DATA EVALUATION AND METHODS RESEARCH

The Construction and Utility

of Three Indexes

of Intellectual Achievement:

An Intellectual-Development (ID) Index

A Socio-intellectual-Status (S1S) Index

A Differential-intellectual-Development

(DID) Index

U.S. Children and Youths, 6-17 Years

.

A methodological report on the construction and utility of three

indexes of intellectual achievement. The concept of partitioning a

measure of intellectual dm’elopment into measurable components

and the method of criterion scaIing are seen as pro~tiding a structure

for use by behavioral scientists in general as \vell as in the particular

case of the search for contributing and impeding conditions associated with intellectual development.

DHEW Publication No. (H RA) 78-1348

U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE

Public Health Service

Health Resources Administration

National Center for Health Statistics

Hyattsville, Md. September 1977

Series 2

Number 74
/

I

—

Library of Congress Cataloging in Publication Data

L)upuy, lIw-old J.

The construction and utility of three indexes of intellectual achievement.

(Vital and health statistics: Series 2, Data evaluation and methods research; no. 74)

(L)HEW publication; (HRA) 78-1 348)

Includes bibliographical references.

Supt. of Dots. no.: HE20.6209:2/74

1. Intelligence tests. 2. Psychological tests for children. I. Gruweus, Gunnarl joint

.iuthor. II. Title. III. Series: United States. .National Center for Health Statistics. Vital and

health statistics: Series 2, Data evaluation and methods research; no. 74. IV. Series: United

States. Dept. of liealth, Education, and W’elfare. L)HEW publication; no. (IIR.\) 78-1348.

[DNLhl: 1. Intelligence tests -Infancy and childhoo&United States-- Sta~istics. 2. Intelli-

~encc tests–In adolescence-United States–Stiitistics. \Y2 A N 148vb no. 74 I

RA409.LJ45 110. 74 [BF431] 312’.07’23s {153.9’3]

1S13N 0-8406 -0106-9 ;7-608 140

— —— .—
NATIONAL CENTER FOR HEALTH STATISTICS

DOROTHY P. RICE, Director

ROBERT A. ISRAEL, Deputy Director

GAIL F.

JAMES T.

JACOB J. FELDMAN, Ph.D., Associate Director for Analysis

FISHER, Associate Director for the Cooperative Health S tatistks System

ELIJAH L. WHITE, Associate Director for Data Systems

BAIRD, JR., Ph.D., Associate Director for International Statistics

ROBERT C. HUBER, Associate Director for Management

MONROE G. SIRKEN, Ph.D., Associate Director for Mathematical S tutistics

PETER L. HURLEY, Associate Director for Operations

JAMES M. ROBEY, Ph.D., Associate Director for Program Development

PAUL E. LEAVERTON, Ph.D., Associate Director for Research

ALICE HAYWOOD, Information Officer

DIVISION OF HEALTH EXAMINATION STATISTICS

MICHAEL A. W. HATTWICK, M.D., Director

HAROLD J. DUPUY, Ph.D., Rsychobgical Adviser

LINCOLN OLIVER, Chief, Psychological Statistics Branch

ROBERT S. MURPHY, Chief, Survey Planning and Developing Branch

Vital and Health Statistics-Series 2-No. 74

DHEW Publication No. (HRA) 78-1348

Library of Congress Catalog Card Number 77-608140
ACKNOWLEDGMENT

This study was made possible through the support of Dr. Nicholas Zill of the

Foundation for Child Development (345 East 46th Street, New York, N.Y.

1001 7) and of the Foundation itself. When the concepts of a Socio-IntellectualStatus index and a Differential-Intellectual-Development index were first mentioned to Dr. Zill he immediately grasped their conceptual implications and their

potential utility. He provided the assistance of Gunnar Gruvaeus for a 6-month

period and the Foundation paid all costs attendant to Mr. Gruvaeus’ services.

Mr. Gruvaeus’ statistical and programing expertise and his subject-matter

knowledge were critical in carrying this study to. the scope and level of technical

attainment it reached.

Harold J. Dupuy, Ph.D.

...

Ill
CONTENTS

Acknowledgment ....................................................................................................................................... iii

Summary ..................................................................................................................................................... 1

Method .................................................................................................................................................. 1

Uwlty .......................................................................................................................................... .......... 1

Substantive Findings .............................................................................................................................. 1

Index Development .....................................................................................................................................

Introduction ..........................................................................................................................................

Criterion Scaling of Predictor Variables .................................................................................................

The Index of Intellectual Development (ID) ..........................................................................................

The Index of Socio-Intellectual Status (S1S) ..........................................................................................

The Index of Differential-Intellectual Development (DID) ....................................................................

Race-Specific S1S and DID Indexes ........................................................................................................

Examined Sample Compared to Population Estimates ...........................................................................

Intercorrelations of the Indexes .............................................................................................................

2

2

2

2

2

7

7

9

9

Substantive FMings ................................................................................................................................... 10

Application of the ID and Race-Specific SIS and DID Indexes to Substantive Examination Findings

from Cycle II, Children 6-11 Yemsof~e .......................................................................................... 10

References ................................................................................................................................................... 15

Lkt of Detailed Tables ................................................................................................................................ 16

Appendix: Technical Notes ........................................................................................................................ Z4

LIST OF TEXT TABLES

A. Response levels and percents of variance accounted for in general and in race-specific indexes, by

race, of intellectual achievement by independent variables for children and youths aged 6-17 years

with means and standard deviations of indexes ................................................................................... 4

B. Percent variance accounted for by four independent predictor tiables ................................................ 4

C. Unwei@ted sample size, mean Intellectual-Development (ID) scores, standard deviations, and constructed variables, by sum of both parents’ education in years, with percent variance accounted for

and correlation ratios .......................................................................................................................... 5

D. Unweighed sample size, mean Intellectual-Development (ID) scores, standard deviations, and constructed variables, by amuaf family income per person under 21 years of age in howehold, w-ith

percent wmkmce accounted for and correlation ratios ......................................................................... 6

E. Unweighed sample size, mean Socio-Intellectual-Status scores, means and standard deviations of

Intellectual-Development scores and Differential-Intellectual-Development scores, by each vslue of

the Socio-Intellectual-Status index, with percent variance accounted for and correlation ratios ....... 8

F. Obtained means, standard deviations, range of scores, and Socio-Intellectual-Status and IntellectualDevelopment correlations for race-specific Socio-Intellectual-Status indexes .................................... 8

G. Examin ed sample and population estimates summary statistics, by race and intellectual indexes .......... 9

v
H. Matrix of product-moment intercorrelations of the indexes, by race ..................................................... 10

J. Correlation coefficients, means, and standard deviations for intellectual indexes and selectedvariables.. 11

K. Sample size and mean index scores of intellectual achievement, by number of pregnancies previous to

birth of examined child, with percent variance accounted for and correlation ratios ........................... 12

L. Sample size and mean index scores of intellectual achievement, by attendance at nursery school or

kindergarten, with percent variance accounted for and correlation mtios ............................................ 13

M. Sample size and mean index scores of intellectual achievement, by nature of talking problem, with

percent variance accounted for and correlation ratios .............................................i........................... 13

N. Sample size and mean index scores of intellectual achievement, by twin status, with percent variance

. .

accounted for and correlation ratios .................................................................................................... 13

0. Sample size and mean index scores of intellectual achievement, by school-judged intellectual level,

with percent variance accounted for and correlation ratios ................................................................. 13

P. Sample size and mean index scores of intellectual achievement, by recommendations for special

school resources, wrth percent variance accounted for and correlation ratios ....................................

. .

14

Q. Sample size and mean index scores of intellectual achievement, by diagnostic impressions of neurological, muscular, or joint conditions by the examining physician, with percent variance accounted

for and correlation ratios .................................................................................................................. 34

SYMBOLS

Data not available-------------------------—----- ---

Category not applicable----——------------— . . .

Quantity zero ------------------------------------ -

Quantity more than Obut less than 0.05---- 0.0

Figure does not meet standards of

reliabilityy or precision-—-— --------------

*

vi
THE CONSTRUCTION AND UTILITY OF THREE INDEXES

OF INTELLECTUAL ACHIEVEMENT

Harold J. Dupuy, Ph.D., Psychological Adviser,

Division of Health Examination Statistics

and

Gunnar Gruvaeus, M.A., Foundation for Child Development

SUMMARY

This report describes the construction of

three indexes of intellectual achievement for use

in analyses of the National Center for Health

Statistics’ Health Examination Survey findings

for U.S. chiIdren (aged 6-11 years) and youths

(aged 12-17 years).

Method

The index of Intellectual Development (ID)

was developed through the application of standard psychometric procedures. However, the

derivation of the other two new indexes, SocioIntellectual Status (S1S) and DifferentialIntellectual Development (DID), should be of

major methodological significance to behavioral

scientists who are concerned with advancing

measurement capability into a heretofore intractable area. The elaboration and successful

application of the method of criterion scaling

as described in this report should encourage

applications in many diverse areas of scale or

index construction.

A note of caution is in order. The numerical

index values derived in this report are specific

and limited to the data of the Health Examination Survey Cycles II (children) and Cycle 111

(youths). However, the anticipated use of these”

data bases both within the National Center for

Health Statistics (NCHS) and outside NCHS is

the justification for presenting the obtained

values and their incorporation, as individual

examination components, into each exarninee’s

data tape record for these two nationaI examinations. Copies of these tapes can be purchased

from NCHS.

Utility

The index of Intellectuzd Development (ID)

can be used as a surrogate measure comparable

to the Full Scale IQ (intelIigence quotient) of

the Wechsler Intelligence Scale for Children .

(WISC), 1949. The Socio-Intellectual-Status

(S1S) index can be used as a single control,

moderator, or covariate index for determining

the contribution of the S1S family background

factor in analytical studies of other examination

findings.

The utility of the Differential-IntellectualDevelopment (DID) index is seen in terms of

its potential for studying and identifying other

examination findings that bear on intellectual

development when the confounding intrusiveness of S1S is removed. The DID index provides

an indicator of intellectual achievement that

is independent of the concomitant relationship

of the index of Intellectual Development and

the family background factors used to construct

the Socio-Intellectual-Status index.

Substantive Findings

The use of the three indexes in studying

some examination findings from the Cycle II

children’s survey (aged 6-11 years) of 1963-65

helps to clarify some persistent issues related to

intellectual achievement.
The first-order analyses revealed statistically

significant relationships between the index of

intellectual development and ( 1) number of

pregnancies previous to the birth of the examined child, (2) twin versus nontwin birth

status, and (3) attendance versus nonattendance

at nursery school and/or kindergarten. However,

these relationships were mostly accounted for

by the family background factors reflected in

the Socio-Intellectual-Status index. No important amount of variance was found in the

residual component of the index of Intellectual

Development as measured by the DifferentialIntellectual-Development index. Thus the firstorder relationships with the index of Intellectual

Development were accounted for by the differential prevalence of these conditions among

children coming from family backgrounds with

different S1S index values.

INDEX DEVELOPMENT

introduction

This report presents the methods of constructing three indexes of intellectual achievement derived from data collected by the NCHS’

national Health Examination Surveys of U.S.

children (6-7 years of age) and youths (12-17

years of age). The children’s survey was conducted from 1963-65; the youths’ from 1966-

70. These surveys have been described in previous NCHS publications. 1

The applications of these indexes in the

analyses of some data from the Cycle II children’s examination survey are also presented.

While these findings may be of substantive interest to some readers, they are not exhaustive of

the issues they reflect.

The three indexes of interest in this report

bear on the measurement of intellectual achievement of our Nation’s children and youths.

These are labeled descriptively as indexes of:

Intellectual Development (ID)

Socio-Intellectua.l Status (S1S)

Differential-Intellectual Development (DID)

The index of Intellectual Development (ID)

is basically comparable to an Intelligence

Quotient (IQ) index. The Socio-IntellectualStatus (S1S) index is somewhat analogous to a

Socio-Economic-Status (SES) index. However,

the components of S1S were rigorously calibrated to reflect the contribution of certain

family background factors to intellectual development which existed independently of the

child’s or youth’s own control. The DifferentialIntellectual-Development (DID) index is taken

as reflecting intellectual achievement of the

child or youth independent of the S1S family

background contribution to the index of Intellectual Development.

The concept of a SIS-type index emerged

from the perception of the confounding or intrusive relationship of certain family background

characteristics in studying the associations

among health-related variables within g~oups

of individuals (in contrast to intra-individual

associations). This seems to be especially relevant to studying the associations of certain

somatic insults with intellectual development.

For example, if a strong (negative) relationship

were found between scarIet fever and intellectual development, the next question would be,

Is this association accountable by a (possible)

joint relationship of these two conditions with

a common SIS-type family background? Also

important in the conceptualization of S1S was

the possibility of identifying a parsimonious set

of family background factors which could be

ordered along some dimension (scaled) so that

none of the many other family background factors, which are or may be associated with intellectual development at the single variable

level, would show an association when the scaled

dimension is taken into account. The given investigator could then “control” on this one

dimension rather than having to consider the

many other singular variables. Thus S1S could

serve as a moderator or covariate dimension in

the study of associations among any health

variables that also may covary along this family

background dimension. As an example, if one

wanted to study the association of the number

of decayed teeth with diseased tonsils, the investigator might want to “partial out” the common variance of these two conditions with S1S.

The conceptualization of DID was a rational

extension of a more general concept to a specific

application. The general concept is that the

variance in common between two (or more)

2
variables can be extracted and the residual variance in the variable of interest can be resealed

as an index for use in measuring its singular

dimensionality. For example, raw score performances on a general vocabulary test are highly

correlated with age from about age 2 to age

15. The age factor can be “taken out” and the

vocabulary score achievement can be resealed

to be independent of age.

