Army Alpha and Beta Tests: Scoring, Letter Grades and the Mental Age of 13 Myth

Army Alpha was the written group intelligence test the US Army gave to recruits from 1917, and Army Beta was its pictorial version for men who could not read English well. Alpha has eight timed tests and a maximum score of 212; Beta has seven and a maximum of 118. Neither reported an IQ: scores became letter grades from A, the top, down to D-, with E reserved for men recommended for rejection or discharge. By 31 January 1919 the Army's psychologists had examined 1,726,966 men. The famous claim that they proved the average American soldier had a mental age of 13 comes from a figure in the Army's own 1921 report, but that report said it could not conclude the draft was three years below the norm. This guide gives the tests, the scoring, the real grade distribution and the checked history of the claim.

What were the Army Alpha and Beta tests?

A committee of seven psychologists met at the Training School in Vineland, New Jersey, from 28 May to 7 July 1917 and built the group scale, drawing heavily on Arthur Otis's methods of group testing that needed no writing and could be scored objectively. Robert Yerkes headed the Army's psychology section. Field trials began on 16 September 1917, and the War Department approved extension to the whole Army on 24 December 1917. The Army's stated aim was to classify recruits by intellectual ability, remove the unfit and spot unusually able men; the officers' handbook added that the tests did not measure loyalty, bravery or the power to command.

Alpha was for "literates", men who could read and write English fairly well. Beta was, in the handbook's words, Alpha translated into pictorial form, so that pantomime and demonstration replaced written and spoken directions. It was devised after Alpha was already in use, to cope with men of low literacy and little English. Men who scored below D on Alpha were recalled for Beta, and men who did badly on Beta were given an individual examination, which was the Point Scale, the Stanford-Binet or the Performance Scale. Each test had a short time limit and groups of up to 500 men sat together.

• Alpha (8 tests, maximum 212): directions or commands, arithmetical problems, practical judgment, synonym-antonym, disarranged sentences, number series completion, analogies, general information
• Beta (7 tests, maximum 118): maze, cube analysis, X-O series, digit-symbol, number checking, pictorial completion, geometrical construction

The 1920 handbook prints the examiner's sample items. In the analogies test the examiner says: sky is to blue as grass is to table, green, warm or big; then day is to night as white is to red, black, clear or pure. The handbook also says it was practically impossible for highly intelligent subjects to finish the tests in the time allowed, and that no single test ran longer than about five minutes. For Alpha it reports a reliability coefficient of about .95, a probable error of about 5 points that is one-eighth of the standard deviation for unselected soldiers (so a spread of about 40 points, our arithmetic), correlations of .80 to .90 with the Stanford-Binet and .50 to .70 with officers' ratings, and .80 between Alpha and Beta. These are the Army psychologists' own figures, not an independent check.

How were Army Alpha and Beta scored? The letter grades

Each Alpha test was scored by right answers, or right minus wrong, and weighted, to a total of 212 (the eight maxima are 12, 20, 16, 40, 24, 20, 40 and 40). Beta's seven weighted maxima sum to 118. The total was then turned into a letter grade, and the table the Army printed in its 1920 handbook is below. Alpha is first, then Beta.

• A, very superior: Alpha 135 to 212, Beta 100 to 118
• B, superior: Alpha 105 to 134, Beta 90 to 99
• C+, high average: Alpha 75 to 104, Beta 80 to 89
• C, average: Alpha 45 to 74, Beta 65 to 79
• C-, low average: Alpha 25 to 44, Beta 45 to 64
• D, inferior: Alpha 15 to 24, Beta 20 to 44
• D-, very inferior: Alpha 0 to 14, Beta 0 to 19 (a recall band: Alpha D- meant recall for Beta, Beta D- meant recall for an individual examination)
• E: no score band; reserved for men recommended for rejection, discharge, a development battalion or a service organization

The handbook told officers what to expect. Grade A was ordinarily earned by only four or five per cent of a draft quota and, with leadership, marked officer material; B by eight to ten in a hundred; C+ by fifteen to eighteen per cent, who were non-commissioned-officer material; C by about a quarter, excellent privates; C- by about a fifth, usually good privates; and D by about fifteen per cent, who rarely rose above private. Men below C+ were not to enter officer training unless they had exceptional leadership.

What did the final Army letter grades look like for 167,035 white draftees?

The Army's 1921 report prints the final distribution, using each man's highest grade across all his examinations, for 167,035 white drafted men (page 423):

• A: 4.04 per cent
• B: 7.90 per cent
• C+: 14.93 per cent
• C: 25.39 per cent
• C-: 25.40 per cent
• D: 20.66 per cent
• D- or E: 1.68 per cent

Adding the shares from the top, A and B together are 11.94 per cent of the sample and A, B and C+ together 26.87 per cent (our arithmetic). The report says the grade lines were drawn so as to skew the distribution considerably toward the low end, and that the A range was made wide because military value above a certain level depended chiefly on other factors. So a grade describes where the Army chose to draw a line, and the shares are not percentiles of a norm group.

