'THE PROBABLE ERROR OF A MEAN' by Student:

Now any series of experiments is only of value in so far as it enables us to

form a judgment as to the statistical constants of the population to which the

experiments belong. In a greater number of cases the question finally turns on

the value of a mean, either directly, or as the mean difference between the two

quantities.

Gloss: if the test doesn't give us knowledge of the underlying population distribution, it is not relevant.

Student > C&B

Bam.

Ref:

Biometrika, 6 (1908), pp. 1–25, reprinted on pp. 11–34 in “Student’s” Collected Papers, Edited by E. S. Pearson and John Wishart with a Foreword by Launce McMullen, Cambridge University Press for the Biometrika Trustees, 1942, p.1Hahahaha, did you just quote an article from 112 years ago that doesn't define "test statistic" to defend your misunderstanding of the definition of test statistic? That's amazing stuff.

The quote is even less relevant since it's already been explained how the coefficient can be used in hypothesis tests on population parameters -- compare it to a t distribution scaled by the standard error. Done. Sad you're too dim to get this basic stuff. Maybe ask a random person on the bus to explain it to you? I'm sure they could get it.

The contention is not that the coefficient is used in the test statistic but that it *is* the test statistic. You're equivocating in order to wriggle your way out of a statement that is clearly wrong.

Student's paper is relevant because it lays the groundwork for the hypothesis test we're talking about.