Criterion Scaling of Predictor Variables

The concept of criterion scaling is rather

simple and its application straightforward. In

this context it refers to the scahg of, or assigning weights or numerical values to, response

options within an item or to the original values

along a measured dimension (e.g., inches of

height), in terms of certain numerical wdues of

the criterion of interest. At least two conditions

must be met. Within a given data set, at least

one data element must be considered the criterion and at least one or more of the other data

elements must have more than a zero correlation

with the criterion. A criterion, in this context,

is a variable that discriminates the sample of

observations along some dimension, or into

categories, of interest. The criterion can be

viewed as the dependent variable and the other

variables as independent, predictor, or discrimination variables. The Technical Notes section

provides a more complete description of the

method of criterion scaling and compares the

results of criterion scaling with multiple linear

regression.

The Index of Intellectual Development (ID)

The index of Intellectual Development (ID)

was constructed from the Vocabulary and Block

Design subtests of the Wechsler Intelligence

Scale for Children (wISC). These t%vo subtests

were given to both the chiIdren and youths. The

total examined sample for 6-17 years of age was

13,887. A number of NCHS reports describe

these two tests, tie basis for selection, and procedures for examination and scoring.1

Independent research studies have found

that the sum of the ,scaled scores for these two

subtests correlates about .85 to .88 with total

WISC IQ scores.z The raw scores on these subtests were transformed and normalized on the

population estimates by 4-month age groups

and within sex. The transformation was to T

scores which are set to a mean and median of

50.0 and a standard deviation of 10.0 with the

raw score population estimates of observations

distributed according to the area under the normal curve. The T scores for the two subtests are

thus sex-age independent. That is, the variance

attributable to sex and age was removed. The

two T scores were then summed. This provided

a mean of 100.0. The population estimates were

then redistributed to have a standard deviation

of 15.0. These two properties are similar to the

WISC Total Scale IQ score. The obtained range

of ID scores was 46-152 which was very similar

to the obtainable range of 46-154 for the WISC

Total Scale IQ. The sample skew value of -.08

and kurtosis value of –. 14 indicate a very close

distribution fit to the normal curve.

In summary then, the high correlations

found between the sum of the Vocabulary and

B1ock Designs subtests with Total Scale WISC

IQ, and the equivalence in means, standard

deviations, ranges, and distributions provide

sufficient support for accepting the ID index

as a comparable measure of WISC Total Scale

IQ and as suitable for making agWegate compmisons of intellectual development.

The Index of SOcio-intellectual Status (S1S)

The next step was to select a set of variables

out of the total number of variables obtained for

each child and youth that would reflect family

characteristics and demographic factors that a

priori wouId seem to be independent of any

personal contribution of the children or youths.

Also excluded were any variables that would be

of substantive interest in their own right in later

analyses. Excluded under these two considerations were such variables as age of father and age

of mother at birth of examined person, number

of previous pregnancies of the mother, birth

weight, attendance at kindergarten, any childhood diseases, school questionnaire items, etc.

The final selection included 4 “control” variables and 13 “predictor” variables that seemed

to meet all specifications. Each of these 17 variables was then subjected to an analysis of variance computation with the ID index as the

dependent variable for criterion scaIing. The per3
Table A, Response lwels ma percenls of .acmnm mm.nmd for m geoeral and in rema.%peciflc mdwm, bv mm, of intellectual achlevemem by mdependmt varlablm for children md youths mad 6.17 Yew% with means and standard

Indem.dm vamble

Control W?,able

Constructed wmbte

Sum of both mrent$ education ,,,,,,.,..,,,,..,,,,.,..,...,,.,..,,,,., ,,,.,.,.

Annual fmulv income range per person under 21 yews of We ,,

n,.

92”,,

1,”,1,

—

2

1:

6

21

21

12

3

10

4

1:

1:

3

;

13

12

dwatmm of indew

-

General index Rac.w)edfi, index

ID

—,

Sls DID Sls DID

White Whim Wh it.? white Whit,%

All and ~leck All and

Black ‘[1 ‘“e Black ’11 and Black ,:;:, ~:h;r

,..,! other races other mm, other

Black

race, other

race, rwx, ,.,,s races ,,.,$

0.01

0,03

0,06

0,17

24,52

21.23

2030

13,15

7,69

5,20

3.54

3,46

3,08

2,83

1,52

,94

71

27.38

21,54

100,0 ~

15,0

0,00

0.02

0.04

0,30

21.35

1953

15,20

4,92

2,31

1,46

1,50

3,25

1,00

1,49

1,64

2,27

25,03

16.02

02,2

14,3

0. m

0,01

0.37

0,03

12.61

8,66

7,S1

5,11

6.13

0.75

0,84

5,26

0,46

3,97

8.27

0.51

13.48

9,92

86,7

11,9

0.12

0.27

0.31

0.58

74,22

60.49

59,45

10.70

23.40

7,01

5,92

6,29

5.06

5.61

2..95

3,25

3,23

85,07

66,96

100.0

8,52

0,08

0,35

0.41

0,s2

74,20

62,35

57.64

20,31

3,59

3.38

3,60

7,.55

2,97

4,47

5,10

6.70

95,73

64.86

101.?

S.11

0.00

0.37

0.79

0.41

64,95

42.30

42,10

21.00

12,7s

3,74

4.97

4,S1

4,14

6.27

12.28

0.73

76.04

55,39

93. !

7,69

Percent of VWimce accounted f.,

0,02

0,31

0.39

0,05

0,35

0,54

0,09

4,61

0,16

1 ,W

0,47

0,63

1.48

0.4s

0,73

0,36

0,06

0,04

0,05

100,0

12.34

0,03

0,30

0.37

0,08

0,51

0.31

0,26

0,34

0.33

0,23

0,4s

0,97

0,35

0.23

0.23

0,00

0,16

0.50

101.1

12.18

0,13 0.16

0,29 0,09

0.70 0.?3

0,20 0.38

4,68 67,63

4,05 53.91

3,31 55.27

36,54

1,22 20,27

1,37 S,29

0,36 8,10

1,28 8,37

1,1? 3,47

1,29 7,66

0.16 2,92

1,18 1,42

0,03 1,55

6,33 75,78

4.38 59,79

Ed._%

0,07

0,21

0,25

0,84

78,0s

64,39

53,8S

.,.

17,25

3,61

3,31

3.49

7.32

2,99

4.26

4.92

6.95

90.20

58.14

102,2

7,52

0,00

0.38

0,60

0.41

64.40

41,25

42,54

21,44

12,60

3,10

4.94

4,81

4,14

6.30

12,32

0.72

77,34

58,26

86.6

4,87

0,03

0,7s

0,23

0,04

0,32

0,33

0,03

0,01

0.12

0,49

0.16

0.41

0,76

0,30

0,07

0,21

0.02

0,05

0.03

00.0

11,98

—

0/32

0.19

0,25

0,06

0,39

0,31

O,c@

0:13

0,4.2

0.25

0,47

0.95

0,33

0.21

0.21

0.02

0,07

O,(M

00,0

12,15

—-

0,13

0,16

0,55

0,10

1,15

1,62

0,77

,,,

0,60

2,13

0,27

0,65

2,52

0.59

1,12

2,99

0,16

7.12

0.66

100.?

10,87

cent of variance accounted for and the correla- be the most relevant under this functional

tion ratio of each of these 17 variables with the

ID index were also obtained. Table A presents

the list of 17 variables and the percent. of variance accounted for in the ID index for the total

sample, and the two race categories of black and

white and other races. The detailed tables (1-3)

present the mean ID values for each response

level for the 17 variables plus other detailed

statistics.

A number of analytical methods were then

tried in a search for a procedure that could be

used to combine the variables in a way that

would account for the most variance in the ID

index and that would also seem to be most

meaningful in terms of the purpose to be

achieved. A multiple regression of the 13

criterion-scaled predictor variables with the ID

index was not performed. Instead a suggestions

was made to give first consideration to variables

that would seem to reflect a “functional” factor among parents. A variable was considered

as functional if a given parent could have exercised some degree of control or influence in

the development of that parent’s own life style

or status attainment. Four of the first five predictor variables shown in table A accounted for

the most criterion variance and also seemed to

aBy Lincoln I. Oliver, Chief, Psychological Statistics

Branch, DHES, NCHS.

direction. The fourth most important variable,

race, was not considered as functional in the

sense just used. Percent variance accounted for

in the ID index is shown in table B.

Again in order to simplify the more direct

meaningfulness of these four functional variables, they were combined into two “constructed” variables: (1) sum of both parents’

education (.Xl ) and (2) annual family income

per person under 21 years of age in the household (X2 ). The combined response Ievel:s were

then subjected to analyses of variance with the

ID index. The response levels were then grouped

on the basis of approximately’ equal mean ID

values with a progressive increase in mean ID

for group division. The grouped response levels

were then criterion scaled for response weights.

A scrutiny of tables C and D should help to

Table B, Percent variance accounted for by four independent

predictor variables

TZ

First parent’s education ...........................................

second parent’s education ....................... ................

Family income ................................................. ........

Number in household under 21 years of age ............

24.52

21.23

20.30

7.69
Table C. Unweighed sampla size, mean intellectual-Dwelopment (ID) scores, standard deviations, and constructed variables, by sum of

both ~arents’ education in years, with percent variance accounted for and correlation ratios

Sum of both parents’ education

Total ....................................................................... ..........

None ........ ............................................ ........ ............ .. ...... ...... .... ...... .

1 year ...... ...... .. .... ............................ ........ .................. ............ .. ..........

2 years ......... ........ .... .......... .................. .............. ........ .................. .... .

3 years .... ............................................................................... ...........

5 years ................................................. .. ............ ...... .................. ...... .

6 years ................ .............................................. ................................

7 years ..............................................................................................

8 years ................................................. ...... .................... ...... ........ .... .

9 years ................ .............. ............ .................... ........ .... .............. ......

10 years ......................................................................... ...................

11 years .. ...... ....................................................................................

12 years ........ ....................................................................................

13 yaars ............................................................................................

14 yaars .t................................ ...... .. .... .. .... ............................ .......... ..

15 years .............................................. ...... ........ .................... .... .. .... ..

16 yaars ........ ...... .......................... ...... ........ ........................ .. .... .. ......

17 years ........ .............................................. .... ............................ ......

18 years .. .... .. ........ .... .. .................. ...... ...... .. ...... ............ .. ...... .... .. .... ..

.19 years .. .................... ...... ............ ............ ................ .... ............ ........

20 years .............. .............. ...................................... ...... .............. ......

21 years ........................................ ....................................................

22 years ........ ......................................................................... .... ...... .

23 years ............................................................................................

24 years ..................... .................... ............................................. ......

25 years .. .................. .............. ...... .. ............ ...... ...... ...... .. ...... ...... ......

26 years ............................................... .............................................

27 years ....... ............................................................................. ........

28 years .................... ..... ................ .................. ...... .................... .......

28 years .. .................. .............. .................. .. ............ ............ ...... ........

30 years ............... ..... ........................................................... .............

31 years ............................................................................................

32 years ............. ........ ............. ..... ............................................ ........ .

33 years ........ .................. .................... ...... ...... .................... ............ ..

34 yaars and more ..... .. .... .. ........................ ...... .............. ...... ...... ........

Percent variance accounted for ..... ...... .... .. ...... .................... ..............

Correlation ratio ............... ...... ...... .................. ........ ..........................

n

13,887

52

8

37

42

83

51

129

53

151

111

217

108

228

165

400

223

913

389

747

514

1,082

647

981

638

2,772

414

498

218

603

353

245

155

322

211

127

. . .

. . .

Mean

ID

100.0

82.4

90.5

79.1

81.9

78.1

81.1

80.9

89.6

85.7

87.5

83.9

85.3

89.3

87.3

88.5

91.9

93.2

93.6

94.4

96.5

98.7

100.9

100.2

102.0

104.0

107.1

106.0

109.4

108.3

111.5

111.3

112.1

112.1

116.6

111.0

27.74

.53

SD

15.0

10.3

11.4

11.2

11.6

10.9

14.0

9.4

11.2

12.3

12.8

13.2

12.6

12.9

11.3

13.0

12.8

13.8

11.6

12.8

12.9

13.2

12.9

12.8

12.7

12.6

12.1

12.2

13.6

12.9

12.0

12.7

11.7

12.8

13.8

14.3

. . .

. . .

Constructed variable Xl

. . .

080.7

085.7

088.5

092.9

094.1

088.0

100.4

103.7

106.5

108.6

111.4

112.1

114.5

. . .

. . .

n

. . .

402

640

793

1,135

1,136

1,586

1,628

3,410

912

821

598

477

338

. . .

. . .

Mean

ID

. . .

80.7

85.7

88.5

92.9

84.1

98.0

100.4

703.7

106.5

108.6

111.4

112.1

114.5

27.38

.52

SD

. . .

11.1

12.8

12.7

13.6

12.4

13.2

12.9

12.6

12.2

13.1

12.3

12.5

14.3

. . .

. . .

NOTE: n = sample size; SD = standard deviation.

5
Table D. Unweighed sample size, mean intellectual-Develqxment (1D) scores, standard devjati~ns, a“d c~”structed variables, by annual family in~Ome per

person under 21 years of age in household, with percent I

Annual family income per person under 21 years of age

in the household

lStandard deviation not computed.

ante a[

_

n

3,887

148

706

859

1,054

588

915

1,027

545

789

817

270

808

581

461

87

66

1,249

100

186

227

504

281

259

262

190

101

51

118

121

72

67

47

26

17

8

13

56

57

49

34

19

26

13

9

. . .

4

. . .

.

IUnted f

_

Mean

ID

100.0

83.6

85.0

88.4

92.2

94.1

97.3

99.4

101.0

101.9

102.2

102.9

105.2

102.7

106.1

97.9

109.0

106.5

100.3

110.1

102.8

108.0

113.5

106.4

110.6

107.4

109.8

99.3

100.4

98.9

101.3

93.9

90.8

91.8

88.6

85.1

84.2

105.8

103.7

98.9

101.0

98.6

93.6

95.7

90.6

,..

