As a teen I believed the World was run by super-geniuses, but after years of emailing super high IQ people and doing more of my own research, I gradually realized that IQ is to political and economic power as height is to physical power. Just as the World’s most physically powerful man (i.e. heavy weight boxing champ) is typically about 2 standard deviations taller (about 6’3″) than the average American man (about 5’10”), the World’s most powerful man (U.S. President) is typically about 2 standard deviations smarter (IQ 130) than the average American man (about IQ 100). The latter assertion was mostly based on averaging the IQs of JFK (119) and Richard Nixon (IQ 143) both of whom had taken the Otis allowing an apples to apples comparison.

But commenter Ridin with Biden informed me of the following Quora comment:

Kennedy took the original version of the Otis Test, which was in vogue during the first half of the 20th century. The median on that test was 100, and the standard deviation was 10 points. Sometime later in the 20th century, the proprietors of the original test replaced it with a new version, called the Otis-Lennon School Ability Test (OLSAT). But scores between the two tests are not directly comparable, because the OLSAT has a standard deviation of 16.

As for the Wechsler – which is probably the most widely known and respected test – the median is 100, and the standard deviation is 15.

Hence, on that old, original Otis, a score of 119 corresponds with 96th or 97th percentile of all test takers. A Wechsler score of 128 is the 96th or 97th percentile of that test also.

But if the smaller SD upgrades Kennedy to 128 (actually 129), then it should also upgrade Nixon to a freakishly high 165, suggesting the average IQ of U.S. Presidents might be 147! Perhaps the World is run by super geniuses after all!

I decided to do a bit of research.

I found this study showing the Otis did indeed have a standard deviation around 10, at least in children:

Source

But what about teenagers, since this was the age that Nixon and JFK were when tested. For this I turned to the Otis Gamma which was used with older kids and adults.

It should be noted that unlike most tests of that era, which calculated IQ as the ratio of mental age to chronological age, the Otis (or at least the Otis Gamma) assigned IQs based on how far you deviated from the mean of your age group, so if your raw score on the test was 43 points above the mean for your age (as Nixon’s apparently was) you were assigned an IQ of 143. This should not be confused with the deviation IQ where the standard deviation is held constant from age to age.

The test author noted that Gamma IQs found by this method tend to be “somewhat less variable than ordinary IQ’s”; “somewhat closer to 100”. However given that the SD of old Standford Binet age ratio IQs was 16.4, “somewhat closer to 100” needn’t imply less than 15.

I then found a 1971 study where 45 men from the University of Oklahoma part-time employment sample took the Otis Quick scoring Gamma test form C and the 40 minute Raven Advanced Progressive Matrices:

The raw Otis scores ranged from 43 to 76 with a mean of 61.6 and an SD of 9.2. Since the mean score for 18+ year-olds was 42, the assigned IQs ranged from 101 to 134 with a mean of 120. Meanwhile the Raven scores ranged from 14 to 35 with a mean of 24.9 and a standard deviation of 4.6. Using 1962 norms, a score of 14 = 75 percentile and 24 = 95 percentile (a difference of one standard deviation on a normal curve).

Assuming the lowest Otis Gamma IQ (101) of this group was also one standard deviation below the average score (120), then an SD of 19 is implied! Of course extrapolating from just two data points is unreliable and further complicated by the Flynn effect (Raven norms were a decade old and who knows how old the Gamma norms are) and the likely non-interval nature of raw test scores.

Nonetheless, it seems unlikely that the Otis Gamma had an SD as low as 10 (at least in adults).

Update Nov 10, 2020

A quick way of converting Otis raw scores to IQ at different ages:

source

Update Nov 12, 2020

The following source claims the Otis Gamma had an SD of 12.

Source: Mason, E. P., Adams, H. L., & Blood, D. F. (1966). Personality characteristics of gifted college freshmen. Psychology in the Schools, 3(4), 360–365.

If so, JFK’s 119 IQ would become 124 and Nixon’s 143 IQ would become 154 on the 15 sigma scale.

There’s also this:

Source: Traxler, A. E. (1934). Reliability, constancy and validity of the Otis IQ. Journal of Applied Psychology, 18(2), 241–251. doi:10.1037/h0075882 

The 1937 ediction of the Stanford Binet had a mean IQ of 101.8 with an SD of 16.4. Assuming the 1916 edition had the same distribution and was created four years earlier than the Otis (which appeared in 1920), we’d expect it to have a mean of 102.36 at the time of the Otis norming (The Stanford-Binet Flynn effect from 1916 to 1937 was only 1.4 points per decade). Thus:

Otis IQ 111 = +1.01 SD Binet

Otis IQ 108.3 = +0.95 SD Binet

Otis IQ 114.8 = +1.15 SD Binet

Otis IQ 111.4 = +1.05 SD Binet

The line of best fit suggests 9.91 Otis IQ points equates to 1 Binet SD, suggesting the Otis had an SD of 9.91. This suggests JFK’s IQ would be 129 on the 15 sigma scale and Nixon’s would be a superlative 165. But perhaps at this high extreme, Otis scores were not normally distributed and like a Binet IQ of 171 (recall the Binet mean was a bit above 100 and the SD was 16.4) which had about a one in 5000 level rarity, thus equating to a normalized IQ of 153 (sigma 15). These IQs might also be slightly inflated by the Flynn effect ao JFK was perhaps 126 and Nixon was perhaps 152, suggesting U.S. presidents average 139.