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So, here's the situation:

I have some simulation results, from a simulation driven by two parameters. One of these parameters has two settings, the other has four each was replicated ten times for a total of 80 sets of results.

Each simulation produces results for each of four groups. The progress of each group was measured by seven variables. Thus there are 28 results from each simulation.

I am certain (due to the implementation of the simulation) that these results are to some extent influencing each other. Three of the outcome variables describe how well the group did in intergroup competitions (which influenced the quantity of rescources available to the group) and four describe the behaviours that the agents learned to use (which is influenced by the quantity of resources available to the group)

What I'd like to test is: Did the two parameters influence the four behaviour outcomes and if so in what direction? Did the groups that performed well or poorly in the intergroup competitions (as measured by three variables) behave differently (as measured by these four variables) and if so how?

For some reason I'm struggling to get my head around the right approach to take here, but I've got the nagging sensation that it should be obvious.

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Let me see if I'm getting this right: You have two input parameters, one with two levels and one with four, for a total of 8 combinations. For each combination, you ran a simulation with 4 learning agents which cooperated (?) with each other. During the simulation, you measured (by three output variables) how successfully the four agents obtained resources and also whether they learned four behaviors (4 output variables). Now you want to know whether the parameters influenced the ability to learn the bevaviors and if so, did the more successful teams behave differently? Is that right? – Wayne Jul 15 '11 at 18:05
Essentially that's correct. Technically it's not quite, since there are 4 groups, each consisting of several hundred agents, but since the outcome variable is "average X for agents in group 1, average X for agents in group two etc." I assume you could analyse it in the same way. If it helps the agents are all learning agents and the outcomes are expressions of the rules they adopt (i.e. how many agents in group one adopted a cooperating rule, how many adopted a cheating rule etc.) I tried to keep the details of the simulation to a minimum to avoid confusing the issue regarding the stats. – Greg Jul 15 '11 at 21:52
"Now you want to know whether the parameters influenced the ability to learn the bevaviors and if so, did the more successful teams behave differently? Is that right?" This is pretty much on the money, I was actually wondering whether more successful teams behaved differently as a result of their success, if there's a test that'd let me show the direction of that effect that'd be great, but I assume that there wouldn't be and I'd have to show the relationship was there and then argue the causality from the nature of the simulation? – Greg Jul 15 '11 at 21:56
Each group (of the 4) do share the same two parameter settings, correct? I think so, but it also sounds like the groups are somehow competing or different from each other. – Wayne Jul 16 '11 at 1:47
Yes, each group shares the same parameter settings (in a given simulation) The agents in the groups are initialised randomly, so there are differences between them from the start. They also learn individually, so the learned behaviours in one group may differ from another. Additionally they are competing with each other (The total resources of the agents in one group are compared to the total resources of the agents in another group, the winning group gets some additional resources) – Greg Jul 16 '11 at 9:23

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