86.2

22.53

.47

and cc

_

SD

15.0

12.4

12.7

12.5

14.0

13.1

13.8

13.3

14.2 }

13.1

12.5

14.7 I

12.5

12.7

12.8

13.8 I

14.5

12.8

14.3

12.0

lfL7,112.4 13.5

12.3

12.9

12.5

12.5 I

11.9

13.8

16.3

14.9 I

14.7

12.8

13.0

16.8

12.4

13.9 I

12.8

15.5

14.1

15.0 I

8.9

16.7

16.7

7.4

. . .

6.2 I

. . .

Jation ratios

Constructed yariable (X2)

Value

. . .

_

083.6

085.0

088.4

092.2

094.2

097.3

099.9

102.2

104.3

106.2

109.2

099.9

091.1

102.2

094.2

. . .

. . .

n

. . .

148

706

859

,054

588

915

,572

,876

,937

1,828

1,597

362

178

196

71

.

.

Mean

ID

. . .

_

83.6

85,0

88.4

92.2

94.1

97.3

100.0

102.2

104.3

106.2

109.2

99.9

91.1

102.6

94.5

.

. . .

——

12.4

12.7

12.5

14..0

13.2

13.8

13.9

13.2

12.9

13.3

12.9

(1)

14.3

(1)

(1)

21.54

.46

[1]

[21

[3]

[2]

[31

[11

NOTES: n = sample size; S1) = stmdard deviation, [ ] . grouped together in final variable construction.

6
clarify these procedures. The resultant outcome

for each of these two constructed variables was

to reduce response levels in (1) from 35 to 13

with only a slight decrease in percent variance

accounted for from 27.74 percent to 27.38 percent and in (2) from 45 to 12 with about a

l-percent decrease in accounted for variance

from 22.53 percent to 21.54 percent. Table A

presents the percent variance accounted for by

the two constructed variables.

A linear multiple regression equation of the

two criterion-scaled constructed variables with

the ID index was then computed. The values of

the equation were:

Y’ (ID) = .7382 (Xl) + .5598 (X2) - 29.80=S1S

The “predicted” values of the ID index (Y’)

were then taken as S1S index values. The productmoment correlation between S1S and ID was

.5676 and the correlation “ratio was .5690.

Since these two values are so close, a linear relationship between the two variables is indicated.

The mean value for S1S was 100.0 which is the

same as the mean for the ID index; the median

was 102.0. The standard deviation of S1S was

8.52 compared to 15.0 for ID which reflects

the remaining unaccounted for variance in ID.

The range of S1S index values was 76.6-115.9

and the distribution of observations was clearly

skewed toward the lower values of S1S. However,

the skew value of -.53 is not so great as to preclude the use of the S1S index as a dependent

variable in an analysis of variance design. A

description of the skewness and kurtosis tests

used is presented in the Technical Notes.

The Index of Differential-Intellectual

Development (DID)

The construction of the Differential-InteUectual-Development (DID) index was straightforward. The DID index score was obtained by

simply subtracting the S1S index score from

the ID index score for each individual and

adding a constant of 100.0: DID = ID - S1S +

100.0. Thus if an ID score was 120 .md S1S was

110, the DID index value would be 10 + 100.0

or equal to 110.0 which indicates a differential

intellectual development of 10 ID index scores

higher than expected based on the S1S index

value. The constant of 100.0 was added to give

the DID index the same mean as the ID and S1S

indexes; it also eliminates negative values and

permits a readily perceived comparison of DID

performance compared to ID and S1S. Thus a

DID score, for example, of 100.0 indicates that

the person’s ID score was the expected vaIue

based on the person’s S1S score.

The product-moment correlation between

DID and ID was .8225 and the correlation ratio

was .8215. The closeness of these two coefficients indicates an almost perfect linear relationship between DID and ID. The mean and median

for DID was 100.0 and the standard deviation

was 12.34. The product-moment correlation between DID and S1S was -.0015, which indicates

a near zero relationship. An analyses of variance

test was computed using S1S as the independent

variable and DID as the dependent variable.

S1S accounted for ordy 0.19 percent of the variance in DID; the correlation ratio was .04. Inspection of the mean DID values for each value

of S1S in table E, also reveals only slight random

variations of mean DID values across the whole

S1S range of values.

The range of the DID index values was 47-

143; the skew and kurtosis values of -.03 and

.14 respectively indicate an almost normal distribution of observations on DID.

Race-Specific S1S and DID Indexes

The S1S and DID index values were entered

in the data tape file of each child and youth and

analyses of variance were then run for all control, predictor, and constructed variables. The

amount of variance accounted for in the DID

index was 4.61 percent by race, 1.48 percent by

population change, and 1.00 percent by geographic region. None of the remaining variables

accounted for as much as 1 percent of the variance in DID (table A). SeveraI procedures were

used in trying to take out the race variance in

DID without using race. These included adjustment of criterion weights by geographic region

and population change jointly and the recalibration of the two constructed variables by optimal

criterion scaling within race. None of these

worked. The final procedure used was to compute race-specific (white and other races and

black) multiple regression equations for race7
Table E. Unweighed sample size, mean Socio-lntellectualStatus scores, means and standard deviations of Intellectual-Development

scores and Differential -I ntel Iectual -Development scores, by each value of the Socio-1 ntel Iectual -Status index, with percent variance

accounted for and correlation ratios

Sls

Total ............. .....................................................................

077 ........................... .................................................................. .......

079 ...... ........ .... .. ........................ ...................................................... ..

060 ....... ................................................................................ ...... .......

081 ....................................................................................................

082 ....................................................................................... .. .... .......

083 .... .. ...... .. ...... ...... .. ............................ ................ ............ ........ ...... ..

084 .................... ...... .. .................... ........ ...................................... ......

085 ............. ............................................ ...... .............................. .......

086 .................... ................................................................................

087 .......................... .......................................................... ...... ..........

088 ....................................................................................................

089 ................................................. ...................................................

090 ......................................... ...........................................................

081 ....................................................................................................

082 ....................................................................................................

083 ............................................................... .....................................

094 ........................................................................................... .........

095 ......................................................................................... ...........

086 .................................................................... ................................

087 ..................................................... ...............................................

W8 ......................................................................................... ...........

089 ....................................................................................................

700 .... ...................................................................................... ..........

101 ......................... ...........................................................................

102 ....................................................................................................

103 ....................................................................................................

Percent variance accounted for ..........................................................

Correlation ratio ....................................................c.............. .............

NOTE: n = sample size; SD = standard deviation.

specific S1S indexes. The resultant equations

were:

S1S (white and other races) = .7488 (Xl)

+ .4293 (X2) - 16.53

S1S (black) = .4625 (Xl) + .3613 (X2) + 8.62

The obtained summary statistics for race-specific

S1S indexes are shown in table F.

These mean S1S values were now comparable

to the mean ID values within race whereas the

n

13,887

121

82

30

243

38

264

47

177

214

222

263

183

306

413

219

195

452

321

467

523

708

338

572

819

206

868

990

934

797

186

699

198

521

342

296

44

445

144

. . .

.,.

Mean

Sls

100.0

77.2

79.3

80.3

81.1

82.4

83.0

84.3

85.0

86.2

87.1

88.2

89.2

90.2

91.3

92.1

93.1

94.1

94.9

95.9

97.0

98.3

99.1

100.0

101.2

102.0

102.8

103.9

105.1

106.2

107.2

108.0

108.8

109.9

111.0

112.1

113.1

113.9

115.9

99.94

.9997

Mean

ID

100.0

77.6

78.2

81.1

82.2

83.6

82.7

87.4

86.1

85.3

86.3

89.2

88.6

89.5

91.4

91.6

93.3

93.8

95.2

95.4

97.3

98.1

99.6

99.8

101.5

101.0

103.1

103.3

105.4

106.7

106.7

107.6

109.2

109.3

110.8

112.9

112.7

114.3

116.1

32.38

.5690

ID

SD

15.0

11.3

9.2

12.0

11.0

12.8

11.5

10.9

11.6

12.1

10.8

11.9

11.6

12.0

12.9

12.3

12.7

13.2

13.5

12.4

12,9

12.8

12.2

13.0

12.1

13.3

12.0

12.3

11.9

12.3

12.2

11.8

13.5

12.2

12.6

12.5

15.9

11.8

13.9

. . .

. . .

Mean

DID

100.0

100.4

98.9

100.8

101.1

101.2

99.8

103.1

101.1

99.0

99.2

101.0

99.4

99.3

100.1

99.5

100.2

99.7

100.3

99.5

100.3

99,8

100.5

99.8

100.3

99.0

100.4

99.4

100.3

100.5

99.5

99.6

100.3

99.4

99.6

100.8

99.6

100.4

100.2

0.19

.0361

DID

SD

12.34

11.3

9.2

12.0

11,0

12.8

11.5

10.9

11.6

12.1

10.8

11.9

11.6

12.0

13.0

12.3

12.8

13.2

13.5

12.4

12.9

12.8

12.2

13.0

12.1

13.3

12.0

12.3

11.9

12.3

12.2

11.7

13.5

12.2

12.7

12.5

15.9

11.8

13.9

. . .

. . .

Table F. Obtained means, standard deviations, range of scores,

and Socio-intellectual-Status and intellectual-Development

correlations for race-specific Socio-intellectual-status indexes

SIS4D

Race Mean SD Range correlation

All races .......... 100.0 9.04 76-116 .6011

White and other races ...... 102.0 7.52 80-116 .5258

Black race ........... ............ . 86.6 4.87 76-101 .4034

8
originrd S1S values were not (table A). S1S was

stifi skewed for all races, for white and other

races, but not for blacks.

The DID index values were obtained from

the race-specific S1S indexes as before. The

mean race-specific DID values were equal to

about 100.0 for both race groups, while the

original DID means were quite different for the

two race groups (table A). Analyses of variance

were run for the race-specific S1S and DID indexes with all 19 variables. It is apparent in

table A that differences in mean Intellectual

Development (ID) among the predictor and constructed variables were due to S1S influences.

Less than. 1 percent of the variance in the racespecific DID index was accounted for by any of

the 19 variables for all races and white and other

races. Among blacks, about half of the predictor

and constructed variables accounted for over 1

percent of the variance in DID. Inspection of the

mean DID values by response levels for blacks

(see detailed tables) did not reveal strong consistent trends sufficient to justify carrying the

race-specific S1S index construction any further.

The race-specific DID index for all races

had a mean of 100.0, standard deviation of

11.98, and a range of 44-142, and was still

almost norrmdly distributed.

Examined Sample Compared to

Population Estimates

Since the examined sample (n = 13,887) was

used in the development of the S1S and DID indexes, a comparison of the results from the

examined sample was made with the sample

weighted population estimates. No important

differences emerged between the sample and the

population estimates within all races, white and

other races, and blacks for means, standard

deviations, skewness, and kurtosis (table G).

However, the statistical values shown in this report should not be taken as population estimates;

they are sample values only.

Intercorrelations of the Indexes

The product-moment intercorrelations

among the indexes are shown in table H. The

race-specific S1S and DID index coefficients

with ID in the total sample was .601 and .798,

respectively. S1S and DID correlated -.003.

Analyses of variance were run with ID as the deTable G. Examined sample and population estimates summarv statistics. bv race and intellectual indexes

Race and index

All racas (n) ....................................................... ...........

lD .......... ............................ ...........................................................

S1S (general) ......... .... ........ ........ ....................................................

DID (general ) ..................... .................................................... .......

S1S (race-specific) ...... .. ...... ............................ .... .. ...... ...... ...... .. .....

DID (race.specific) ..................... ...................................................

White and other races (n) ......... .... .. .... .................... .......

lD .......... ........ .............................................. ............ ........ .............

S1S (general) ........ ...... .. ...... ...... .... .. ................ ...... .........................

DID (general )....... ............ ........ ........ ............ ........ .... .....................

S1S (race-specific) ........ .................................................................

DID (race.specific) ........................................................... .... ........ .

Black (n) .............................. .................... ........ .... .........

lD .... ............ ........ ................ .. ........ ...... .............. ............ ...... ...... ...

S1S (general) ............l ..................................................... ...............

DID (general )...... ........ ...... ...... ...... ........ ............ ...... ...... .. ...... .... .. ..

S1S (race-specific) .......... ................................... .......................... ..

DID (race.specific) ... .. .... .. ............ .. ...... .. .................. ............ ...... ...

Examined sample

(13,887)

100.0 14.99

100.0 8.52

100.0 12.34

100.0 9.04

100.0 11.98

-.08 .-.14

-.53 ‘.27

-.03 .14

-.51 -.57

-.04 .20

(11,901)

102.2 14.29

101.1 8.11

101.1 12.18

102.2 7.52

100.0 12.15

-.13 .07

-.68 .14

-.06 .18

-.65 .12

-.06 .18

(1,986)

86.7

93.1

93.5

86.6

100.1

11.88

7.69

11.25

4.87

10.87

.17

.13

.06

.13

.12

.00

-.50

.37

-.50

.23

Sample weighted

population estimetes

Mean SD I

Skew I

Kurtosis

I I I

(46,476,063)

100.0

100.0

100.0

100.0

99.9

15.00 -.09 -.15

8.67 -.54 -.31

12.30 -.02 .15

9.11 ‘.52 ‘.58

11.95 -.03 .20

(40,1 80,771 )

102.1

101.1

101.0

102.2

99.9

14.31 -.14 .05

8.29 ‘.69 .09

12.13 -.05 .18

7.68 -.67 .07

12.10 -.05 .18

(6.295.292)

86.5

93.1

93.4

86.6

100.0

11.98 .18 .01

7.78 .14 ‘.52

11.29 .06 .40

4.93 .14 ‘.52

10.92 .13 .25

9
Table H. Matrix of product-momant intercorrelations of the index(

Race and index

All races (n = 13,887)

lD .................. ............................................................................. .............. ......................

S1S (general). ..................... ...................... .. .............. ............................ .............. ...... ...... .

DID (general ) ...... ........ ............................. ................ ................................ ................ .......

S1S (race-specific) ........ ...................................................................................................

DID (race.specific) ........................................................ ..................................................

