A but inhibition in region B, while Test2 shows excitation of some other substance in region B but inhibition in region A.

Now the results of the ANOVA does show significant interaction of test and body region, however there is no significant main effect of region (p=0.86) - how can that be...? For both tests, the regions have clearly different measurement values. Help appreciated

• Yes, the main effect of a factor is computed by integrating over all the levels of the other factors or predictors. If $A_1$, $A_2$ and $B_1$ and $B_2$ are the values of test 1 and 2 in region A and B, respectively, a significant main effect of "region" would indicate that $\frac{{\left( {{A_1} + {A_2}} \right)}}{2}$ is different from $\frac{{\left( {{B_1} + {B_2}} \right)}}{2}$ Jan 10 '18 at 14:12