Paul Taubman

Terence Wales

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research
Volume Title: Education, Income, and Human Behavior
Volume Author/Editor: F. Thomas Juster, ed.
Volume Publisher: NBER
Volume ISBN: 0-07-010068-3
Volume URL: http://www.nber.org/books/just75-1
Publication Date: 1975
Chapter Title: Appendix B: Mental-Ability Tests and Factors
Chapter Author: Paul Taubman, Terence Wales
Chapter URL: http://www.nber.org/chapters/c3706
Chapter pages in book: (p. 405 - 410)eAppendix 1*cdYCental-
ETiStS and
by Taithman and 'Wales
The 17 tests used in obtaining the four factors discussed in the text
are listed in Table B-i. A brief description of the tests appears in
Thorndike and Hagen (1959, PP. 9—11), and a detailed discussion
can be found through the entire book. From the titles and de-
scriptions, it is clear that many of the tests measure different facets
of the same ability. Rather than use all the tests or any arbitrary
TABLEB-IFactor
Ability test
Factor loading
1 2 3 4
Reading Comprehension 0.4123 0.0700 0.7186 0.0136
Mechanical Principles 0.0149 0.3522 0.7210 0.0247
Dial and Table Reading 0.6990 0.2566 —0.0129 0.3260
Spatial Orientation II 0.0658 0.1042 0.3117 0.6420
Spatial Orientation I 0.2217 0.1379 0.0311 0.7642
Numerical Operations I & II 0.7822 0.0597 —0.2183 0.1030
Speed of Identification 0.0500 0.1008 0.0643 0.7831
General Information—Navigator 0.4842 —0.1199 0.5605 0.1495
General Information—Pilot —0.0811 0.0329 0.5874 0.3567
Mathematics B 0.7444 —0.01 04 0.3514 —0.0717
Mathematics A 0.7464 —0.0469 0.3060 0.0571
Rotary Pursuit 0.0304 0.6772 0.0453 0.0396
Two-Hand Coordination —0.0385 0.6870 0.2703 0.0572
Complex Coordination 0.1251 0.7026 0.1877 0.2028
Aiming Stress —0.0111 0.4128 0.0009 0.0093
Discrimination Reaction Time 0.3891 0.3800 0.0940 0.2636
Finger Dexterity 0.1974
SOURCE:All data in this table are from NBER-Thorn
0.5438
dike sample.
—0.1664 0.1253
405Education, income, and human behavior 406
subset,we used factor analysis to obtain measures of a few types of
ability.
The basic idea in factor analysis is that any test contains infor-
mation on one or more general abilities and on test-specific com-
ponents. That is:
F =SC+ u
whereS is the set of scores, F represents the set of general abilities,
and u is the test-specific components. Using the scores in each of
the tests, it is possible to estimate C by imposing certain conditions•
on u. Estimates of the F can then be found from SC where the C
are known as the factor loadings. Each F is, of course, just a
weighted average of the test scores.1 In some instances, however,
the major weights in each average are attached to items that
measure one type of attribute. The factor is then labeled by this
attribute.
For the test scores in the NBER-TH data, the factor loadings for
the four factors are given in Table B-i. Consider, first, the second
factor, in which Rotary Pursuit, Two-Hand Coordination, and Com-
plex Coordination all have loadings in excess of 0.65. In addition,
Finger Dexterity, Aiming Stress, Discrimination Reaction, and
Mechanical Principles have weights in the range of 0.35 to 0.54.
The common element in all tests is coordination; consequently, we
refer to this as the complex coordination factor. For the fourth
factor the only important tests are Speed of Identification and
Spatial Orientation I and II. Given the description of the Speed of
Identification test, it seems clear that the fourth factor measures
spatial perception and perhaps abstract reasoning.
Both these factors are easy to interpret or identify, whereas the
first and third are somewhat more difficult. In the first factor the
most important items with loadings of at least 0.69 are Numerical
Operations, Mathematics A and B, and Dial and Table Reading,
all of which are concerned with mathematics and quantitative
skills. Unfortunately, secondary but still important weights (0.49