White and other races (n = 11,901)

lD ....................... ............................................. ...............................................................

SIS (general) ......... ............ .. ...................... .................... ........................................ ..........

DID (general) ............. .................................... .................................................................

S1S (race-specific) .............................................................. .............................................

DID (race.specific) ............................................................... .................. .. .......................

Black (n = 1,986)

lD .............................. .................... ........ ...... ........ .............. ...... .. .................... .................

SIS (general) ............................................................. ...... ................ .................... ............

DID (general) .......... ........ ...... .. .... ................ .. ...... ............................ ...... ...................... ....

S1S (race-specific) .... ...... .............. ...... ................ ...... .............................. .........................

DID (race+pecific) . ....... ...... ........ .. ...... ...................... ...... .............. .............. .. ............ ......

NOTE: G = general, RS = race-specific.

pendent variable with race-specific S1S and DID

indexes. S1S accounted for 36.26 percent and

DID accounted for 63.79 percent of the variance

in ID for a total of 100.05 percent. Since these

S1S and DID indexes were essentially independent indexes (r = - .003), this indicates that the

total variance in ID was separated into two

nonoverlapping independent components.

As a check on the stability of these index

values across diverse groups, the results from the

analyses of variance with the four control variables were inspected (table A and detailed table

1). No significant variance occurred across these

subgroups for any of the indexes. A further

check on the limits of possible shrinkage of the

strength of relationship of S1S and ID was made.

Analyses of variance were made of the full-range

variable sum of parental education, None-34

years and more, with ID for Cycles II and III

separately. The percent of variance accounted

for in ID was 28.04 and 27.96 and the correlation ratios were .530 and .529 respectively for

the two cycles. These checks support the position that the strength of relationships reported

for the combined sample would have’ been very

close had one cycle b;en used to

dexes and then cross-validated

cycle.

10

develop the inon the other

ID

1.000

.568

.822

.601

.798

1.000

.524

.824

.526

850

1.000

.403

.780

.403

.912

bv race —

SISG

1.000

-.002

.944

-.003

1.000

-.051

.998

-.001

1.000

‘.258

1.000

-.008

_

DIDG

1.000

.078

.970

1.000

-.048

.998

1.000

-.258

.968

“SRS

1.000

-.003

1.000

-.001

1.000

-.007

—

D’DRS

1.000

1.000

1.000

Since the correlation between ID and racespecific S1S was .60 and since other studies3 indicate a correlation of IQ of about .55 between

siblings reared together, the position is taken

that the S1S index is measuring a generalized

sociological family background factor relating

to intellectual achievement. However, DID

cannot be taken, at least at this time, as independent of other intrafamily characteristics,

orientations, and interactions.

Future research investigations intc~ family

contributors to children’s intellectual achievement should include direct measures of parental

intellectual achievement as well as intellectual

achievement orientations and supports within

the family.

SUBSTANTIVE FINDINGS

Application of the ID and Race-Specific S1S and

Dl D indexes to Substantive Examination

Findings from Cycle 11,Children 6-11

Years of Age

About 500 data elements were available on

an extended data tape for the 7,119 children

6-11 years of age examined in Cycle IL

Sixteen data elements or variables were
selected to “test out” the indexes. The following nine variables were selected for which

product-moment correlations were computed

with the three indexes.

The two constructed variables

1, Sum of parental education

2. Annual family income per household

person under age 21

The two Wechsler Intelligence Scale for Children (WISC) subtests used in constructing ID

3. T-scored Vocabulary sub test

4. T-scored BIock Design subtest

Two tests from the Wide Range Achievement Test (WRAT)

5. T-scored Reading Test

6. T-scored Arithmetic Test

The Harris-Goodenough Draw-A-Person Test

(D~)T-scored DM Test

An educational achievement composite score

of the two WRAT tests (mean 100.0, standard deviation 15 .O–the same as ID)

8. Education achievement

A total measured performance index made

of the two WISC, ~wo WRAT, the DAP Test

scores (mean 100.0, standard deviation 15.0)

9. Total performance

The correlation coefficients are shown in

table J.

The intercorrelations among the three indexes were almost identical to those found on

the combined Cycles II and 111 sample. Neither

one of the two constructed variables that were

used for deriving the S1S index correlated with

DID. The WISC Vocabulary subtest contributed

more to S1S than Block Design contributed, and

the reverse occurred for DID. The WRAT tests

had slightly higher correlations with S1S than

with DID; the reverse was true for the Draw-APerson (DAP) Test.

The correlations of S1S with the WRAT and

the DAP Test are reasonable expectations. The

DID correlations with these three tests indicate

that it has a meaningful measurement property

and is not just a random residual component of

Table J. Correlation coefficients, means, and standard deviations for intellectual indexes and selected variables

Index and variablel

Index

lD .............. ...... .................... ...... ................ .... .. .................... ...... ...... ...................................

Sls ..... .......................... .................................................................. .. ................ .. ................

DID .................................................................................................................. ..................

Constructed variable

Sum of parental education ...... ............ ................ ...................... .. ........................ ...... .........

Annual family income per household person undar age 21 ....... ...... ....................................

Wlsc

T-scored Vocabulary subtest ............. .................. .. ...... ............ ............ .. .... ...... .. .... .............

T-scored Block Design subtest ......... ............ .................... ...... ........ .....................................

WRAT

T-scored Reading test .............. ...... ...... ...................................... ...... .............. ...... ...... .........

T-scored Arithmetic test ..................... ........ ............ ...... ...... ...... .. ............ ............................

Draw-A-Person Test ................... ......................................... .......................................... ......

Educational achievement composite ................................................................................. ..

Total performance composite .................................. ...... ...... .................... ............ ...............

+3ample size = 7,119.

E

Correlation coefficient

1.000

.603

.793

.523

.4s6

.859

.857

.633

.612

.481

.679

.895

.603

1.000

-.008

.880

.790

.581

.464

.505

.463

.263

.530

.589

.793

-.008

1.000

‘.016

.006

.633

.727

.408

.413

.402

.447

.671

-

Mean

100.2

99.7

100.5

100.1

88.0

50.3

50.2

50.2

50.2

50.4

100.1

100.2

SD

14.91

9.09

11.90

7.83

6.99

9.82

9.76

9.81

9.77

9.86

14.94

14.88

11
the ID index after S1S variance was taken out.

The next seven variables were selected because of interest in their substantive properties.

Analyses of variance were used to try to explicate their relationships with intellectual achieve -

ment and as further tests of application of the

S1S and DID indexes. The dependent variables

were the ID and race-specific S1S and DID indexes. The substantive variables are as follows:

1. Number of pregnancies previous to the

birth of the examined child as reported

at the time of examination.

2. Parental reporting of attendance at nursery school or kindergarten of the examined child.

3. Parental reporting of a talking problem of

the examined child.

4. Twin status as determined from parental

interview and birth certificates.

5. Judged intellectual level by school personnel as given on the school questionnaire.

6. Need for special school resources as indicated by school personnel on the school

questionnaire.

7. Diagnostic impressions of neurological,

muscular, or joint conditions by the examining physician. Interest in this variable

was centered on the relationships of the

neurolagical conditions and intellectual

achievement indexes.

In the following description of findings, if

at least 1 percent of variance is accounted for in

any of the three indexes, then this will be considered as statistically significant or of practical

importance.

A guide in the interpretation of the relative

contribution of S1S versus DID in reflecting

their respective parts of the Intellectual Development (ID) index is that the percent of variance

accounted for in the S1S index must be almost

two times as great as in the DID index to show

equal accounting. A more precise indicator is

to multiply each percent of variance by .364

for S1S and .629 for DID. This indicates how

much of the ID index variance was accounted

for in the S1S and DID indexes. The sum of

these computed variances will not necessarily

equal the ID variance due to S1S and DID interactions with a given condition.

While a substantial relationship is shown between number of previous pregnancies (or approximate birth order) and the index of Intellectual Development, the variance was almost completely accounted for by S1S (table K). These

findings thus indicate that birth order per se

has little to do with the intellectual achievement

of the child when the Socio -Intellectual-Status

index of the family is taken into consideration.

That is, children further down in birth order

also come from families with lower S1S.

Attendance at nursery school or kindergarten was associated with the index of Intellectual

Development and S1S but had little relationship

with the index of Differential-Intellectual Development (table L). Thus attendance did not contribute to the Differential-Intelle ctual-Develop -

ment index.

While reported talking problems were related

to the index of Intellectual Development, a part

of this relationship was due to more talking

problems among lower S1S families (table M).

However, “hard to understand” does seem to

have a negative relationship on the index of

Table K. Sample size and mean index :cores of intellectual

achievement, by number of pregnancies previous to birth of

examined child, with percent variance accounted for and

correlation ratios

Number of pregnancies previous

to birth of

examined child

No pregnancy ........ .. ...

One pregnancy ............

Two pregnancies .........

Three pregnancies .......

Four pregnancies ..... ...

Five pregnancies .........

Six pregnancies ...........

Seven pregnancies .......

Eight pregnancies ........

Nine pregnancies or

more ............. ..........

Blank item ..................

Percent variance accounted for .............

Correlation ratio .........

Mean index scores

n

I

ID

T

1,700 102.2

1,620 101.9

1,323 101.5

864 100.4

539 97.3

352 95.3

218 93.3

131 90.1

78 92.1

114 88.8

180 100.9

. . .

I

4.44

. . . .21

NOTE: n = sample size.

Race-specific

Sls

101.9

101.8

I 00.9

99.2

97.1

94.8

92.4

91.6

90.3

88.3

98.8

12.11

,35

DID

100.3

100.2

100.6

101.1

100.3

100.5

100.9

98.6

101.8

100.5

102.1

0.18

.04

12
Table L. Sample size and maan index scores of intellectual

achievement, by attendance at nursery school or kindergarten, with parcent varianca accounted for and correlation

Table N. Sample size and mean index scores of intellectual

achievement, by twin status, with percent variance accounted for and correlation atios

Mean index scores

ratios

Mean index scores

Attended nursery

school or

kindergarten

Yes ......... ....................

No ..............................

Blank item .......... ........

Don’t know ............... .

Percent variance accounted for .............

Correlation ratio .........

Twin status l“ Race-specific

ID

Race-specific ID

100.2

99.9

96.3

84.9

0.36

.06

n

m

99.7

100.7

97.8

92.8

0.21

.05

DID

100.5

99.2

98.5

92.2

0.12

.04

S1S I DID

Not a twin ..................

Twin, identical ............

Twin, not identical .....

Twin, unknown if

identical ..................

6,965

43

93

101.7 101.0

95.2 99.4

98.5 95.0

93.5 97.2

4,932

2,159

16

12

102.7

94.6

93.5

90.7 18

Percent variance accounted for ...... .... ...

Correlation ratio .........

. . .

. . .

. . .

. . .

NOTE: n = sample size.

Table M. Sample size and mean index scores of intellectual

achievement, by nature of talking problem, with percent

NOTE: n = sample size.

Table O. Samole size and mean index scores of intellectual

achievement, by school-judged intellectual level, with pervarianca accounted for and wrelation ratios cent variance accounted for and correlation ratios

n

Mean index scores Mean index scores

ID

Nature of

talking problem

School-judged

intellectual level

Race-specific n Race-specific

ID

Sls DID SE DID

No talking problem reported .....................

Loping ............... .........

Some other talking

problem ............. .....

Mora than one listed

problem ..................

Stammering or stuttering ...........................

Hard to understand .....

Percent variance accounted for .............

Correlation ratio ....... ..

Clearly above average

(top 25 percent) ......

About average (mid50 percent) ........ .....

No school questionnaire ........................

No basis for judging ...

Clearly below average

(bottom 25 percent) ...

Percent variance accounted for ........... ..

Correlation ratio .........

6,563

81

137

5

144

189

. . .

. . .

100.7

101.8

97.8

92.0

91.7

91.1

1.82

.14

99.9

100.6

99.6

101.4

93.2

97.5

1.25

.11

100.8

101.1

98.2

90.6

98.5

93.6

1.12

.11

1,584

3,646

322

288

1,258

. . .

. . .

110.9

100.4

95.4

93.7

89.0

22.79

.48

106.5

100.5

98.3

97.8

94.1

11.24

.34

104.4

99.9

97.1

95.9

95.0

11.97

.35

NOTE: n = sampl~ size.

NOTE: n = sample size. ally so for the question specifically requesting

an” evaluation of ‘intellectu&l level (table; O and

Differential-Intellectual Development. Thus this P). Besides the three special resources shown in

table P (gifted, SIOW learner, retarded), six other

resources were provided in the questionnaire

checklist (hard of hearing, “sight” saving, speech

therapy, orthopedicalIy handicapped, emotionally disturbed, and “other”). If any of these

were recommended but not also recommended

for the three shown here, they were coded in the

“other resource recommended” category. It is

evident that this group, as a group, was very

close to average on all three intellectual achievement indexes. The finding of interest here is

type of talking problem does- seem to reflect

impeded intellectual achievement.

Twin status had only a very weak association

with the index of Intellectual Development

(table N). These data indicate that twin versus

nontwin birth is not importantly related to individual intellectual achievement particularly

when the family factor of S1S is removed.

Two evaluations were obtained from school

personnel that were highly associated with the

index of Intellectual Development, and especi13
Table P. Sample size and mean index scores of intellectual

achievement, by recommendations for special school resources, with percent variance accounted for and correlationretios

Recommendation

for special

school resources

For gifted ...................

None recommended ....

Other resources recommended ............ ..

No school questionnaire ........................

For slow learner ..........

For mentally retarded

Percent variance accounted for .............

Correlation ratio .........

n

307

4,767

751

322

889

83

. . .

. . .

NOTE: n = sample size.

Mean index scores

ID

114.9

102.3

98.0

95.4

89.5

77.3

15.41

.39

Race-specific

SIs

105.0

100.8

98.7

97.1

94.6

92.7

7.54

.27

DID

109.9

101.5

99.4

98.3

94.9

84.6

8.30

.29

that the strong association of DID with school

evaluation indicates that these judgments reflected differential teacher assessments of students’ inteHectual achievement beyond what

would be expected based on family background.

