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It is frequently observed that percentage data are not normally distributed. If the data are not normally distributed, then they must be transformed prior to ANOVA. The usual transformation for proportional data is arcsine square root, although other transformations e.g. logarithms may give the data a normal distribution. When data have been transformed, the SEM must not be back-transformed. Consequently, it is customary to present the untransformed means and untransformed SEM and say that the statistical analysis was done on the transformed data. Alternatively, the back-transformed means can be presented with confidence limits that have been calculated on the transformed data and back-transformed for presentation.
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