Pre-1974 SAT to IQ Conversion Table

The table is from the paper 'Conversion Tables for Otis Gamma and Scholastic Aptitude Test,' by Warren W. Willingham and James A. Strickland in the Personnel and Guidance Journal,  41(4), 1962, 356-358.  It took some effort and luck to dig up this obscure paper.  The experience was a bit like finding a Rosetta stone.  ;-)

Some things to note from the paper:

• 'The data are based upon a sample of 403 students who visited the Office of Guidance and Testing at Georgia Institute of Technology during the years of 1957-1960.'
• In this group: Otis Gamma mean = 117, SD = 7.2; SAT mean = 980, SD = 126.
• 'Equi-percentile Scaling: The line of relation between the Otis Gamma and the SAT total score was plotted on the basis of 12 selected percentile points.  The line of relation was almost perfectly linear with no evidence of abrupt curvature at either extreme.  Table 1 shows equivalent scores read from the smoothed line of relation.  In no case did the smoothing amount to more than one point on the Otis scale.'
• 'The correlation between the two scores was 0.58.  The standard error of estimate for the SAT total score was 102; the standard error of estimate for the Otis was 5.8.  This correlation of 0.58 gives a spuriously low impression of the correlation between the SAT and the Otis due to restriction in the range of ability in this sample.'
• 'The best interpretation of the IQ equivalents in Table 1 is as follows: "This is the IQ John would achieve if he were to take the Otis Gamma and do exactly as well (or poorly) as he did on the SAT." '
• 'Tables 1 and 2 should not be extrapolated beyond the values presented.  It is virtually certain that the line of relation and the regression line are not linear throughout the range of possible scores.  In fact, it is probable that abrupt curvature sets in a score levels higher and lower than those included here.'  Based on high-IQ society entrance criteria, this seems to be true.  The line would abruptly curve up at the higher end.  Note that the Mensa criteria of a SAT score of 1250 being equivalent to an IQ of 132 is quite consistent with the table below.  If someone knows why they have 1300 for scores before 1974, please send an email to enlighten me.  Otherwise, I'd consider this table valid for scores before 1974 and after (until the re-centering of 1995).
• The Otis Gamma has a 15.6 SD according to http://groups.yahoo.com/group/cybele/files/pages/col82nrm.htm

Table 1
Equivalent Scores for Otis Gamma and Scholastic Aptitute Test Total Score

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