The examining physicians did detect some

medical conditions that also had strong relationships with the index of Intellectual Development

(table Q). Interestingly these noted conditions

occurred almost independently of S1S family

background. Thus these data seem to clearly

indicate that the 61 children with listed conditions 1-8 (in table Q) suffered direct personal

impairment in intellectual achievement attendant to these conditions.

These findings indicate that the three indexes, ID, S1S, and DID, can provide differential

information on the association of intellectual

achievement with other health-related variables.

Table Q. Sample size and mean index scores of intellectual achievement, by diagnostic impressions of neurological, muscular, or joint

conditions by the examining physician, with percent variance accounted for and correlation ratios

Diagnostic impressions of neurological, muscular, or joint conditions

by the examining physician

1. Mongolism or other developmental ............ .......... ...... ...................... .... ..................................

2. Mental retardation unknown etiology . ...................... ...... .......... ...... ...... .............................. ...

3. Eye and muscular-skeleton ..............................................................................................t .....

4. Cerabral palsy and brain damage ... .........................................................................................

5. Minimal cerebral dysfunction ................................................................................................

6. Cerebral problem.. .................... .............................................................................................

7. Epilepsy ......................... ............................................................................................. ........ ...

8. Other neurological .. .. .................... ...................... .......................................... .............. ...........

9. Other muscular, skeleton, joint condition ........... ...................... ............ .................................

10. Traumatic neurological residual ............................................. ..............................................

11. Muscular-skeleton-joint ................. ...... .. .................... ...... ...... .. ........ .... ........ .........................

12. Eye muscular imbalance or eye condition ....................... .............. .......................................

13. Ear condition including deafness ......... ...... ................ .... ........ ........ ...................... ...... ...... ....

None of the above noted ...................................................................................... ......................

Percent variance accounted for .................................. .. ...... .............. .. .... ........ .............. ...............

Correlation ratio .......................................... ...................... ................................................ .........

n

8

11

1

16

9

7

3

6

3

8

81

34

2

6,930

. . .

.,.

Mean index scores

ID

65.8

70.7

88.0

88.7

83.1

90.7

102.3

97.2

86.0

98.6

99.5

97.3

99.0

100.4

1.63

.13

Race-specific

SE

99.2

99.4

102.5

101.2

93.8

100.1

107.1

101.2

87.2

99.7

99.9

96.8

98.1

99.8

0.22

.05

.—

DID

66.6

71.3

85.5

87.5

89.3

90.6

95.2

96.0

98.8

98.9

99.5

100.5

100.9

100.6

2.36

.15

NOTE: n = sample size.

000

14
REFERENCES

lNational Center for Health Statistics: CzmrentListing and Topical Index to the Vital and Health Statistics

Series, 1962-1975. DHEW Pub. No. (HRA) 76-1301.

Human Resources Administration. Washington. U.S.

Government Printing Office, Apr. 1976.

2National Center for Health Statistics: Sub test estimates of the WISC full scale IQ’s for children. Vital

and Health Statistics. Series 2-No. 47. DHEW Pub.

No. (HSM) 72-1047. Health Services and Mental Health

Administration. Washington. U.S. Government Printing

Office, Mar. 1972.

3Jensen, A. R.: How much can we boost IQ and

scholastic achievement. Harvard Educ. Rev. Winter,

1969.

4Beaton, A. E.: Scaling cxiterion of questionnaire

items. Socio-Economic Plan. Sci. Vol. 2. Pergamon

Press. pp. 355-362. Reprints may be obtained from Dr.

Beaton at Educational Testing Service, Princeton, New

Jersey 08540.

5Kendall, M. D., and Stuart, A.: The Advanced

Theory of Statistics. Vol. I, 3rd ed. New York. Hafner

Publishing Co., 1969.

15
LIST OF DETAILED TABLES

1. Unweighed sample size and mean index scores of the intellectual achievement indexes for children and youths aged 6-17 years,

by race and independent control variables, with standard deviations of total, percent variance accounted for, and correlation

ratios .................................................................................... ....... ................ ....... ............................................................................. 17

2. Unweighed sample size and mean index scores of the intellectual achievement indexes for children and youths aged 6-17 years,

by race and independent predictor variables, with standard deviations of total, percent variance accounted for, and correlation

ratios . .. .. ........ .............. ................................ .............. .. ............ .......... .............. ...........................t.................................................... 18

3. Unweighed sample size and mean index scores of the intellectual achievement indexas for children and youths aged 6-17 years,

by rata and independent constructed variables, with standard deviations of total, parcent variance accounted for, and correlation ratios ..................... .............. ............... ....... ....................................................... ........................................................................ 22.

16
TabIt! 1. Unweighed sample stze and mean index scores of the intellectual achievement indexes for children and youths agsd 6-17 years, by race and Independent control variable, with standard deviations of total, percent variance

accounted for, and correlation iatios

[ Unweighed examined sample = 13.887 chddren and youths. aged 6-17 YCatS]

Mean index score

General index Racewx?cific index

Nhite

and

other

races

Sls DID

Black

SK+

White

and

other

races

f 02.2

7.52

102.4

102.0

0.07

.03

101.9

102.6

0.21

.05

102,0

101.9

102.0

101.7

101.8

101.8

102,5

102.5

102.7

102.3

102.8

102.7

103,0

0.25

.05

100.8

91.9

102.3

97.4

102,3

0.84

.09

Black All

races

DID

Nhite

and

nther

races

00.0

12.15

99.8

00.2

0.02

.02

00.5

99.4

0.19

.04

00.3

00.5

00.1

01.1

00.3

00.6

99.4

99.7

99.3

99.5

99.3

99.5

LIG.5

0.25

.05

98.8

101.1

95,4

96,9

I00.0

0.06

.02

Black

100.1

10.87

_

99.7

100.4

0.13

.04

100.5

99.6

0.16

.04

101.3

99.7

100.3

100.6

100.7

100.7

99.9

99.9

99.3

100.2

99.8

97.8

102.3

0.55

.07

98.1

105.8

102.0

104.2

100.0

0.10

.03

All

races

ID

Black

88.7

11.9

31ack

1,988

.

943

I ,043

. . .

.

9B7

999

156

172

192

15s

142

15a

198

171

1B9

157

15CI

128

lb

!7

3

6

5

1.963

White White

and

other

races

White

and

other

races

All

races

Oo.o

8.04

00.3

89.6

0.18

.04

99.7

IKU2.3

0.08

.03

89.8

98.7

99.6

99.6

99.9

98.6

16+3.1

IOG,3

I00.3

100.2

[00.5

100.4

99.2

0.13

.04

99.2

91.4

8%2

95.8

Im.o

0.38

.06

All

races

and

other

races

102.2

14.3

All

races

All

races

Black

Total, 12.17 vears ...

Standard dewat{on

13,8B7

.

1,801 loa.o

150

100.0

8.52

100.3

99.7

0.12

.03

99.5

100.4

0.27

.05

98.6

99.5

99.6

99.4

88.6

99.4

100.3

100.3

100.5

100.3

100.7

100.7

100.6

0.31

.06

99.4

90.0

99.8

84.8

100.0

0.58

.08

101.1

8.11

93.1

7.69

I00.0

12.34

101.1

12.18

93.5

11.25

66,6

4.B7

00.0

11.98

Male

Female .

100.1

99.8

0.01

0.01

100.2

99.7

0.03

.02

1003

100.1

99.B

1S+7.6

100,3

16+3,1

99.6

1000

995

~9.8

899

99.7

91:2

0.06

.02

97.9

92.8

98.0

93.4

100.0

0.17

.04

86.3

87.0

0.03

0.03

66.6

86.5

0.01

.01

67.5

86.1

B7.2

86.7

67.0

86,5

87.0

86.5

86.4

67.2

86.5

84.8

90.7

0.37

06

86.7

69,7

69,5

85.6

667

0.03

.02

101.3

100.9

0.O8

.03

100.6

101.6

0.35

.06

100,6

100.6

100.7

100.5

100,6

100,6

101,5

101.5

101.7

101.4

101.8

101.8

102.2

0.41

.06

89.9

90.1

101.2

85.9

101.2

0.62

08

93.2

93.1

0.00

.00

92.7

93.6

0.37

.06

82.6

92.9

93.6

92.4

82.7

91.8

83,9

93.0

83.8

93.7

83.2

93.7

96.0

0.78

.09

96.2

88.8

94.5

B5.O

93.2

0.41

.06

99.9

I 00.2

0.02

.01

100.7

99.3

0.31

.06

100.7

100.6

100.2

101.3

100.7

100.8

99.3

88.7

89.0

99.5

99.3

99.0

96.6

0.38

JX

98.5

102,8

86.2

96.6

100.0

0.05

.02

I00.9.

101.3

0.03

.02

101.7

1OQ.4

0.30

.05

101.6

101.6

101.4

102.3

101.6

101.8

100.5

100.7

100.2

100.5

ICQ.2

I 00.3

97.3

0.37

.06

99.7

103.0

86.5

88.4

101.1

0.06

.02

93.1

93.9

0.13

.04

84.1

82.9

0.26

.05

94.8

93.2

93.6

94.3

94.3

94.7

83.1

93.5

92.5

93.5

93.3

91.1

94.6

0.70

.OB

90.5

I 00.9

95.0

100.6

93.5

0.20

.04

86.6

B6.6

0.00

.005

86,3

66.9

0.38

.06

66.3

86.4

B6.9

66.1

86.3

B5.8

87.1

66.5

B7.1

87.0

86.7

B7.o

6.2.4

0.60

.09

8S.5

B3.8

87.4

81.4

86.8

0.41

.86

98.8

00.2

0.03

.02

100.5

99.5

0.18

.04

100.5

I00.4

100.2

101.0

100.4

100.6

99.6

89.7

89,3

99.6

98.4

99.2

!38.0

0,23

.05

98,7

101.4

96.8

97.6

100.0

0.64

.02

7,177

6,710

. . .

7,119

6.75S

1,111

1,241

1,231

1,184

1,160

1,120

1,262

1.208

1,204

1,116

1,092

900

58

.,.

69

45

2B

49

13,686

6,234

5,667

6,132

5,769

955

1.089

1,039

1,026

1,o18

862

1,064

1.037

1.015

959

942

772

43

60

42

22

44

11,733

102.2

102.2

O.WJ

0.00

102.4

102.0

0.02

.01

102.4

102.4

102.1

1026

102.2

102.4

101.8

102.2

1020

101.9

102,0

102.2

99.5

0.04

.02

99.6

930

977

943

1023

0.30

.05

Penxmt var,a.m accounted for, ...............

Correlation ratio.

Ex8mmat10n cycle

[children !md youths)

Cycle II, 6.11 years .

Cycle Ill, 12-17 years, ................. .. ...... ..

Percem variance accounted for..., ..............

Currelatton ratio ......................................

Percent varmnce accaumed fro .................

Corre{at,on ratio.,,.,, .....

Vocabulary and 61t%k Des!g. Test

qualif,catnons

Percent varmwe accounted for..., ........

COrrelat,On ratnO..................................

-3
Table 2. Unweiqhted samole size and mean index scores of the intellectual achievement indexes for children and vouths ,med 6-17 vears. bv race and independent twedictor variables. with standard deviations of total. oercent variance

02 accounted for, and correlation ratios

[ Umwighted examined sample= 13,887 children and ycmths. aged 6-17 yews j

31ack

1,986

Mean index mom

General index Race.speci fic index

White

and

other

Independent predictor variable All

races

10 Sls DID Sls DID

Black Black Black

White

and

other

races

102.2

14.3

83.1

82.3

S4.9

85.1

87.1

90.2

93.8

93.6

98.2

98.9

100.5

100,9

104.7

107.5

108.1

110.0

110.7

112.7

101.7

91.1

93.7

21.35

,48

82.3

82.3

84.6

86.1

86.7

87.4

90.4

92.8

96.2

97.4

99.2

101.7

105.5

109.1

109.8

110.1

113.1

1 13.s

98.6

99.1

97.9

19.53

.44

White

and

White

and

other

races

Wh&te

and

other

races

races Wh$te

and

other

races

100.0

12,15

All

,Flces

All All

races

100.0

12.34

100.5

89.0

100.6

100.2

98.9

100.3

100.7

99.0

101.3

99.9

99.5

98.2

100.3

88.7

lCO.O

100.2

100.1

99.9

105.3

97.6

95.6

0.55

.07

180.4

101.7

98.3

101.2

100.5

1Q3.3

lCL1.3

99.4

100.6

98.6

98.9

98,5

100.7

100.6

100.1

100.2

100.8

29.4

98.4

100.4

100.8

0.54

.07

All All

81ack

races other races

races

Total, 12.17 yews ..... ... . . .........

Standard deviaticm ... .. .. ..........

13,887

,..

I 1,901 100.0

15.0

86.7

11.9

100.0

8.52

101.1

8.11

93.1

7.69

101.1

12.16

93.5

11.25

100.0

9.04

102.2

7.52

86.6

4.67

100.0

11.98

lCO.1

10.87

_ _ _ _

First parent’s education (completed years)

164

75

185

257

254

297

382

586

1,632

984

1,117

762

4,107

374

524

206

960

?23

3

86

189

. .

69

37

89

144

171

193

319

362

1,053

794

1,108

853

4,857

403

481

222

586

182

1,015

827

122

. .

. .

125

51

115

170

754

182

256

413

1,437

804

914

640

3.748

343

505

197

855

705

3

56

126

.

. . .

61

23

67

124

133

150

259

283

898

643

950

677

4,559

375

451

213

566

173

662

526

86

. . .

39

24

50

67

100

115

126

173

195

180

203

142

359

31

19

9

25

18

30

61

.

. . .

8

14

22

20

38

43

80

79

155

151

158

176

29S

28

30

9

20

s

333

301

34

. . .

. . .

