@Scortchi the paper is by cognitive scientists. and not ecologists. At this point I would settle for arcsine, or any transform, as opposed to untransformed percent correct.
@StrongBad: Well the arcsine square root transformation isn't so bad for binomial data when the counts are not too low, the sample sizes about the same, & the main problem with an ANOVA on untransformed data is therefore heteroskedasticity.