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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.

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  • $\begingroup$ Different measurements are simply different dependent features, all of them are of interest, but "in parallel", they do not constitute a RM-factor which levels are to compare. However, if different "measurements" are of the same units, output table "Multivariate effects" is still valid for them combined. Example is strength of left arm vs right arm across three month of physical training. Month is the RM factor, Arm (left or right) - you can decide whether make it the second RM factor (so interaction can be tested) or leave it simply as another measurement (feature) explored in parallel. $\endgroup$ – ttnphns Jul 18 '19 at 13:41
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The discussion above is largely accurate in distinguishing between measures and levels of repeated measures factors: measures are distinct dependent variables that you want to include in multivariate analyses but do not want to compare to each other as you would the levels of a within-subjects factor.

In running a two-way repeated-measures model, you can also look at the effects of methods separately within environments by looking at simple main effects using the EMMEANS subcommand with the structure:

/EMMEANS TABLES(method*environment) COMPARE(method)

This requires using the command syntax; there is currently no way to specify it in the dialog boxes.

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