81.9

81.0

83.8

83.7

84.9

86.2

90.6

90.9

96.6

96.4

98.1

99.0

103.6

106.5

107.4

109.4

110,2 112,3

101.7

86.1

90.7

24.52

.50

81.9

83.9

81.3

85,2

65.6

86.6

88.7

90.6

94,5

94.9

97.4

99.2

104,6

107.6

108.9

109.5

112.5

;13.1

94.6

94.5

94.6

21.23

.46

78.2

78.2

81.2

S0.8

81.6

85.1

84.3

64.6

84.9

85.6

67.3

90.7

92.2

94.8

91.2

96.9

93.7

98.2

82.4

84.5

12.61

.36

78.9

86.6

71.1

79.4

81.8

83.8

81.4

82.5

84.9

84,4

86.6

89.7

90.7

87.9

95.5

95.0

94.8

S7.7

66.4

86.3

86.0

8.66

.29

81.4

82.0

83.2

83.5

86,0

87.9

89.9

91.9

95.3

96.6

98.6

100.6

103.2

106.8

107.5

109.3

110.1

112.4

96.4

90.5

95.1

74.22

.86

81.6

82.2

63.0

84.0

85.1

86.3

88.4

91.2

93.9

96.2

96.5

t 00.8

103.9

107.0

108.9

109.3

111.7

I 13.7

96.2

94.1

93.8

60.49

.78

81.5

61.7

83.2

83.6

86.0

88.2

90.5

92.5

95.8

97.6

99.4

101.5

103.5

107.1

107.5

I 09.4

I 10.2

112.4

96.4

80.7

95.9

74.20

.86

61.5

81.9

83.5

64.1

65.4

86.4

88.9

92,2

94.5

97.2

99.1

101.7

104.2

107.7

109.1

I 09.4

111.9

I 13.8

97.9

96.2

95.1

62.35

.79

81.1

82.7

63.1

83.1

86.0

87.4

88.8

SQ.4

92.1

92.0

95,3

97.6

100.2

102.9

105.5

107.3

108.6

I1O,9

. . .

80.2

93.3

84.95

.81

82.0

82.6

81.6

83.3

84.3

65.6

86.5

87.7

90.7

92.1

94.7

97.0

99.6

98.1

105.6

107.1

105.2

:! 1.4

92.6

90.4

90.3

42.30

.65

101.6

100.7

101.7

101.5

101.0

102.0

103.3

101.1

102.5

101.3

101.1

99.4

101.1

100.4

103.5

100.7

100.5

100.2

105.3

100.4

97.7

0.51

.07

1008

100.3

101.1

102.0

101.3

101.0

101.5

100.6

101.7

100.3

100.1

100.0

101.3

101.4

100.7

100.7

101.2

100.0

100.7

102.9

102.8

0.31

.06

97.1

95.5

98.1

97.7

95.6

97.7

95.4

94.2

92.8

93.5

92.0

93.1

92.0

91.9

85.7

89.6

85.1

87.3

92.2

91.2

4.69

.22

96.9

104.0

89.6

96.1

97.4

98.2

94.9

94.8

94.2

92.3

91.9

92.6

91,2

89.8

89.9

87.9

89.5

86.3

93,8

96.0

95.7

4.05

.20

62.5

82.8

83.8

83.9

85.7

87.3

89.4

91,3

95.7

96.5

98.3

100.2

103.3

106.6

107.8

109.4

110.5

112.7

97.2

89.9

93.7

67.63

,82

83.1

82.5

64.0

85.4

86.1

86.9

89,2

91.4

94.3

96.0

98.4

100.0

104.2

107.2

108.9

109.7

111,9

113.5

95.0

93.1

93,1

53.91

.73

83.6

64.1

85.3

85.6

88.0

90.1

92.1

94.0

97.1

98.8

00.5

102.6

104.5

07.9

06.3

10.1

10.9

13.0

97.2

92.6

97.1

78.09

.88

83.6

84.1

65.5

66,2

87.5

86.4

90.7

93.7

95.9

98.4

00.2

02.8

05.1

08.5

09.8

10.3

12.5

14.3

99.2

97.9

96.3

64.39

.80

79.0

80,0

60.3

80.3

82.1

83.0

83.9

84.9

86.0

85.9

87.9

69.4

91.1

92.8

94.4

95.6

96.4

97.8

64.7

66.7

64.40

.80

80.1

80,0

79.3

80.4

81.1

61.9

82.4

83.1

85.0

85,9

87.6

89.1

90.6

89.8

94.5

95.5

84.2

W.!

86.3

64.9

66.1

41.25

.64

99.4

98.2

103.0

99,8

99.2

100.9

101.3

99.6

100.9

103.0

99.9

9S.8

100.2

99.8

99.6

100,0

98.7

99.6

104.5

96.2

97.0

0.32

.06

98.8

101.4

97.3

99.8

99.5

89.6

99.5

99.2

100.2

98.9

98.0

99.2

100.4

100.4

100.1

99.8

100.6

99.6

99.6

101.3

101.5

0,33

.06

99.5

98.3

99.6

99.4

99.1

100.1

101.7

99.6

101.2

100.0

100.0

96.3

100.1

99.6

99.7

99.9

99.6

99.6

104.5

96.5

96.6

0.39

.06

98.8

96.2

99.1

99.9

99.2

99.0

99.7

99.2

100.3

99.0

99.0

96.9

I 00.4

89.2

96.2

100.9

100.5

99.5

102.1

100.4

99.7

99.0

99.7

99.3

101.3

101.1

102.0

96.8

101.3

97.3

300.4

97:7

97.8

1.15

.11

98.8

106.6

91.8

99.0

100.7

101.9

99.0

99.4

99.8

96.5

98.0

100.6

100.1

98.1

101.0

99.5

100.6

99.6

100.1

101.5

101.2

1.62

.13

Percem variance accounted fcm.............. ......

Correlation ratio..., ......................................

Second parent% education

(completed years)

100.5

I 00.0

99.8

100.6

g~.~

99.4

101.2

101,6

0.31

.06

Percent variance accounted for..., ................

Correlation ratio .............. ............................
Annual family income

01 Under $500 ...........................................

02 $mo.ww .............................................

03 sl,om-$l,w9 .......................................

04 $2,000-$2,988 ..... .......... .. ...................

05 $3,wo.$3,9m .......................................

06 $4,000.$4iw9 .....................................

07 $5,~0.$6,9W .......................................

08 $7,000-89,999 ..... . .... .

09 $10,030.$14,999.., ................................

10 S15,000 and O“ti, . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 Don’t how. .....................................

12 61a.k m refused to answer ....................

104

28E

709

939

1,084

1,142

2.737

3,008

2,090

981

540

267

Pcrce,ntvariance accounted fax,, ..................

Correlation ratio....................................... . . .

Percem variance xccmntcd for.., ................. . . .

Correlation ratio.......................................... . . .

Number of persons in household

under 21 years of agi I

Percent variance accounted far ....................

Correlation ratio ......................................

Percent variance accounted for ....................

Correlation ratio..., ......................................

6olh parents” relationship m childlyouth

Father and mother .................. ........... .......

Father witho.t mother ................................

Mother wnhout father .................................

Both foster parents......................................

All other ......................................................

Percem variance accounted for., ..................

Correlation ratio..,, ..................................

First parent’s relationship to childlyouth

1,264

2,836

3,229

2,558

1,567

1,007

599

371

181

276

. .

3,423

3,653

3,411

3,400

...

...

11,148

240

2,055

85

359

..

...

18

11,388

1,519

536

4

107

69

162

437

628

745

927

2,422

2,S30

2,02a

966

449

237

...

...

.

.

...

...

.,.

1,121

2,611

2,957

2,199

1,279

766

417

261

117

173

.

...

I

3,011

3,311

2.443

3.136

...

10,029

186

1,410

65

209

...

16

10,217

988

42U

35

126

272

311

339

215

315

17G

61

15

!71

30

.

.

143

225

272

359

2s8

241

182

110

64

102

412

342

868

264

1,119

52

645

20

150

. . .

2

1,171

531

116

4;

856

66.8

66.9

69.7

92.5

96.4

100.2

104.1

106.9

110.6

97.0

100.5

20.30

.45

102.2

86.7

104,2

13.15

,36

102,6

103.2

103.1

100.2

97.4

93.6

93.1

89.9

91.0

86.2

769

.28

102.3

102.0

94.0

101.4

5.20

.23

101.3

96.6

95.0

94.6

90.0

3.64

.19

83.9

101.2

94.8

95.6

94.5

91.1

68.o

89.9

69.8

92,1

95.2

98.5

101.7

1047

107.4

110.8

99.0

102.3

15.20

.39

104,3

104.5

104.3

1022

l@3.1

96.1

96.6

934

96.1

923

4.92

.22

104.0

103.4

98.1

102.3

2.31

.15

102.9

995

888

97.3

95.0

1.46

.12

64.3

102.6

99.1

96.0

94.6

96.6

80.8

82.7

82.2

84.9

86.6

.37.7

66.4

!33.6

91.s

950

87.1

85.6

7.81

.26

.

. .

. . .

.s9.5

88.7

90.2

879

85.8

65.4

85.0

81.6

81.8

81.3

5.11

.23

89.9

88.4

83.7

90.3

6.13

.25

87.0

87.6

86.8

85.6

83.2

0.75

,09

80.5

07.0

66,9

86.6

. . .

64.2

84.3

S6.1

87.3

8+J.3

93.1

97.0

100.1

1036

106,9

1105

96.7

100.4

59.45

.77

101.1

93.1

101 G

10.70

.33

103.1

103.7

102.5

100.3

96.6

93.9

93.0

91.1

91.6

86.1

23.40

.48

101.7

101,6

961

1003

701

.26

1043.9

96.7

96.1

99.6

93.0

5.92

.24

95.4

100,9

96.4

97.9

96.9

92.4

828

86,7

87.1

90.6

93,2

97.4

100.5

103.0

1070

110.6

97.4

1010

57.64

.76

907

103,8

104.2

103.1

101.3

97.6

g4,9

94.1

92.0

94.1

20,31

.45

102.6

102.0

98.4

1028

3.56

.19

101.7

100.3

97.7

102.5

96.7

3.36

.16

94.9

101.7

97.2

98.8

96.9

96.2

85.3

85.3

67.7

89.6

92.8

95.1

96.7

101.3

105.0

105.0

930

96.4

42.10

.65

,..

!)7.1

97.4

96.8

94.2

92.G

90.6

90.7

69.1

67.0

64.6

21.08

,46

95.2

97.1

!704

84.8

12.78

.36

94.1

93.1

92.5

90.9

69.2

3.14

.18

S9.o

94.0

92.1

84.4

.

67.5

101.2

100.6

99.5

99.5

99.4

98.5

106.1

10Q4

100.0

1001

100,3

lm.a

0.08

.03

101.1

93.5

102.6

4,61

.21

99.6

69.!?,

100.5

99.9

100.6

99.7

100.1

98.8

69.5

100.1

016

.04

100.6

100.4

979

101 1

1.00

.10

100,4

98.2

96.9

94.6

971

0.47

.07

88.6

lfF3.3

8?J.6

97.6

97,6

98.7

104.2

103.2

102.7

101.5

101.9

101.1

101.1

160.9

1004

1003

101.6

101.4

0.28

.05

.

.,,

. .

1oit,5

100.3

101.2

1009

102.5

101.2

102,6

101.4

102.0

102.1

0.34

.06

101.4

101.4

99.7

iO1.5

0.33

.06

101.2

99.2

101.1

94.8

99.3

0.23

.05

69.4

101.2

102.0

99.1

97.6

100.4

95.5

97,3

94.5

95.3

94.0

92.6

91.7

92.2

w t?

901

Y4.O

89.3

3.31

.18

924

!71.3

93.4

937

93.2

94.8

94.3

~2.5

94.8

96.7

1.22

.11

94.7

91.3

93.3

95.5

1.37

.12

92.9

94.7

94.3

94.9

94.0

0.36

.06

81.6

93.0

84.6

92.2

96.6

85.2 87.1

862 89.7

E7.2 S9.7

90.0 92.S

92.4 95.1

96.8 98.~

100.2 101.7

1038 1046

fn7.1 t 07.5

110.6 11(38

969 CM.n

100.7 t 02,2

55.27 53.88

.74 .73

f 02.2

86.6

102.7

36.54 .

.60

102,5 104,2

103.6 104.8

102.7 104.0

100.4 102.5

96.9 99.2

94.0 96.8

929 !36.3

91.3 94.3

91.5 96.3

88.4 92.7

20.21 17.25

.45 .42

101.7 103.6

101.6 103.1

95.5 89.7

100.9 102.0

6.29 3.61

.29 .19

101.2 102,6

96.1 101,3

95.1 99.2

99.2 103,5

91.6 96.9

6.10 3.31

.26 .16

96.6 96.3

101.1 102.7

84.3 86.7

97.4 100.2

97.8 97.6

91.0 97.3

81.6

816

83. I

844

86.4

878

889

91 B

,34.I

~4,,

865

887

42.54

.65

89,2

89.4

38.9

373

86.2

85.0

85,0

84.0

62.7

81.2

2144

.46

87.9

89.1

64,9

67.7

12.60

,36

67.2

86.6

86.2

85.2

84.1

3.10

.18

80.3

87.2

65.9

67.4

63.1

1003

IC06

99.7

99.7

1(X).1

!3$ 7

1M7o

1(X)2

298

10IJO

100.1

99.8

003

02

100.0

1120.1

101.4

0.01

.01

100.1

!39.6

100.4

!+9..9

1006

89.6

1002 :j~,6

99.5

99,6

0.12

.03

10Q.6

100.2

96.5

1(YJ5

049

.07

100.1

96.9

99.9

95.4

96.4

0.16

.04

88.2

lm.1

100,6

96.1

96.7

100.1

100.9

1fxf.z

Ioo.1

993

1flu rJ

EE.ti

1U3.O

I ‘:.:

100.0

100.0

1002

0.04

.02

1C120

99.7

100.3

98.7

100.8

99.3

100.4

88.0

996

997

0.13

.04

103.4

100.3

984

100.4

0.42

.06

100.1

98.2

99.6

93.6

98.0

0.25

.0s

88.0

100.1

100.4

97.9

96,7

89.3

99.2

101,0

99.1

100.6

1004

999

995

101.8

97.6

101;,9

100.5

970

0.77

.03

..

