Percentile ranks of SAT subscores

__Discussion__: In the Sixth Norming of the Mega Test, Dr. Hoeflin estimated that a factor-of-3 shift in SAT
percentiles would be reasonable to find general-population percentiles, since approximately the best third
of high school seniors take the SAT. He showed that results obtained using this estimate agreed closely
with results obtained from five standard I.Q. tests (up to the 4-sigma level). The following table, which
comes from my [DTM] 1977-78 student report, compares "college bound seniors" (i.e., those who
normally take the SAT) and a "national sample of high school seniors" (i.e., all high school seniors, whether
or not they are college bound, which would hence include seniors who would not normally take the SAT).

Dr. Hoeflin's factor-of-3 estimate agrees rather well for subscores of 500 and above, as shown in the table below. As an example of how Dr. Hoeflin applied his factor-of-3 shift, for a Mathematical score of 500, 73 percent of college-bound seniors would score below that level and 27 percent would score above it. He then divided 27 by 3 and got 9, and so assumed that if all 18 year olds had taken the SAT, 9 percent would have scored above 500 and 91 percent would have scored below it. The actual figure was 88 rather than 91. This is equivalent to an I.Q. discrepancy of only 2 I.Q. points, since the 88th percentile is about 119 IQ and the 91st percentile is about 121 IQ [Note: I have placed IQ equivalent values in parentheses that correspond with the percentile ranks, assuming a normal distribution]. Dr. Hoeflin's estimates get more accurate as one gets to higher and higher levels, although the College Board's pamphlet is of no use above 700 (or 650 in the verbal section of the table) because it doesn't use precise percentiles above the 99th percentile.

Dr. Hoeflin provides part of a similar table (from the 1979-80 SAT student report) and similar discussions
in the January 1991 issue of *In-Genius* (#25) and in the April 1993 issue of *OATH* (#10).

Verbal | Mathematical | |||||

Score | College bound seniors | National high school sample (IQ equiv.) | Dr. Hoeflin's estimate for all 18 year olds (IQ equiv.) | College bound seniors | National high school sample (IQ equiv.) | Dr. Hoeflin's estimate for all 18 year olds (IQ equiv.) |

800 | 99+ | 99+ | . | 99+ | 99+ | . |

750 | 99+ | 99+ | . | 99 | 99+ | . |

700 | 99 | 99+ | . | 96 | 99 (137) | 98.7 (136) |

650 | 96 | 99 (137) | 98.7 (136) | 92 | 98 (133) | 97.3 (131) |

600 | 92 | 97 (130) | 97.3 (131) | 84 | 94 (125) | 94.7 (126) |

550 | 84 | 93 (124) | 94.7 (126) | 73 | 88 (119) | 91 (121) |

500 | 72 | 86 (117) | 91 (121) | 58 | 80 (114) | 86 (117) |

450 | 57 | 76 (112) | 86 (117) | 43 | 69 (108) | 81 (114) |

400 | 40 | 64 (106) | . | 29 | 56 (103) | . |

350 | 23 | 49 | . | 16 | 41 | . |

300 | 11 | 33 | . | 6 | 23 | . |

250 | 4 | 17 | . | 1 | 5 | . |

200 | -- | -- | . | -- | -- | . |

Average score | 431 | 368 | . | 472 | 402 | . |

This table is the source for the percentile ranks for the SAT-verbal and mathematical scores found on Admissions Testing Program Reports. Percentile ranks for the national high school sample are based on the scores earned by representative high school juniors and seniors in October 1974. Percentile ranks for college-bound seniors are based on the most recent scores earned by students in the 1975-76 graduating class who took the SAT at any time while in high school.

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