Excerpt from a Letter from Ronald K. Hoeflin

(reprinted from Noesis #129)

March 15, 1997

In issue 125 there seems to be a contradiction in Kevin Langdon's contention that there should be a straight ``best fit'' line for scaling IQ's vs. raw scores on the Mega Test, and his contention that allowance may be made for a ``ceiling bumping effect.'' On the first horn of this dilemma he remarks on page 13, paragraph 5: ``[there is a] strictly linear relationship of IQ to scaled score which I insist upon as reflecting the conclusions that can be validly drawn from the data.'' On the second horn of the dilemma he remarks in paragraph 3 on that same page: ``we can reasonably allow one point for ceiling bumping and accept 46 [raw score]/175 [IQ] as our qualifying level [on the Mega Test].'' My reply is that the curves both at the top and the bottom of my scaling for the Mega Test [see the graph in Rick Rosner's comments on the LAIT in this issue --KL] are precisely there to allow for both the ``ceiling bumping'' effect as well as a floor-bumping effect. Moreover, the curve at the bottom of my graph is based in part on calculated points, not purely on guesswork. The curve at the top of my graph could reasonably be regarded as the mirror image of the effect of floor-bumping at the bottom of the graph. Furthermore, I have repeatedly reminded Kevin over the years of the article titled ``Equivalent Scores for the Graduate Record Verbal and Miller Analogies Tests,'' by Edward E. Cureton and Thomas B. Scott, that was published in Educational and Psychological Measurements (1967, vol. 27, pp. 611-615). Their method clearly permits curved and not just straight lines in scaling one test against another (as my test was scaled against the SAT). Of course one can rationally disagree about just how much to bend one's line in order to allow for ceiling- (or floor-) bumping effects. But clearly Kevin's insistence upon a ``strictly linear relationship'' is contradicted even by his own remark that allows an adjustment to be made for ceiling-bumping. And my ``mirror-image'' argument provides at least a prima facie case in favor of the degree to which I bend the line at the upper end of the scale, since the bend at the lower end was calculated, not merely imposed by fiat.