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I have a randomized experimental dataset with six treatments with each approx. N=60. The outcome is a time-series, namely deforestation in a land-use simulation game over 40 rounds.

I managed to show that the impact of the treatments on the state of the land (i.e. number of cummulative cells deforested) is highly significant in a single year, but I have a hard time finding the right method to show that the impact on the ENTIRE TIME SERIES is significant. I'm afraid testing in a single year is overestimating significance, as I can choose any year, adding "researchers degrees of freedom". I could (and successfully did) test every year seperatly, but that seems to be a very unelegant solution.

In more general terms:

I have a single independent variable from one 1 to 6, and my dependent variables is time series for every observation. What I want to do is basically an ANOVA, but feeding it with a whole time series as dependent variable instead of single values for each observation.

If possible, it would be cool if the method also allows for controling for other independent fixed factors, such as player age, occupation etc., and ideally for more than one time series as dependent variable, as I also have data for intensification, savings, cows sold and some other values for every year in the game.

Any expert insights?

My data is a SQL database with a single entry for every round of the time series for every subject, linked to the subject-properties via a unique ID => I can bring it into any shape needed for the analysis. My problem is not to shape it but to find the right test. I'm using mySQL & R.

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A really simple and modest improvement to your approach would be to perform a multivariate ANOVA on the time series treating each year as a separate dependent variable. This would be a multivariate analysis of covariance if you include age as a continuous covariate and occupation as a nominal between-subjects factor. This would be an omnibus test of differences in number of cells deforested across all years based on your independent variables (IVs). When (doesn't sound like a matter of "if") that gives you a significant result, you'd want to follow up with separate univariate ANOVAs for each year, and probably post hoc tests for significant main effects and interactions of your IVs.

This is only a modest improvement because it ignores the likely relationships between consecutive years (in contrast to the likely weaker relationship between the first and last years, for instance). Hopefully another answer can point you in that more sophisticated direction in case you're interested in pursuing it; I wouldn't know how, myself. Also, number of cells deforested may follow a Poisson distribution, because it's a count-of-events kind of variable. You may be able to incorporate this feature with another, better-suited analysis of which I'm also ignorant...but there's a hint to you (and future answerers, hopefully), anyway!

Can't resist adding one more...It sounds like the mere significance of your results won't be particularly surprising or interesting, so you should also take a look at your effect sizes. You may find a trend across your time series (e.g., effect sizes may shrink or grow over the years, despite remaining significant throughout) that turns out to be more informative than the significance of the effects or any failures to reject the null, especially if you're using that tired old $\alpha = .05$ rule to decide when to reject. If you have trend theories to test across levels of your IVs, you might consider contrasts as well (Rosnow & Rosenthal, 2002). Maybe this method could even be adapted to testing trend theories across the dependent variables in the multivariate ANOVA...but there's probably an established way of doing this already about which I don't know, so with respect to the dependent variables, that's more of an aside than a recommendation.

Reference

Rosnow, R. L., & Rosenthal, R. (2002). Contrasts and correlations in theory assessment. Journal of Pediatric Psychology, 27(1), 59-66. Available online, URL: http://jpepsy.oxfordjournals.org/content/27/1/59.full.pdf.

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