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An Israeli reader asked me to convert Israel’s Psychometric Entrance Test to IQ.  According to Wikipedia:

The Psychometric Entrance Test (PET, colloquially known in Hebrew as “the Psychometric“—ha-Psikhometri, הפסיכומטרי) is a standardized test in Israel, generally taken as a higher education entrance exam. The PET covers three areas: mathematics, verbal reasoning and the English language. It is administered by the Israeli National Institute for Testing and Evaluation (NITE) and is heavily weighed for university admissions.

The test may be taken in Hebrew, Arabic, Russian, French, Spanish, or combined Hebrew/English. There are generally five dates the test may be taken each year, between February, April, July, October, and December. Hebrew may be taken at any date; Arabic at four dates; Russian and combined Hebrew/English at two dates; and French and Spanish at one date. Taking the test on two consecutive dates is not allowed; this results in the test being disqualified. The results are valid for university admission for seven years.

Wikipedia provides the following percentiles for the PET

Of course the above percentiles apply only to the subset that takes the PET and not the general Israeli young adult population.  In order to know how select this group is, we need to first know how many Israelis become university age each year (even if they never attend university).

Based on stats from this article, I was able to infer that about 179,000 babies were born in Israel in 2015.  Assuming this is typical of how many are born there each year for the past few decades, then 179,000 become old enough to take the PET each year.  Of these, how many make it through high school and then go on to take the PET?  According to my Israeli reader, only 70,000 take the PET each year which means that the top 2% of test takers (those scoring 725+ overall and 145+ on the subsection) reflect 1400 people.

If we assume that 100% of the most academically skilled Israeli youth take the PET and whatever shortfall there might be is balanced by top foreign talent, then those top 1400 scores reflect not just the highest among the 70,000 test takers, but the highest among all 179,000 Israelis that age.  In other words, the top 0.78% of the general Israeli population.

What IQ does this equate to?  On a scale where the white mean and SD are defined as 100 and 15 respectively, the general U.S. mean and SD are 97 and 15.5.  Israeli’s mean IQ is reportedly 94 (103 for Israeli Ashkenazi, 91 for Israeli Sephardics and 86 for Israeli Arabs) and given it has an ethnically diverse population like the U.S., it’s SD is likely also as high as 15.5.  The normal curve predicts that in a country with a mean IQ of 94 and an SD of 15.5,  the top 0.78% have IQs of 131 (white norms).

Thus:

PET overall score of 725 = IQ 131 (U.S. white norms); 133 (U.S. norms)

PET subsection score 145 = IQ 131 (U.S. white norms); 133 (U.S. norms)

The next question is what is the average IQ of people who write the PET.  About 39% of Israelis of a given birth cohort write the PET each year (70,000 out of 179,000) so PET takers reflect the top 39% of Israeli educational status, which means the median PET taker reflects the top 19.5% of education status.  Normalizing the education distribution, the median PET taker is +0.93 SD in education status.  I don’t know the correlation between IQ and education in Israel, but in the U.S. it used to be 0.7, but has sunk to 0.55 in recent decades.  Let’s split the difference and assume it’s 0.63 in Israel.  This implies PET takers who are +0.93 SD in education would be +0.93 SD(0.63) = 0.59 SD in IQ.  And assuming an Israeli IQ mean and SD of 94 and 15.5 respectively, this equals 0.59(15.5) + 94 = 103.

Thus:

median overall PET score 538 = IQ 103 (U.S. white norms); 106 (U.S. norms)

median subsection PET score 108 = IQ 103 (U.S. white norms); 106 (U.S. norms)

Now that we’ve estimated the IQ equivalents for both the median and the high extreme of the PET distribution, we can tentatively deduce the following linear equations (assuming the relationship is roughly linear):

IQ (white norms) = 0.1497(overall PET score) + 22.44

IQ (U.S. norms) = 0.1444(overall PET score) + 28.32

IQ (white norms) = 0.7568(subsection PET) + 21.27

IQ (U.S. norms) = 0.7297(subsection PET) + 27.19

Because of ceiling bumping, I suspect these formulas greatly underestimate IQ equivalents as you approach the test ceiling.

According to my Israeli reader “most universities, at least the famous ones in Israel require 740 to enter medicine, 700 computer science.”