The Psychophysics Psyber Lab




Why transform-average mean ROC curves?

by Vit

In 1997, Sue Galvin was working through a draft of the
Type 2 paper and emailed me wondering why we had used
arcsine-transform-averaged hit rates and false alarm rates
to calculate mean ROC curves.

Here was my reply...

It hath to do with averaging
(At least that's my reply)
Of any probabilities
That you may care to try.

With floor and ceilings in effect
It happens near the edge
Of ROC-type spatial squares
Or so I doth allege.

You takes your set of ROCky points
And if they're left alone
Untransformed then ARITH-aved
The axis ain't their home.

Coz any H or F A R
That isn't nought (or one)
Affects your arithmetic curve
The axis will it shun.

Disproportionate effect
Is something to avoid
So transforms of the R O C's
A trick that is employed.

Typically in literature
(That's if they get that far)
Authors might transform to zeds
And give themselves a star.

They take the zeds and average them
And transform back to start
So R O C and axis line
Won't be so far apart.

All this guff was covered well
In nineteen-eighty-five
When MacMillan and Kaplan too
In Psych. Bull. did arrive.

That paper seemed to cover lots
About this thing you seek
But not exactly what you want
So do not spend a week.

Arcsine's used instead of zed
Because it's plain to see
That phi-inverse of nought or one
Will hit infinity.

And thus you need a sigmoid shape
Defined at one and nought
So PC and/or Macintosh
Won't shudder and abort.

Related points are made throughout
The psycho-literature
Most with regards to gamma-phi
Or d-prime to be sure.

A recent paper comes to mind
(though d-prime was its aim)
By Hautas out of Auckland U.
Extreme-zed was the game.

The thing appeared in 'ninety-five
Behavior Research Meth...
Instrums and Computer beasts
You'll see what he sayeth.

If the info content Sue
Of this here little rhyme
Is smaller than one itty-bit
I've wasted all your time.

But if in fact it doth turn out
That handy it may be
P'raps redraft the Type 2 script
In terms of poetry!

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