Data from the

NATIONAL HEALTH SURVEY

Readingand

Achievement

Series 11

Number 136

Arithmetic

Among

Youths12=17Years

as Measured by the Wide Range

Achievement Test

United States

Findings from the reading and arithmetic subtests

of the Wide Range Achievement Test, administered

in a national survey of youths in 1966-70.

DHEW Publication No. (HRA) 74-1618

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

Public Health Service

Health Resources Administration

National Center for Health Statistics

Rockville, Md. February 1974
Series 11 reports present findings from the National Health Examination

Survey, which obtains data through direct examination, tests, and measurements of samples of the U.S. population. Reports 1 through 38 relate

to the adult program, Cycle I of the Health Examination Survey. The

present report is one of a number of reports of findings from the children and youth programs, Cycles II and HI of the Health Examination

Survey. These latter reports from Cycles II and 111are being published

in Series 11 but are numbered consecutively beginning with 101. It is

hoped this will guide users to the data in which they are interested.

Vital and Health Statistics-Series 1l-No. 136

For SS1Oby the Superintendent of Documents, U.S. Government Printing Office, Washhrgton, D.C. !20402- Prico 65 cents
NATIONAL CENTER FOR HEALTH STATISTICS

EDWARD B. PERRIN, Ph. D., Director

PHILIP S. LAWRENCE, SC.D., Deputy Director

.GAIL. F. FISHER, Assista~t Director for Health Statistics Development

WALT R. SIMMONS, M.A., Assistant Director for Research and Scientific Development

JOHN J. HANLON, M.D., Medical Advisor

JAMES E. KELLY, D.D.S., Dental Advisor

EDWARD E. MINTY, Executive Officer

ALICE HAYWOOD, Information Officer

DIVISION OF HEALTH EXAMINATION STATISTICS

ARTHUR J. McDOWELL, Director

GARRIE J. LOSEE, Deputy Director

PETER V. V. HAMILL, M. D., Medical Advisor, Children and youth Program

HENRY W. MILLER, ChieJ Operations and Quality Control Branch

LINCOLN I. OLIVER, Chief Psychological Statistics Branch

HAROLD J. DUPUY, Ph. D., Psychological Advisor

COOPERATION OF THE BUREAU OF THE CENSUS

In accordance with specifications established by the National

Health Survey, the Bureau of the Census, under a contracted

agreement, participated in the design and selection of the sample,

and carried out the first stage of the field interviewing and certain

parts of the statistical processing.

Vital and Health Statistics-Series 11 -No. 136

DHEW Publication No. (HRA) 74-1618

Library of Congress CataZog Curd Number 73-600253
CONTENTS

Page

Introduction -------------------- ---------- “--------- ------------------

The Wide Range Achievement Test --------------------------------------

Field Testing Procedures -------------------- -------------------- ---.--

Results . “-------- -------------------- -------------------- ------------

Reading Subtest-Raw Scores --------------------------- -------------

Arithmetic Subtest-Raw Scores ------------------ --------------------

Percentiles and Standard Scores --------------------------- -----------

Comparison of HES Findings With Other Data . . . . . . -------------------- ---

Summary -.. ---------------------------- -------------------------- .----

References -------------------- -------------------- ---------- _-.------

List of DetailedTables --------------------------------------------------

Appendix I. Definitions -------------------- -------------------- ------

Appendix II. Technical N~tes -.-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -

The Survey Design ------------------ -+ ------- -----------------------

Reliability ---------- ---------------------------- ---------------------

Extent of Missing Test Results and Imputation Procedures --------------

Sampling and Measurement Error -------------------- -----------------

Hypothesis Testing --------------------------- ----------------------

Small Categories ---------------------------------------------------

Appendix 111. Instructions for Administration of the Wide Range Achievement

Test for the Health Examination Survey, Cycle 111------------------------

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5

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Ill
SYMBOLS

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

Category not applicable -------------------

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

Quantity morethan O but less than 0.05----

Figure doesnot meet standards of

reliabilityor precision ------------------

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iv
READING AND

AMONG

ARITHMETIC ACHIEVEMENT

YOUTHS 12-17 YEARS

AS MEASURED BY THE

Dale C, Hitchcock and Glenn D.

INTRODUCTION

This report presents information on the

levels achieved in reading and arithmetic, as

measured by the Wide Range Achievement Test,

by U.S. youths aged 12-17. The data were obtained

in the Health Examination Survey that was conducted from March 1966 to March 1970 by the

National Center for Health Statistics. Information

presented here is essentially a continuation of

that reported in a previous publication for children

ages 6-11.1 The present report is limited to

presentation of the findings on adolescents by

sex, age, and grade in school (appendix I).

The Health Examination Survey (HES) is an

ongoing program which collects data by direct

examination of representative samples of the

noninstitutionalized population of the United

States. Since 1960 the survey has conducted a

series of separate programs (called “cycles”)

concerned with segments of the total population

and focused on certain aspects of the health

of the selected subpopulation. The data in this

report were obtained during Cycle III, in which

youths aged 12-17 were examined. That program

was a continuation of the immediately preceding

cycle, in which children aged 6-11 years were

given an examination which focused on health

factors related to growth and development. Details regarding the surveys can be obtained in

comprehensive reports on the childrents program 2 and the youths’ program. 3 Further

WIDE RANGE ACHIEVEMENT TEST

I?inder, Division of Health Examination Statistics

information about the Cycle HI survey design

is presented in appendix H.

