Dear,
I've trasformed my data to avoid problems of non-normality and heteroscedasticity. Then I made the statistical analysis and the post-hoc test. Now, when reporting my data, which data should I report?
The original one or those transformed?
Thanks.
Either can be reported, or both. If the transformation is simple and common, it sometimes makes sense to report the transformed values: "mean log10(concentration)". In other cases, you can report the "back-transformed" data, or data "on the original scale." In a plot, sometimes using the original data makes the plot unreadable.
If you don't transform, you don't need to decide on that;
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
Either can be reported, or both. If the transformation is simple and common, it sometimes makes sense to report the transformed values: "mean log10(concentration)". In other cases, you can report the "back-transformed" data, or data "on the original scale." In a plot, sometimes using the original data makes the plot unreadable.
Giacomo -
Since you mention heteroscedasticity, I assume you are talking about regression.
Transformations can really complicate interpretation of results. Do you really need to do that? Is the relationship really nonlinear, or are the data just skewed, and you may still have a linear regression?
I have noted that many people seem to think the data need to be 'normally' distributed when the estimated residuals (or better, the random factors of the estimated residuals when you account for heteroscedasticity) are what are ideally close to normally distributed, but as long as the central limit theorem comes into play, even that is not a big concern. If you have skewed data, but linear regression with heteroscedasticity, here are a number of examples of that from the area of official statistics, where an example there, and the reference list, might be helpful:
https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development
Regarding heteroscedasticity in particular, here are a couple of papers explaining it in detail, concentrating on population statistics, not time series:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity
If you actually have a nonlinear regression, you could research that. If you have count data, you may need poisson regression.
Further, would a transformation even put your data into a form close enough to be helpful?
The following is a very good book, which may be helpful:
Carroll and Ruppert(1988), Transformation and Weighting in Regression, Chapman & Hall, Ltd. London, UK.
I read that entire book a number of years ago, and recall it was informative.
I hope that something above may address your issue.
Cheers - Jim
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