[R] Freeman-Tukey arcsine transformation

[roger koenker]

As a further footnote on this, I can't resist mentioning a letter  
that appears
in Technometrics (1977) by Steve  Portnoy who notes that

	2 arcsin(sqrt(p)) = arcsin(2p - 1) + pi/2

and asks: "it would be of historical interest to know if any early  
statisticians
were aware of this, and if so, why the former version was  
preferred."  The
latter version seems more convenient since it obviously obviates the  
need
for special tables that appear in many places.



url:    www.econ.uiuc.edu/~roger                Roger Koenker
email   rkoenker at uiuc.edu                       Department of Economics
vox:    217-333-4558                            University of Illinois
fax:    217-244-6678                            Champaign, IL 61820


On Mar 13, 2007, at 1:48 PM, Sebastian P. Luque wrote:

> On Tue, 13 Mar 2007 14:15:16 -0400,
> "Bos, Roger" <roger.bos at us.rothschild.com> wrote:
>
>> I'm curious what this transformation does, but I am not curious  
>> enough
>> to pay $14 to find out.  Someone once told me that the arcsine was a
>> good way to transform data and make it more 'normal'.  I am  
>> wondering if
>> this is an improved method.  Anyone know of a free reference?
>
> My Zar¹, says this is just:
>
>
> p' = 1/2 * (asin(sqrt(x / (n + 1))) + asin(sqrt((x + 1) / (n + 1))))
>
>
> so solving for x should give the back-transformation.  It is  
> recommended
> when the proportions that need to be "disciplined" are very close  
> to the
> ends of the range (0, 1; 0, 100).
>
>
> +---- *Footnotes* ----+
> ¹ @BOOK{149,
>   title = {Biostatistical analysis},
>   publisher = {Prentice-Hall, Inc.},
>   year = {1996},
>   author = {Zar, J. H.},
>   address = {Upper Saddle River, New Jersey},
>   key = {149},
> }
>
>
> -- 
> Seb
>
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