Einstein was about 5.53 standard deviations (SDs) more academically successful than the average Ashkenazi Jew. The correlation between IQ and academic success is 0.65, so based on simple linear regression, Einstein’s IQ was likely 0.65(5.53 SD) = 3.59 SD higher than the average Ashkenazi Jew.
On a scale where the average white has an IQ of 100 and SD of 15, Ashkenazi Jews likely have a mean IQ of 110. We don’t know their SD so we’ll assume 15. So if Einstein is 3.59 SD smarter than the average Ashkenazi, his IQ would be 3.59(15) + 110 = 164.
On the other hand, Einstein’s brain size was probably 1.93 SD smaller than the average Ashkenazi Jewish male of his era. The within sex correlation between IQ and brain size is generally thought to be about 0.4, so based on simple linear regression, Einstein’s IQ should be 0.4(1.93 SD) = 0.77 SD lower than the average Ashkenazi Jew. Thus based on brain size, his expected IQ would be 110 – 0.77(15) = 98.
So if academic success predicts an IQ of 164, but brain size predicts an IQ of 98, what is his IQ likely to be? Averaging these two estimates would be extremely sloppy. Instead, many years ago a Promethean advised me to use multiple regression. This requires us to know not only how well each predicting variable (i.e. academic success, brain size) correlates with IQ, but also how well they correlate with one another. Well assuming the correlation between brain size and academic success is mediated entirely by IQ, then the product of each variable’s correlation with IQ (0.65*0.4=0.26) tells us their correlation with each other, and from their we can calculate how well each variable predicts IQ independent of the other.
In this case, the standardized regression equation would be:
IQ Z score = 0.59(academic success Z score ) + 0.25(brain size Z score)
So plugging in the variables for Einstein
IQ Z score = 0.59(+3.59 ) + 0.25(-1.93)
IQ Z score = 2.12 – 0.48
IQ Z score = 1.64
In other words, Einstein’s IQ should be 1.64 SD above the Ashkenazi Jewish mean.
In other words:
Einstein’s IQ = 1.64(Ashkenazi SD) + Ashkenazi mean
Einstein’s IQ = 1.64(15) + 110
Einstein’s IQ = 135
Even though an IQ of 135 is extremely high, many people will claim it’s ridiculously low for Einstein and will hate me, and consider me an idiot for even entertaining the possibility that he is anything less than 160. How dare I, a mere blogger, put a number on someone as brilliant as Einstein? I don’t know what Einstein’s IQ was, but 135 would be the statistically expected IQ for an Ashkenazi Jew of his academic success and brain size, assuming I didn’t make any errors and assuming linear correlations through the full range. The combination of academic success and brain size should be quite g loaded, yet perhaps it still gives a wildly wrong number in Einstein’s case.
On the other hand, scholar Arthur Jensen stated:
There are two famous scientific geniuses, both Nobelists in physics, whose childhood IQs are very well authenticated to have been in the mid-130s. They are on record and were tested by none other than Lewis Terman himself, in his search for subjects in his well-known study ofgifted children with IQs of 140 or above on the Stanford-Binet intelligence test.
Although these two boys were brought to Terman’s attention because they were mathematical prodigies, they failed by a few IQ points to meet the one and only criterion (IQ>139) for inclusion in Terman’s study. Although Terman was impressed by them, as a good scientist he had to exclude them from his sample of high-IQ kids. Yet none of the 1,500+ subjects in the study ever won a Nobel Prize or has a biography in the Encyclopedia Britannica as these two fellows did.
It should be noted that the Stanford-Binet back then was an age ratio scale, and thus gave increasingly generous IQs above 130.