R help - Mar 2011 - Normalising proportional binomial data that has a set top value

I've got some data in proportional format which has a set maximum value of
0.5 and I want to know how to normalise it.

I've calculated a lateralisation index to determine whether an organism
deviates from an equal number of left and right turns within a trial (as
opposed to measuring the proportion of left and right turns in total).  My
proportions are therefore between 0 (equal number of left and right turns)
and 0.5 (all turns in the same direction, either left or right).

I want to analyse the data using an ANOVA to test repeated measures for the
repeatability coefficient but recognise I will have to normalise the data
for it to work properly.

Any help is much appreciated.

SB

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