100.3

99.4

101.2

100.6

99.6

100.4

100.0

97,6

!39.1

100.1

0.60

.06

102,0

99.2

W3.8

t 02.7

2.13

.15

99.6

101.2

100,6

lIM.5

99.0

0.21

.05

90.2

99.9

101.0

89.1

.

101.1
Id

o

Table 2. Unweighed sample size and mean index scores of the intellectual achievement indexes for children and youths aged 6.17 years, by race and independent predictor variables, with standard deviations of total, percent variance

accounted for, and correlation ratim -Con.

[ Unweighed examined sample= 13,887 children and youths. aged 6-1’1 years]

Black

Mean index score

General index Race-specific index

P/h me

and

other

<aces

ID

While

and

other

races

93.9

95.0

1OQ.9

97.4

101.7

1.50

.12

99.4

101.6

101.7

106.3

3.25

.18

92.0

102.7

97.9

98.2

93.4

99.0

97.3

101.7

98.8

1.00

.10

101.1

104.5

100.6

1.49

.12

103.7

105.3

103.6

100.8

515 DID Sls

White

and

other

races

93.3

98.9

98.0

103,5

97.2

3.49

.19

99.2

102.2

103.2

104.6

7.32

.27

97.8

102,7

103.0

97.4

99.2

98.6

103.5

97.2

98.7

2.89

.17

102.1

104.2

100.5

4.26

.21

103.9

104.5

103.8

101.9

Independent predictor varmble All DID

White White

and

White

All and

races

68.1

90.5

95.6

93.7

101.7

3.46

.19

98.4

88.7

97.7

104.4

3.08

.18

92.8

101.0

96.6

92.4

89.1

94.0

94.6

101.7

94.5

2.83

.17

97.7

102.3

99.6

1.52

.12

100.5

103.0

100.4

97.7

All

races

and All

<aces

99.3

94.8

98.0

94.6

105.3

0.63

.0s

101.1

99.6

97.8

101.7

1.48

.12

91.4

I 00.2

95.5

99.7

93.0

95.2

94.8

105.3

99.3

0.48

.07

96.5 c

1W.3

101.0

0.73

.08

99.1

100.6

59.4

98.9

All

races

All

races

1133.1

96.6

89.4

85.6

104.5

0.41

.06

99.8

89.7

98.7

101.6

0.76

.08

98.6

100.0

95.7

101.3

84.6

88.6

95.4

104.5

100.4

0,30

.05

88.5

100.3

100.1

0.07

.03

100.2

100,9

99.8

99.0

Black Black Black Black 31ack

99.5

87.5

89.0

99.6

0.65

.08

95,6

102.0

99.5

100.9

2.52

.16

100.3

99.7

100.O

101.9

95.3

97.3

100,5

100.8

0.59

.08

100.9

99.7

97.5

1.12

.11

101.5

101.7

100.1

99.4

other mher other

races races races

Fwsr parent% relationship m

child /youth —COn.

87

119

12

94

3

3,42B

3,442

3,662

3,355

4

1,685

65

106

85

15

85

3

839

.

4,182

4.797

4.908

2,913

1,6o9

1,590

1,112

47

71

9

66

3

3,253

2,827

2,727

2,894

1

0,452

55

58

54

8

65

3

1,205

.

3,068

4,205

4.627

. . .

. .

2,228

1,554

1,294

901

40

48

3

28

175

615

835

361

3

1,233

10

46

31

7

20

83i

. .

1,113

592

281

.

.

685

255

296

211

81.3

83.8

79.7

85.0

0.64

.08

79.2

89.1

85.9

SE.7

5.26

.23

83.0

67.0

89.4

86.5

81.5

68.3

85.6

66.4

0.46

.07

88.3

86.2

81.3

3.97

.20

69.8

89.5

66.5

84.2

88.6

95.7

97.6

98.1

96.4

6.29

.25

97.3

100.0

99.6

102.8

5.06

.22

101.3

100.6

101.1

82.7

96.1

88.8

99.6

86.4

95.2

5.61

.24

99.3

102.0

96.6

2.95

.17

101.3

102.4

101.0

98.6

91.7

97.6

97.0

102.5

86.4

3.60

.18

97.8

101.1

102.2

103.7

7.65

.’28

97.2

101.6

101.6

86.3

88.2

97.8

102.5

86.4

97.2

2.97

.17

101.0

103.2

S9.2

4.47

.21

103.0

103.6

102.9

100.8

85.5

92.6

99.5

91.2

4.87

.22

66.5

93.8

92.8

85.1

4.81

.22

102.7

94.1

97.5

88.4

92.5

100.0

90.9

91.5

4.14

.20

94.4

92.8

66.7

6.27

.25

86.0

95.1

92.8

90.4

102.3

97.2

103.8

84.9

I 05.3

0.48

.07

101,6

I 00.4

59.4

102.6

0.87

.10

94.8

101,1

96.1

101.9

95,2

101.2

84.6

105.3

101.6

0.35

.06

ICQ.1

I 01.3

101.5

0.23

.05

100.7

101.7

100.6

100.1

95.8

81.2

80.2

93.9

1.26

.11

90.6

95.2

93.1

93.6

1.15

.11

80.3

92.8

81.9

97.2

89.0

68.2

84.9

84.8

1.29

.11

93.8

93.3

92.6

0.16

.04

93.9

84.5

93.7

93.8

88.o

93.8

96.2

98.1

97.2

8.37

.29

98.4

99.9

98.9

102.8

3.47

.18

94.0

101.0

100.9

91.1

94.4

95.2

88.2

97.2

94.2

7,66

.26

86.2

102.0

99.6

2.92

.17

100.2

102.2

100.6

96.7

81.8

86.3

80.7

85,4

4.94

.22

83.6

87.1

86.4

87.9

4.81

.22

92.7

87.2

89.4

83.6

66.2

91.0

85.2

.

85.6

4.14

,20

87.4

86.5

83.8

6.30

.25

86.4

87.6

86.4

84.9

100.6

96.1

102.8

93.9

104,5

0.47

.07

100.2

99.4

98.5

101.7

0.95

.10

84.2

100.0

94.9

100.8

94.2

100.2

83.8

104.5

100.1

0.33

.06

89.0

100.4

100.2

0.21

.05

89.8

100.7

89.8

98.8

Percent variance accounted 10,. ............ .......

Correlation ratio ................... .... .......... ........

Percmt variance acccmmted for ............ .... ....

Correlation ratio ....... ........................... ........

Pemem variamx accounted for.., .......... .......

Correlation ratio .......................................

Standard metropolitan statistical area

(5MsAI

In SMSA, central city., ............ ............... .. ...

1“ SMSA, not in central city . .......................

Not in SMSA ...............................................

Percent variance accounted for, ...................

Correlation ratio ..........................................

Twe of Place and population size

Urbm i. m urbanized area (3 rnillio”

persons or more) .................................... ...

Urban, in an urbanized area (1 million-2.9

milfion persons) . . .. . . . .. . ... ..

Urban, in an urbanized area

(250,000-988$799 persons) ... ........ ............

Urban, in an urbanized area (less thm

250.0Wpers0ns) ......................................
Urban. not m urbanized area (25,0c0

permns or morel, ..................................... 634

Urban, not in urbanized area {10,000.

24.9* persOns)........................................ 397

Urban, not in urbanized area (2,5CQ.9.999

persons) .................................................... 817

Rural ........................................................... 4.615

Percent variance accoumed fro ................... . . .

Correlation ram.. .................................... ,.,

Forezgnlanguage spoken in home

Yes .............................................................. 1,663

NO............................................................... 11,672

Blank or don’t know ................................... 552

Percem variance accounted far .................... .

COrrelaliOn ratio ...................................... .,.

617

369

17

28

99.2 99.4

100.8

102,3

100.6

92.4 5%6 99.7 93.7

1

99.7 99.7 98,8

99.8 100.6 86.8

160.6 101.6 94.2

100.7 101.5 92.1

0.36 0.23 1.18

.06 .05 .11

100.8 101.0 94.7

99.9 101.1 93.5

99.8 100.9 93.3

0.O6 0.00 0.03

.02 .01 .02

laf.5 100.9 26.9 98.7 98.5 105.5

99.3 79.9 69.5 100.0 93.1 100.2 101.3 80.6 99.1 89.5 93.4

730

4.2o8

67

407

100.3

99.0

83.4

81.7

99.5

98.3

100.7

99.1

69.2

89.7

100.0

99.0

101.9

100.4

24.1

84.4

100.3

100.0

100.5

100.2

99.3

97.3

0.94

.10

1.64

.13

6.27

.29

3.25

.lE

5.10

.23

12.28

.35

1.42

.12

4.92

.22

12.32

.35

0.21

.05

0.21

.05

2.99

.17

...

..

...

...

1,614

9,614

473

49

1,858

79

96.6

100.6

97.9

97.0

103.2

100.1

91.7

66.6

85.3

96.0 86.0 97.0 97.1

100.5

98.4

97.4 89.0

86.6

65.8

99.7

lCQ.O

99.5

99.6

100.1

99.5

102.7

100.0

99.4

100.6

98.2

102.0

99.2

93.1

91.9

103.1

100.5

0.71

.08

2.27

.15

0.51

.07

3.23

.IE

6.70

.26

0.73

.09

1.55

.12

6.95

.26

0.72

.08

0.02

.01

0.02

.01

0.16

.04

...

...

...

...

M
Table 3. Unweighed sample size and mean index scores of the intellectual achievement indexes for children and youths aged 6-17 years, by race and independent constructed variables, with standard deviations of mtal. Dercent

variance accounted for, and correlation ratios

[Unweighed examined sample = 13,887 children and youths. aged 6-17 Years i

Independent constructed variable

Mean index score

General index Rze.wecific index

Vhite

and DID

-

White

and

other

races

Sls

White

and

other

races

102.2

7,52

83,0

87.1

90.8

95.0

96.3

99.8

102.2

I 05.0

107,7

109.3

112.0

112.5

114.8

90.20

.95

86.3

88.0

90.1

93.2

94.9

97.3

98.8

101.5

103.4

104.9

106.7

109,6

58.14

.76

DID

White

and

other

races

AH

races

[3,887

10 SE Ilack

IIack

86.6

4.87

,ther

1

All

races

100.0

12.34

aces mite

1,901

Nhite

and

other

races

All

races

All All

races

and AH

races

81ack Black Black 31ack

races >ther

races

01.1

8.11

,986 I00.0

8.52

93.1

7.69

101.1

12.18

100.8

102.1

102.0

101,8

101.4

101.5

101.2

100.8

100.4

1CH3.7

100.4

101,0

100.8

0.16

.04

104.0

102.9

102.8

101.8

102.1

101.3

101.6

101.7

100,7

100.8

100.5

99.9

0.50

.07

93.5

11.25

97.7

98.2

95.3

93.9

94.8

91.2

91.9

91.8

89.0

82.8

87.4

87.4

88.1

6.33

.25

94.8

98.0

95.8

96.0

94.8

92.9

93.3

90.4

90.4

92.9

90.5

86.6

4.38

.21

100.0

9.04

61.6

65.2

88.3

92.8

94.0

98.0

100.3

103.7

106.9

106.9

111.6

111.9

114.2

75.78

.87

84.0

85.2

66.0

91.2

92.1

94.6

97.1

99.8

102.4

104.3

106.1

108.4

59.79

.77

00.0

11.98

98.9

lmfJ.5

100,1

100.2

I00.2

100.0

100.1

89.9

99,6

89.7

99.8

100.2

I00.3

0.05

.02

99.6

89.8

103.4

1S0.0

100.2

99.4

100.2

100.2

99.8

100.1

100.0

99.8

0.03

.02

100,0

12,15

_

98.8

100.0

100.3

100,3

100.0

100.3

100.1

99.8

99.8

99.9

99.8

100.3

100,2

0.07

.03

100.8

99.8

100.2

99.5

99.9

99.3

100,0

100.4

99.8

99.9

100.0

98.8

0.04

.02

100.1

10,87

Total, 12-17 years ............ .... .....

Standard deviation . ....... . ... .....

00.0

15.0

02.2

14,3

86.7

11.9

Sum of both parents’

education [X, )

78.6

B1,2

62.9

65.1

85.6

87.S

89.7

91.4

94.1

94.9

97.7

95.5

98.7

77.34

.88

81.1

81.7

84.1

84.8

85.7

66.7

88.3

89.5

81.2

91.9

92.8

95.9

56,26

.75

81.8

87.1

91.1

95.3

96.3

00.1

102.3

ICM.8

107.3

109.2

111.7

112.7

115.0

25.03

.50

87.1

87.8

80.3

92.7

94.8

86.6

98.8

101.9

103.2

104.8

106.7

I 09.5

16.02

.40

78.2

82.7

82.5

84.6

86.3

86.3

89.9

92.5

94.0

66.9

98.1

94.6

103.5

13.48

.37

79.3

81.6

84.6

86.0

86.5

66.2

89.0

86.1

90.7

94.3

93.4

94.2

9.92

.32

60.7

84.6

66.5

92.9

84.2

88.1

100.7

103.7

106.7

108.5

111.3

111.6

114.2

85.07

.92

83.7

85.2

64f.o

90.6

92.4

94.8

96.9

99.9

102.3

104.1

106.1

109.5

86.9E

.82

80.8

84.9

69.1

93.5

95.0

98.7

01.1

04.0

06.9

08.5

11.3

11.8

14.2

85.73

.93

83.0

64.9

87.5

90.6

92.7

95.3

87.2

00.2

102.5

134.2

IW3.2

109.8

64.86

,81

80.5

84.8

87.2

90.8

91.5

95.1

98.0

100.7

104.9

106.2

I1O.7

107.3

112.4

76.04

.88

64.5

85.5

89.1

80.0

91.7

93.2

95.7

97.7

1OQ.4

101.4

102.9

107.8

55.39

.74

99.9

1@3.9

98.9

100.0

99.9

99.9

99.8

108.0

89.7

100.2

100.1

100.5

100.4

0.04

.02

99.9

89.8

100.3

100.5

99.6

99.3

100.3

100.1

99.9

100.3

1CM3.1

89.6

0.05

.02

99.5

101.5

99.7

99.5

100.8

96.5

100.2

101.1

99.9

94.0

100.4

99.2

101.7

1.12

.11

96.2

99.8

lLM.7

101.4

100.8

99.5

100.7

98,6

99.5

102.4

100.5

98.3

0.86

.09

402

640

793

1,136

1,136

1,596

1,628

3,410

812

821

598

477

338

. . .

