Brian I use arcsin(square root(proportion)) anytime I'm doing analysis of percent data. The reason may not be justified for the type of simulation your running, which I'm not familiar with. I use this transformation since percent data is inherently not normally distributed. Arcsin(sqrt(proportion)) does transform the data to near normal distribution.
Jordan -- Jordan M. Marshall, PhD Assistant Professor Department of Biology Indiana University-Purdue University Fort Wayne 2101 E. Coliseum Blvd. Fort Wayne, IN 46805 Office (260) 481-6038 Mobile (865) 919-9811 Fax (260) 481-6087 www.jordanmarshall.com >>> On 11/30/2011 at 12:00 AM, ECOLOG-L automatic digest system <[email protected]> wrote: > Date: Tue, 29 Nov 2011 14:33:19 -0500 > From: =?ISO-8859-1?Q?Brian_Mitchell?= <[email protected]> > Subject: Transformation of percent cover data for power analysis > > Hello ecolog, > > I am working on a power analysis simulation for long-term forest monitoring > data, with the goal of documenting our power to detect trends over time. > The simulation is based on a repeated measures hierarchical model, where > future data is simulated based on the initial data set and a bootstrap of > pilot data differences between observation periods, multiplied by a range of > effect sizes (50% decline to 50% increase). > > My question is about the appropriate transformation to use for percent cover > data in this simulation. I don’t want to use raw percentages because the > simulation will easily result in proportions less than zero or greater than > one. Similarly, a log transform can easily result in back-transformed > proportions greater than one. Most other transforms I’ve looked at would > not prevent back-transformed data from exceeding one or the other > boundaries. The exception is the logistic transform, which would indeed > force all simulated data to be between zero and one when back-transformed. > However, the logistic transform gives values of negative infinity for a > percent cover of zero, and positive infinity for a percent cover of one. I > was thinking that adding a tiny number to zeros and subtracting a tiny > number from ones (e.g., 0.00001) would solve the problem (roughly equivalent > to a log of x+1 transform), but I have been unable to find reference to > anyone using this approach for percent cover data. Does anyone have any > thoughts about the validity of my proposed approach or of another approach > that would help solve my problem? > > Thanks! > > Brian Mitchell > NPS Northeast Temperate Network Program Manager > Adjunct Assistant Professor, University of Vermont > [email protected]