to 0.39) are accorded to Navigator— General Information, Reading
Comprehension, and Discrimination Reaction Time. Although the
navigator test emphasizes mathematical material, the other two
'Because the original test scores are standardized and then manipulated as
correlation, all weights have to lie between plus and minus 1. The importance
of each test in a factor is indicated by the absolute size of its loading coefficient.Appendix B 407
TABLE B-2
Regression
coefficients and
C-values
(Entire s8mpie)
Variable
1955 1969
Coefficient t-value Coefficient t-value
Intercept 229 3.6 1356 4.4
Some college 54 4.1 193 4.3
B.A. 58 4.4 341 7.5
Some graduate 75 3.4 287 3.9
M.A. 51 2.5 351 5.1
Ph.D. 61 2.6 670 9.6
M.D. 300 6.9 494 3.8
Teacher —162 7.3 —496 6.1
Age (years) 8 4.1 —2 .3
Ability2 23 1.5 69 1.3
Ability 3 33 2.2 107 2.1
Ability 4 50 3.4 144 2.9
Ability 5 84 5.7 279 •5.5
Health —33 4.4 —205 7.8
Single 122 3.7 —237 2.2
Father, high school 26 2.5 108 3.1
Father, college 21 1.7 97 2.2
Biography 2 0.7 0.1 119 2.4
Biography 3 30 2.0 92 1.8
Biography 4 63 4.3 167 3.4
Biography 5 81 5.6 206 4.2
R2 .10 .11
Observations 3,500 3,700
NOTE:The dependent variable is monthly earnings in dollars. Education variables
are zero-one dummies.
Ability i =valueof 1 if individual is in ith mental-ability fifth and 0 otherwise.
Health =1if excellent, 2 if good, 3 if faim and 4 if poor.
Single =valueof 1 if individual is single and 0 otherwise.
Father, h.s. =valueof 1 if father attended high school and 0 otherwise.
Father, college =valueof 1 if father attended college and 0 otherwise.
Biography i =valueof 1 if individual is in ith biography fifth and 0 otherwise.
SOURCE:NBER-Thorndike sample.
items do not; nevertheless, we treat this as a mathematical-ability
test.
In the third factor, Reading Comprehension and Mechanical
Principles have loadings in excess of 0.7; General Information—
Pilot and General Information —Navigatorhave loadings of aboutEducation, income, and human behavior 408
TABLEB-SRegression coefficients and t-vaIues by occupation, 1969
Professional, sales, Blue-collar, white-
Variable
and technical Managers and owners collar, and service
Coefficient f-value Coefficientt.value Coefficientt-value
Intercept 877 2.0 1781 3.6 866 4.6
Somecollege 86 1.1 95 1.2 32 1.5
BA. 245 3.0 203 2.6 94 2.6
Some graduate 77 .7 180 1 .5 158 1 .8
M.A. 128 1.3 259 2.3
Ph.D. 446 4.0 347 1.6
M.D. .904 7.8
LL.B. 584 5.8 66 2.0
Teacher —198 2.4
Age (years) 6 .6 2 .2 —.3 .1
Ability 2 103 1.5 30 .3 19 .7
Ability3 110 1.6 23 .3 5 .2
Ability 4 130 1.9 90 1.0 55 2.0
Ability 5 30 4.4 225 2.6 30 .1
Health . —157 4.6 —257 5.6 —23 1.5
Single —259 2.1 118 .5 —99 1.5
Father, high school 88 1.9 92 1 .6 20 .9
Father, college 84 1.5 157 2.2 —2 .1
Biography 2 105 1.6 91 1.1 —6 .2
Biography 3 48 .7 54 .6 43 1.4
Biography 4 40 .6 204 2.4 31 1.0
Biography 5 145 2.2 200 2.3 3 .1
Technical 82 1.1
Sales 71 1.1
Service —46 1.9
White collar —103 3.4
.21 .05 .04
Observations 728 1085 208
NOTE:SeeTable8-2 for an explanation of terms.
0.5; mathematics B and mathematics A have loadings of 0.35 and
0.30, respectively; and Spatial Orientation II has a loading of 0.31.
In general, these tests encompass verbal ability, mathematical
skills, reasoning, and mechanical principles. Since the first three
items would be found in standard IQ tests, we have chosen to callAppendix B 409
this third factor IQ. However, it is important to note that Professor
Thorndike believes that the first factor would correlate much more
closely with IQ and should be named as such, while the third tends
toward mechanical principles. The reader should keep this caveat
in mind when examining our remarks about the importanceof the
different types of ability and when comparing the NBER-THresults
with those of Wolfie-Smith.
Reference
Thorndike, Robert L., and Elizabeth P. Hagen: Ten Thousand
John Wiley & Sons, Inc., New York, 1959.

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