# Aligned rank transform on time series data

I have some time-series data that I wish to test to see if a certain factor has an effect. There are few samples per time step (10 on average), but the whole time-series has 306 samples. When divided into groups based upon a factor the result is non-normal and non homogeneous. I wish to test the effect of the factor, and if possible, determine a linear trend over the time-series accounting for this effect.

To test the effect, I performed an aligned rank transform on the data, then used an ANOVA. However this does not take into account time. To do this I tried a General Linear Model on the transformed data using the factor as a fixed effect and time as a covariate. Does this sound correct?

What is the correct way to include time information in a factorial analysis when the number of samples per unit time is quite low?

Time Series

Factor

Note: software used is SPSS, stats experience is beginner.

 please clarify "There are few samples per time step (10 on average), but the whole time-series has 306 samples. " Actually show the data and that might help. – IrishStat Apr 21 '12 at 23:27 @IrishStat I've updated with some graphs. Thanks. – geometrikal Apr 22 '12 at 1:44 Can you please present a table of values of three columns showing time , output value and factor . – IrishStat Apr 22 '12 at 1:44 @IrishStat Rather than a table, I have provided a link to a CSV file of the data. I tried to paste in the values into this post but I would have had to format each line. – geometrikal Apr 22 '12 at 2:04 I'm not familiar with the aligned rank transform, but it seems utilizing multi level models (i.e. MIXED in SPSS command lingo) may be a fruitful approach to be able to incorporate any temporal trends (perhaps in the original units instead of the ranked units). – Andy W Apr 22 '12 at 12:23