First, I am sorry if this seems very silly, but this is the first time I do any statistical analysis.
I did a study with 10 subjects and I have a couple of questions regarding the statistical analysis I want to perform.
In the study, I am measuring a dependent factor $Y$ in 4 different environments ($E_1$,$E_2$,$E_3$,$E_4$), with 3 different treatment methods ($M_1$,$M_2$,$M_3$).
Each environment affects $Y$ differently. $M_1$ is the control, no treatment method, and each subject is measured in every environment, with every method in a random order.
I used SPSS to perform a two-way repeated measures ANOVA (Analyze > General Linear Model > Repeated Measures). Here is my first question: There are two places I can put my factors: The within-subject factor, and the measurements.
If I put the environments and methods as factors, I get the two-way Repeated measures anova. which tells me that the all factors are significant. i.e. $M$ and $E$ have significance in $Y$ and the interaction between them is significant.
That is great. But what does that tell me?
If I put the environment as a measure, and the methods as factors, I get a more interesting analysis table which tells me the performance of each method in each environment.
I am not sure what do I report here or whether what I did in the second method is at all correct.
The first method is the one I find in all tutorials online, but doesn't tell me anything about the performance of each specific algorithm in each environment. It does tell me how each environment is different from other environments, or how each method is different from other methods, but this is really vague.
I would really appreciate it if you can explain to me the difference between the measurement method and the within subject factor method, and if this comparison I did is correct.