D. H. Robinson, H. Wainer, On the Past and Future of Null Hypothesis Significance Testing ETS, Dec. 2001. www.ets.org/Media/Research/pdf/RR-01-24Wainer.pdf
Apart the oppose paradigms P (data| H0) and P (H0| data) we will say something about the author?s verdict in what concerns NHST at the Classical Statistics point of view.
From the author?s Conclusions and Recommendations the quotations, signalled by an asterisk, we follow a comment.
* NHST, as currently constituted, is a tool of limited usefulness. . . It can be valued to affect sizes and confidence intervals . . .
My humble comment:
Tough they are referring to abuses/misunderstandings users are prodigal to show, seemly even in published papers, we couldn?t be more in agreement. However they made a vicious extrapolation, that is NHST´s need to be supplemented by further information in order to be useful. Nothing more wrong. I will give an example. Let be a parameter comparison: The test statistics has the form W= (w´- w0)/s where w´= observed value, w0 the one of H0, s the standard error of the w´- w0 (data size depending). Perform this, for example one tail test, we will compare W with the critical value, cv , associated to a small tail probability say 0.05. So, if W > cv, H0 is rejected, otherwise we got not sufficient evidence to reject the null hypotheses. Evidently one cannot forget that a rejection simply means that the difference w´- w0 is not attributable to random variation of data but contrarily an effect is present. However how large is it we not know. . . This is the point all anti-NHST vehemently point out! And are right . . . However the straightforward introduction of a term D in the numerator to validate/invalidate the difference solves immediately the difficulty. So, is for me very puzzling because I don?t know if it is a forgery trick (to condemn NHST), or simply sloppy statistical learning. . .] Follow up? This simple modification allows us to test if the D is significant throughout its Confidence Interval [U, V] associated to a chosen alpha. Needless more *inventive thoughts* needed.