Is there an IQ for each Army Alpha letter grade?

No. The Army printed score bands, the share of men in each grade and, for the individual examinations, a Stanford-Binet mental-age band for each letter: D- below 9.5 years, D 9.5 to 10.9, C- 11 to 12.9, C 13 to 14.9, C+ 15 to 16.4, B 16.5 to 17.9 and A 18 and over. It printed no IQ for any grade, and "A equals IQ 130" tables online have no Army source we could find. A ratio IQ divides mental age by chronological age, and the report did not apply that formula to a letter grade. For how the two kinds of figure differ, see our guides to IQ and mental age and to deviation IQ versus ratio IQ. Our look at the IQ of lawyers shows what happens when a later Army scale is turned into IQ points without an official table.

Did the Army tests prove the average American had a mental age of 13?

No, and the Army's own report did not say so. Its Table 165 gives the mean mental age of the main white-draft sample, 93,955 men, as 13.08, and the median as 13.15. The report converted a combined-scale score to a mental age with the formula 0.778 times the score plus 2.606; for the white-draft mean of 13.46 that gives 13.08, which checks. Its text on page 785 then adds the qualification that the story leaves out: it is customary to say the mental age of the average adult is about 16, but that figure rested on examinations of only 62 persons, 32 high-school pupils aged 16 to 20 and 30 "business men of moderate success and of very limited educational advantages". The authors wrote that they could hardly say with assurance that the recruits were three years below the average, and that a difference so great was quite unlikely.

The report itself supplied the ammunition for the slogan. On page 789 it notes that if "moron" is read as a mental age under 13, as had recently been done, almost half the white draft, 47.3 per cent, would be morons, and concludes that feeble-mindedness is much more frequent than first thought. (Both words were official categories then and are offensive now.) Dividing 13.08 by the 16 years used as the adult norm gives 0.82, which is how a figure like "82" can be made to look like an IQ, though the report declined to draw that conclusion from a norm based on 62 people.

The retelling came from popularisers. Henry Goddard, in lectures given in April 1919 and published in 1920, put the average person's level at between thirteen and fourteen years. Lothrop Stoddard's 1922 book The Revolt Against Civilization turned it into the claim that the average mental age of Americans is only about fourteen, and that some forty-five million people would never pass a normal twelve-year-old's stage. Walter Lippmann answered in the New Republic on 25 October 1922 that this was as silly as saying the average mile was three quarters of a mile long. Carl Brigham, who analysed the Army data in a 1923 book that Yerkes introduced, wrote that nothing could be more ridiculous than the claim that the Army tests proved the average citizen had a mental age of thirteen, and called "mental age" bad scientific slang for a total score.

The Army's own grading cuts the other way. In its final scheme, a Stanford-Binet mental age of 13 to 14.9 earned grade C, which the handbook labels average. By the Army's yardstick, the average soldier was average.

Did Army Alpha measure intelligence or schooling?

Both, and the Army's books disagree with each other about how much. The officers' handbook says the score is little influenced by schooling and that some of the highest records were made by men who had not completed the eighth grade. The 1921 report prints correlations with years of schooling of about +0.75 in an unselected group and about +0.65 among men who took Alpha, with +0.81 as the highest value, and another section gives 0.67 while arguing that the test does not measure simply the amount of schooling. The authors read the correlation as intelligence keeping men in school. A modern reader sees the confound: Alpha needed written English, so reading ability and schooling and the measured trait were tangled together, which is why Beta existed at all.

How were the Army tests used after the war?

Brigham's 1923 book A Study of American Intelligence used the Army data to argue that Nordic groups had demonstrated superiority and that American intelligence was declining. Yerkes wrote its foreword. Brigham withdrew his racial conclusions in a 1930 paper in Psychological Review; we confirmed the citation, and a 1983 article by Snyderman and Herrnstein reports the recantation, but we could not read the 1930 text itself. Whether the tests influenced the Immigration Act of 1924 is disputed: Snyderman and Herrnstein examined the record and found no support for the claim that Congress relied on intelligence testing. Our blog's guides to eugenics and the history of IQ testing and to the origins of IQ testing place Alpha and Beta in that longer story.

How does Army Alpha compare with a modern IQ test?

• Scale: Alpha gave a raw score out of 212 and a letter grade, not a deviation IQ with a mean of 100 and a standard deviation of 15
• Norms: the grades were cut lines for classifying a draft, not percentiles of a national sample; modern tests such as the WAIS-5 and Stanford-Binet 5 publish norms from stratified samples
• Time: each Alpha test ran only a few minutes and was hard to finish, so speed counted for a great deal
• Format: group paper tests of English, arithmetic and general information, against individually administered batteries
• Drift: norms go out of date, which is why publishers issue new editions and norm updates; see why IQ norms expire

The bottom line: Army Alpha and Beta were real, large and influential, but they produced letter grades and mental ages, not IQs, and the "average American was 13" story is a popular distortion of one figure the Army itself hedged. To see where a score falls today, take the IQ Metrics IQ test and read the result against the IQ percentile calculator.

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