.

148

706

859

178

1,054

659

816

1,934

2,072

1,837

1,628

1,597

. . .

. . .

290

439

112

201

247

256

247

248

246

309

54

24

14

17

11

. . .

. . .

66

318

299

42

325

155

142

272

165

93

76

33

. . .

. . .

—

80.7

65.7

88.5

92.9

94.1

88.0

I00.4

103.7

106.5

108.8

111.4

112.1

I 14.5

27.36

.52

63.6

85.0

88.4

91.1

82.2

84.2

97.3

99.9

102.2

104.3

106.2

I 09.2

21.54

.46

546

660

889

1,348

1,382

3,101

858

787

584

460

327

. . .

.

82

388

560

136

729

604

773

1,662

1,907

1,844

1,752

1,564

. . .

. . .

Percent variance accounted for ................. ...

Correlation ratio ........ .. ............................. ...

Annual family income range

per person under 21 years of age in

household (X2)

None.$124 ..................................................

$125+374 ...................................................

$375@24 ...................................................

Income unknown and 5 or more children ...

ti254874 ...................................................

$875-$1,124 (includes blank or refused to

ansvwr and 5 or more children) ......... .....

$l.12&$l.374 .............................................

$1,375-$1.674 (includes income unknown

and 14 children) .....................................

$1,875-$2,824 (includes blank or refused

to answer and 1-4 ch[ldren) .....................

$2.625.$3 .624 .............................................

$3.626.$6.1 24 .............................................

$6,125 and over ..........................................

Percent variance accounted for ....................

Correlation ratio ..........................................
APPENDIX

CONTENTS

Appendix: Technical Notes .........................................................................................................................

Criterion Scaling ....................................................................................................................................

Comparison of Multiple Unear Regression With the Criterion-Scaled Constructed-Vmiables Method in

Predicting Intellectual Development ................................................................. ...............................

Skewness and Kurtosis Tests ..................................................................................................................

I.

II.

III.

LIST OF APPENDIX TABLES

Number of students and ‘criterion values of predictor elements ...........................................................

Multiple correlation (R) and percent variance accounted for in the ID index by each method

without and with race included ........................................................................................................

Sample characteristics for the two scaling methods .............................................................................

24

24

25

26

25

25

25

23
APPENDIX

TECHNICAL NOTES

Criterion Scaling

The objective of criterion scaling is to determine a set of scale values for the response options of an independent or predictor variable

which will maximally predict a given dependent

or criterion variable. The optimum predictor

value for a response option is the mean criterion

score for the persons who responded to that

response option.

If the data array is subjected to a one-way

analysis of variance, the mean criterion value for

each response option (including blanks on the

predictor variable) can be obtained. A correlation ratio, or eta coefficient, and an F statistic

can be computed to determine the degree of

association and the statistical significance of the

observed mean differences. Beaton4 provides

a fuller treatment of criterion scaling.

The following example is given to help

clarify the concept and to demonstrate the

procedure.

A teacher in a given subject area wants to

identify and scale some variables which might

contribute to an end-of-course comprehensive

subject matter test. The following data elements

are obtained for each student:

Predictor variables

1. A subject matter pretest score at the

beginning of the course.

2. Average number of hours per week

spent on studying the course material.

3. The number of times absent from

class during the course.

NOTE: A list of references follows the text.

Criterion variables

A. End-of-course test score on 70-item

test.

B. Subdivision of the class into two

groups: top 50 percent and bottom

50 percent of the class on the end-ofcourse test.

The variables are then ordered with :mean or

average criterion test scores and proportions

scoring at top 50-percent level for each predictor

response level (table I),

The scale value for each predictor element

response level for criterion A is its mean criterion score, and for criterion B it is the proportion in the top 50 percent. The zero-order

correlation coefficient of each data element with

the criterion can then be calculated using the

scale values to determine the strength of relationship or association. All three predictor elements can be put into a multiple-regression

equation to determine their joint contributions

and beta weights. The appropriate beta weight

can be applied to each response scale value

within each predictor element and a total predictor scale can be derived and correlated with

the criterion. The teacher can now identify how

much each predictor element contributed to

accounting for the variance in the criterion

scores, or in discriminating the category placement, their relative contributions, and their

total combined contribution. The response level

weights can be studied to see if “critical” points

exist. Thus for “times absent from class” the

response levels of O, 1, 2, would seem to indicate that up through two absences were not

important in terms of final-test-score performance. The students (cases) in these three levels

24
Table 1. Number of students and criterion values of predictor

elements

Predictor element

Pretest scores

Total .. ..........................

25 pointa and more ......................

20-24 points ....... ..........................

15-19 points ............... ..................

0-14 points .......... ...... ...................

Studv oer week

Total ............................

5 hours and more ......... ................

4 hours .............. ...... ...... .............. .

3 hours .........................................

2 hours .................... .. .... .......... .....

1 hour ................ ...... ....................

O hours ..... .. ..................................

Absent from class

Total ................... .........

4 times and more ..........................

3 times ............... .. ........................

2 times .......... ...............................

1 time ...........................................

O times .........................................

=

liner

If

unts

—

00

=

20

20

40

20

00

-

2

10

50

25

8

5

00

=

15

20

30

20

15

—

Criterion value

Mean

Proportions

at top

50 percent

65.2

60.0

51.2

30.1

54.6

50.0

54.0

66.6

48.1

26.3

15.1

54.6

20.0

48.0

65.1

65.0

63.1

.750

.600

.450

.250

.500

.000

.500

.660

.400

.250

.000

.500

.133

.300

.667

.650

.600

could be grouped and new weights obtained for

O-2 absences.

An investigator using criterion scahng should

inspect the response weights to see if they make

sense. If these weights are to be presented as

applicable to new samples, they should be crossvaIidated on an independent sample to determine how stable they are.

Comparison of Multiple Linear Regression

With the Criterion-Scaled ConstructedVariables Method in Predicting

Intellectual Development

The five predictor variables used in constructing the two Socio-Intellectual-Status (S1S)

indexes were entered into a muItiple linear regression equation to predict the index of Intellectual Development (ID). The five variables

with their ordinal values were:

Race: black = 1; white and other races = 2

First parents’s education: none = 00; 17

years or more = 17

Second parent’s education: none = 00; 17

years or more = 17

Number of persons in household under 21

years of age: 1 = 1 person; 10 persons or

more = 10

Annual family income: coded as shown in

detailed tables: 01-10.

Two equations weze computed. The first excluded race and the second included race to see

how much added variance race would account

for (see table II).

Table II. Multiple correlation (R) and percent variance accounted for in the I D index by each method without and

with race included

Method

Without race:

Multiple regression .................................

Criterion scaling ........ ...... .............. .........

Including race:

Multiple regression .................................

Criterion scaling .............. .... .................. .

ID relationship

1

Mul- percent

tiple varicorrela- ance action counted

R

for

.554

.568

.563

.601

30.7

32.2

34.0

36.1

In the multiple regression equation computations, any child or youth with a blank or unknown on any variable was deleted from the

computations. This resulted in the sample characteristics shown in table III.

Table I I 1. Sample characteristics for the two scaling methods

Intellectual

Method n

Development

Mean SD

Criterion scaling ................... ........... 13,887 100.0 15.0

Multiple regression .......................... 11,188 101.1 14.8

NOTE: n = sample size.

25
This comparison of’ methods indicates that the

criterion scaling method allowed for the attribution of variable values for all cases and provided

a somewhat greater accounting of variance in

the index of Intellectual Development than

did the multiple linear regression equation

method.

Skewness and Kurtosis Tests

In a symmetrical distribution, mean, median,

and mode coincide. It is thus natural to take the

deviation mean to mode or mean to median as

a measure of skewness. K. Pearson proposed the

measure Sk = (mean-mode)/standard deviation

which is subject to the inconvenience of determining the mode. A more common measure is

(mean-median)/standard deviation. However, for

ease in handling the sampling distribution as

well as for computational convenience the

sample moment Uk is defined as follows:

where U is the mean and k > 1. Denoting the

standard deviation S, then Sz = U2.

It can be shown that for a wide class of frequency distributions, Pearson’s Sk can be expressed exactly in terms of U2, U3, and U4. U3

itself is also a measure of skewness. Clearly,

if the distribution is symmetrical, U3 vanishes

and the ratio U3 /s3 will give some indication of

the extent of departure from symmetry. Obviously, all symmetric distributions are not normal. As a measure oi’ the peakedness or flatness

of the distribution (kurtosis) ratio U4/S4 is

used. For a normal distribution this ratio has a

value of 3 and thus we can define our measures

of skewness and kurtosis as:

bl = U3/S3 andb2 = U4/S4 -3

For normal distributions b ~ and b2 equal zero.

A nonsymmetric distribution is negative or

positive skewed depending on the sign of b ~.

If b ~ <0 the distribution is flat (platykurtic)

and if b ~ > 0 the distribution is peaked (lepto -

kurtic) in comparison with the normal.

This kurtosis test should be used only when

the distribution is symmetric. For testing purposes the null hypothesis assumes that the population distribution is normal. Then the standard

error squared for b ~ and b* is 6/n and 24/n respectively where n is the sample size. See

Kenda115 for further statistical detail.

For Cycle H and Cycle III combined,, n was

13,889 and the standard error would be .02

for bl and .04 for b2. For the index of Intellectual Development (ID) b ~ was -.08 which indicates that the distribution had a significant (but

considering the sample size) slight negative skewness. For the Socio-Intellectual-Status index, b ~

was -.53 and the distribution was markeclly negative skewed. Both b* values were significant

and indicate a plat ykurtic distribution.

For the Differential-Intellectual-Development index, b 1 was -.03 which is not significantly different from zero. On the other hand,

b2 was .14 and thus the distribution is significantly leptokurtic (peaked). For all practical

purposes, however, this distribution cannot be

distinguished from a normal distribution.

000

*US. GOVERNMENT PRINTING OFFICE: 1977–260.937:33

26
series1.

Serk?s2.

series 3.

series 4.

series10.

Sen”es11,

VITAL AND HEALTH STATISTICS PUBLICATIONS SERIES

Formeriy I%blic Health Sem”ce Publication No. 1000

Programs and Collection l+ocedures. –Reports which descriie the general programs of the National

Center for Health Statistics and its offias and divisions, &ta collection methods used, definitions, and

other material necessary for understanding the data.

Data Evaluation and Metho& Research. –Studies of new statiaticd methodology including experimental

tests of new survey methods, studies of vital statistics collection methods, new analytical techrdques,

objective evaluations of reliability of collected data, contributions to statistical theory.

Analytical Studies. –Reports presenting analytical or interpretive studies based on vital and health

statistics, carrying the analysis further than be expository types of reports in the other series.

Documents and Committee Reports. –Final reports of major committees concerned with vital and

health statistics, and documents such as recommended model vital registration laws and revised birth

and death certificates.

Data from tie Health Interview Survey .–Statistics on. illness; accidental injuries; disability; use of

hospital, medical, dental, and other services; and other health-related topics, based on &ta collected in

a continuing national household iriterview survey.

Data from the Health Examination Survey. -Data from direct examination, testing, and measurement

of national samples of the civilian, noni&titutionalized population provide the basis for two types of

reports: (1) estimates of the medically defined prevalence of ipecific diseases in the United States and

the distributions of the population with respect to physical, physiologic~, and psychological characteristics; and (2) analysis of relationships among the various measurements without reference to an

explicit finite universe of persons.

Sen”es12. Data from the Znstt”tutionalized Population Surveys. –Discontinued effective 1975. Future reports from

these surveys will be in Series 13.

Series 13. Data on Health Resources Utilisation. -Statistics on the utilization of health manpower and faciMes

providing long-term care, ambulatory care, hospital care, and family planning services.

Series 14. Data on Health Resources: Manflower and F&cilities. –Statistia on the numbers, geographic distribution, and characteristics of health resources including physicians, dentists, nurses, other health occupations, hospitals, nursing homes, and outpatient facilities.

.%rt”es20. Data on Mortality. –Various statistics on mortality other than as included in regular annual or monthly

reports. Special analyses by cause of death, age, and other demographic variables; geographic and time

series analyses; and statistics on characteristics of deaths not available from the vital records, based on

sample surveys of those records.

Sera”es21. Data on IVatality, Marriage, and Divorce. –Various statistics on natality, marriage, and divorce other

than as included in regular annual or monthly reports. Special analyses by demographic variables;

geographic and time series analyses; studies of fertility; and statistics on characteristics of births not

available from the vital records, based on sample surveys of those records.

Series 22. Data from the National Mortality and Natality Surveys. –Discontinued effective 1975. Future reports

from these sample surveys based on vital records will be included in Series 20 and 21, respectively.

Series 23. .Datu from the National Sumey of Family Growth. –Statistics on fertility, family formation and dissolution, family planning, and related maternal and infant health topics derived from a biennial survey of

a nationwide probability sample of ever-married women 1544 years of age.

kor a list of titles of reports published in these series, write to: Scientific and Technical Information Branch

National Center for Health Statistics

Public Health Service, HRA

Hyattsville, Md. 20782

/
u.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE

Public Health %rvice

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1

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