[R] negatively skewed data; reflecting

[Frank E Harrell Jr]

z.dalton at lancaster.ac.uk wrote:
> Hi,
> 
> This problem may be very easy, but I can't think of how to do it.  I have constructed histograms of various variables in my dataset.  Some of them are negatively skewed, and hence need data transformations applied.  I know that you first need to reflect the negatively skewed data and then apply another transformation such as log, square root etc to bring it towards normailty. How is it that I reflect data in R?  I'm sorry if this seems a very simple task, I think it involves going back to Maths GCSE and relearning reflection, rotation, translation etc!  I have searched the internet, but cannot come up with anything useful on how to reflect data.
> 
>> hist(Lsoc)  #how do I reflect Lsoc in R?
> 
> I am grateful for any help regarding this matter, it is just a very small part of my analysis and doesn't seem worth agonising hours over.  I will probably kick myself when someone tells me the answer!
> 
> Thank you very much,
> 
> Zoe

To add further complication, if the transformation to normality is 
empirically based, the true variance of resulting estimates will inherit 
the variance from the empirical assessment.  For example, if you use a 
histogram or empirical CDF to find the transformation, the imprecision 
of the empirical CDF will add a good deal of true variance to the final 
estimates so that they are no more precise than sample quantiles on the 
original scale.  To put it another way, the sample median seems to be 
inefficient (efficiency 2/pi) compared to the sample mean if normality 
holds, but that relative efficiency rises if normality were "rigged".
-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University