# General Linear Model using proportions as raw data - transformation needed?

#### DeanP

##### New Member
Hi,

I have become confused in my reading of analysis of proportions. I was all set to analyse my data using a general linear model after transforming the proportions using an arcsine-square root transformation, but now I'm not sure if this is a correct approach and more importantly why/why not!

The data comprises time-activity budgets of group-living animals. Each group was followed for a variable period of time (30min to 6hours) and the time they spent alone or with another group was calculated as a proportion of the total observation time. I collected data from multiple groups in six months of two consecutive years (not all groups were present or sampled in each month, nor visited an equal number of times each month). I also collected data from two months in a third year, but because of the gaps in the sampling I'm unsure whether I can include this third year in the same analysis.

I wish to analyse whether the time groups spend associating with one another differs among months within a year and between years (i.e. is it temporally variable? and if so, is this consistent between years?).

The analysis I envisaged was a general linear model with the following parameters:
1) month as a fixed factor
2) year as a random factor
3) month*year as an interaction term
4) group identity as a random factor
5) 'proportion time groups associating' as the response variable once arcsine-square root transformed
Sample sizes were as follows:
Year 1:
Jul - n=6 (first month of study so sampling was poor)
Aug - n=13
Sep - n=15
Oct - n=12
Nov - n=11
Apr - n=20
Year 2:
Jul - n=33
Aug - n=23
Sep - n=4
Oct - n=30
Nov - n=14
Apr - n=14
Year 3:
Aug - n=19
Apr - n=19

QUESTIONS:
1) Is transformation of proportions necessary/appropriate?
2) Can I include the third year in the one analysis? Or should I run a second analysis including only data for Aug and Apr of the three years?

Any advice would be greatly appreciated.

Thanks,
Dean