Reply to Rick Rosner on Comparative Statistics

for the LAIT and the Mega Test

Kevin Langdon

(reprinted from Noesis #125)

Starting from questions raised by Paul Maxim, Rick Rosner published a
study of comparative scores of a sample of testees who reported LAIT scores on their Mega
Test answer sheets in *Noesis* #121. Rick was surprised to find that the Mega
scores of those reporting scores on both tests were significantly lower than their scores
on the LAIT.

Persons who took the LAIT and the Mega usually took the LAIT first and were selected into the population exposed to the Mega Test through memberships for which their LAIT scores made them eligible. One-fourth of this sample reported LAIT scores above four sigma; over four-fifths were above three sigma, with a mean of 3.45 (I.Q. 155). Thus it is not surprising that their LAIT scores tend to be somewhat higher than their Mega scores and scores on other tests reported on Mega answer sheets.

I performed a norming of the Mega Test in September 1996, using Ron's 1984 data set. I used 98 score pairs on five tests: the AGCT, the GRE, the Terman Concept Mastery, the WAIS, and the LAIT. Almost half the data (46 score pairs) was on the LAIT. The overall correlation between the Mega and the previous tests used (weighted by their correlation with the Mega) was only .36, primarily because its correlation with the LAIT for this sample was unusually low, .35, but composite correlations are generally somewhat lower than the average correlations for individual tests. My norming yielded a ceiling of 178 and a floor of 118.

I had put this aside as a statistical fluke, thinking that I had arrived at a result farther from Dr. Hoeflin's than is actually the case; over most of the test range, the I.Q. I assign to a given raw score is one to two points below that assigned by Dr. Hoeflin, an insignificant difference. It's only at the extreme ends of the scale that my figures differ markedly from his. I have added the ``best fit'' line to the chart on the following page, from Dr. Hoeflin's sixth norming report on the Mega Test.

I didn't have Dr. Hoeflin's person x item data, so I could not perform an item analysis or calculate all the statistics I usually do for my own tests. I calculated the correlation between the LAIT and the Mega for this sample, which was .61. Given this correlation, some degree of regression to the mean is clearly to be expected. The actual mean was 24.0 (I.Q. 150, by Dr. Hoeflin's norms; I place it at I.Q. 148). It may be possible to refine the numbers a little bit by working with a larger sample, but any professional statistician (or competent amateur) would come up with a relationship very close to the one indicated here.

I also constructed a stratified sample of 26 LAIT testees with the same distribution of Mega scores as that of LAIT scores in the Mega sample and calculated the correlation between the tests for this sample, which was .65. The mean LAIT score for this sample was 159.0. The mean Mega score was 30.0 (I.Q. 156, according to Dr. Hoeflin; 155 by my calculations). Simply matching the stratification of scores on the LAIT and constructing a subsample reduced the I.Q. discrepancy by almost half.