Double arcsine transformation

[Shannon Lange]

Hello,

I am running a meta-regression of proportions, but before doing so I would like to transform my data using the double arcsine transformation. Can anyone confirm whether "asin" is the correct command here?

generate sens_arc = asin(sqrt(v1))

Thank you to anyone who can shed some light on this, as I see very little in terms of applying the double arcsine transformation to your data in the Stata literature outside of using metaprop.

Shannon

[Nick Cox]

I've never seen this transformation called "double". Can you give a reference for that?

The angular transformation, sometimes called the arcsine, transformation, is indeed the arcsine of the square root. But Stata will return an angle in radians, which may not what you want.

[Shannon Lange]

In the following article on metaprop (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4373114/), it is referred to as double arcsine with reference to

Freeman MF, Tukey JW. Transformations related to the angular and the square root. Ann Math Stats. 1950;21(4):607–611.

[Nick Cox]

I think you'll find that Freeman and Tukey were suggesting something with two terms, not as in your #1.

[Shannon Lange]

Correct me if I am wrong, but a proportion essentially has two terms... those with (v1) and those without (v2)

[Nick Cox]

That's true, but not what I think is meant here. I don't have time to look at the Freeman and Tukey paper right now, but I will come back to this if someone else doesn't resolve it first.

[Nick Cox]

Freeman, M. and Tukey, J.W. 1950. Transformations Related to the angular and the square root. The Annals of Mathematical Statistics, 21: 607-611. http://www.jstor.org/stable/2236611

refer to (in Stata syntax)

asin(sqrt(x / (n + 1))) + asin(sqrt((x + 1)/(n + 1))

where x is a count and n the total possible count.

Perhaps it's this that is being referred as "double".

[Nick Cox]

An extra parenthesis is needed in #7.