Date: Dec 31, 2012 12:45 PM
Author: Luis A. Afonso
Subject: Cohen´s d and the current NHST
Cohen´s d and the current NHST
Facing an observed pair of mean values <x> and <y> Jacob Cohen (1923-1998) knows two things:
____1_____Each one is liable to have random fluctuations,
____2_____The difference, or each one mean, should be scaled by a standard deviation. If fact he got that a large difference <x> - <y> for very dispersive data is much less important/significant than for a very close together one.
So, he defines a ´suitable difference (my say) ´ as
______d= (<x> - <y>)/s (Cohen?s d).
And because he had no idea how to define s: ascribing to the undisturbed y or to the treated x or both, left it to the reader?s expertise to chose. No matter, Wikipedia states he is famous by the find . . . supposedly he was the first psychologist to think about . . .
No important . . .
This and other avatars I come to know about NHST is that Statistics teachers did not emphasize that a single term change all things, namely
_______W= (<x> - <y> - D)/s ,
When the shift D is considered as a constant W it follows the same distribution than the difference <x> - <y> and in consequence one is immediately liable to calculate a Confidence interval for D at a preset level.
Cohen as an inventor . . .
Luis A. Afonso
Happy new Year . . .