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Official Historical SAT to IQ Conversions

These data were combined from two hard-to-obtain sources. The first was A Study of Error: a Summary and Evaluation of Methods Used in Six Years of Study of the Scholastic Aptitude Test of the College Entrance Examination Board by Carl C. Brigham, Associate Secretary of the College Entrance Examination Board (1932). The second was the Otis Self-Administering Tests of Mental Ability (Higher Examination, Form A) IQ Scales (1922-1928). Only raw scores were provided in the first source so the second source was needed to get the corresponding IQ scores. The following two paragraphs are a direct quote from the Study of Error, p.336:

It would be expected that a test designed for use in high schools would not differentiate the upper range of college applicants and this proved to be the case, although this is not a reflection upon the Otis test. 1080 candidates were given the Otis test with a half-hour time limit. The mean scholastic aptitude score of these candidates (randomly sampled) was 499.213 and the sigma was 99.272. The mean Otis score was 58.7435, sigma 8.6839. The correlation between the two examinations was .7931. As the maximum possible score on the Otis examination was 75, the distribution of Otis scores was cut off sharply at the upper end and high score candidates probably were not completely differentiated.

Table XVIII gives the most probable scholastic aptitude test score, percentile, and letter grade for each Otis total score. The Otis I.Q. conversions were not used, and this table applies only to total raw scores. The coefficient of correlation between the Otis test and the Board test (.7931) means considerable uncertainty in predicting one score from another. The probable error of estimating a scholastic aptitude test score from an Otis score is about 40. A "Predicted" S.A.T. score from an Otis score of 50, for example, would be 420±40. This means that the chances are even that the true S.A.T. score is between 380 and 460. The chances are also even that the score is greater than 460 or less than 380, but become increasingly smaller as the distance from these numbers becomes larger.

Otis Raw Score Otis IQ SAT score SAT %ile Otis Raw Score Otis IQ SAT score SAT %ile Otis Raw Score Otis IQ SAT score SAT %ile
75 144 647 92 58 116 492 46 41 99 338 5
74 140 638 91 57 115 483 43 40 98 329 4
73 137 628 90 56 114 474 39 39 97 320 3
72 135 619 88 55 113 465 36 38 96 311 2
71 133 610 86 54 112 456 32 37 95 302 2
70 131 601 84 53 111 447 29 36 94 293 1
69 129 592 82 52 110 438 26 35 93 284 1
68 127 583 79 51 109 429 24 34 92 275 1
67 125 574 77 50 108 420 21 33 91 266 0.9
66 124 565 74 49 107 411 18 32 90 257 0.7
65 123 556 71 48 106 402 16 31 89 248 0.5
64 122 547 68 47 105 393 14 30 88 239 0.4
63 121 538 64 46 104 384 12 29 87 230 0.3
62 120 529 61 45 103 375 10 28 86 220 0.2
61 119 520 58 44 102 366 8 27 85 211 0.1
60 118 511 54 43 101 356 7 26 84 202 0.1
59 117 502 50 42 100 347 3 25 83 193 0.1

This table is of mainly historical interest because SAT scores have changed quite a bit since 1932. One lesson that can be drawn is about the uncertainty in converting scores between tests: the results are not very precise. Please keep this in mind when you are looking at my GRE and SAT (unofficial) estimation pages.

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