A standardized single-visit examination was

given each youth by an. examining team in a

speciaIly designed mobile unit. Along with examinations by a physician and dentist and a

variety of tests and measurements performed by

technicians, a 70-minute psychological test battery was given by a psychologist. The battery

included the following procedures, which were

administered in the order listed: Wide Range

Achievement Test, arithmetic and reading sections; Wechsler Intelligence Scale for Children,

vocabulary and block design subtests; a fivecard, tape- recorded version of the Thematic

Apperception Test; a modified version of the

Goodenough-Harris Drawing Test; the Brief Test

of Literacy; and a self-administered questionnaire

concerning the youth’s attitude and behavior

relating to certain aspects of health. A critical

evaluation of most of the psychological tests used

in the survey, including a literature review of

previous research and evaluations, was made by

S. B. Sells of Texas Christian University. The

results of the evaluation were published in the

Center’s methodological reports series.q

Before sample youths were examined, information was obtained from their parents. The

information included demographic and socioeconomic data on household members as well

as a medical history and behavioral data about

the sample youth. Information regarding per1
formance and adjustment was requested in a

questionnaire sent to the youth’s school. All

information was collected under a guarantee of

strict confidentiality.

Of the 7,514 youths composing the sample,

6,768 (90 percent) were examined. Because of the

sample design, adjustment for nonresponse, and

weighting procedures, examination results can be

considered representative of the approximately

23 million noninstitutionalized youths 12-17 years

of age in the Uhited States at the time of the

survey. Sampling errors associated with estimates in this report are presented in appendix L

THE WIDE RANGE

ACHIEVEMENT TEST

When plans were made to conduct a health

survey of the U.S. population from ages 6 through

17, it was decided that an assessment of educational achievement would be relevant since many

developmental and psychological problems first

come to the attention of teachers, physicians,

parents, and others as “learning” or “school”

problems. Although less widely known and used

than some comprehensive achievement test batteries, the Wide Range Achievement Test (WRAT)

met the survey’s requirements of both brevity

and applicability to the entire age range of the

target population, The choice was supported by

published data and by the opinions of some

clinicians to the effect that the WRAT could be

accepted as a good predictor of performance

on the more traditional achievement tests. 4

The WRAT was developed in 1936 by Jastak

and Bijou as a tool for studying achievement in

the basic school subjects of reading (word recognition and pronunciation), written spelling, and

arithmetic computation. The first edition and a

revision in 19465 had only one scale of achievement, which ranged from kindergarten to college

for each of the three subtests. The 1965 edition a

retained these three subtests, but each was

aIn the previous report on the WRAT findings in the HES

children’s program, 2 it ~a5 reported that a 1963 revision was

used. This was a provisional edition eventually published as the

1965 revision with only slight changes in the word order of the

reading subtest, The 1963 provisional editions of the reading

and arithmetic subtests were used in the survey of youths.

represented by separate scales at two levels. o

Level I was designed for children between the

ages of 5 years O months and 11 years 11 months,

while Level II was intended for persons from 12

years O months to adulthood. At both levels, the

reading subtest consists of recognizing and naming

letters and pronouncing words arranged in order

of increasing difficulty; the spelling section

involves copying marks that resemble letters,

writing one’s name, and writing single words

as they are dictated; and the arithmetic subtest

requires counting, reading number symbols, solving oral problems, and performing written computations normally taught in schools. Jastak

provided tables for converting raw scores on the

three subtests to grade equivalents, percentiles,

and standard scores.

Because of time limitations, only the reading

and arithmetic subtests of the WRAT were given

during the survey of youths. Further discussion

of the WRAT and the survey findings presented

below has been limited to those two subtests,

Adequate validity data on the WRAT are not

presented in the manual for the 1965 revision.

Findings based on limited study of the 1946

version are repeated from the 1946 manual; they

suggest that WIL4T results are closely related

to scores on the New Stanford Achievement Test,

Product-moment coefficients for samples of 7th

and 8th graders. are reported as follows: WRAT

reading with New Stanford Paragraph Reading,

.81 (N= 389); WRAT reading with New Stanford

Word Reading, .84; WRAT arithmetic with New

Stanford Arithmetic, .91 (N= 140). The 1965 manual also includes some data on reliability of

the WRAT.6 From a sample of 200 individuals

selected to represent a typical distribution of

achievement, split-half reliability coefficients

were calculated for the reading and arithmetic

subtests. The split-half measures used were

scores on the odd-even items arranged in order

of difficulty. Correlations for age groups 12

and older for both subtests were all above .95.

As a measure of test-retest reliability, Jastak G

cited a study in which a group of 77 retarded

persons, ranging in age from 15 to 17 years,

were given the WRAT (along with other tests)

five times within a 3-week period. The WMT

scores were found to be very stable, showing

the smallest variations of all the tests included.
To further study the use of the WRAT as a

measure of school achievement, the National

Center for Health Statistics contracted with K.

Warner Schaie of West Virginia University for

a special validation study. The complete findings

of that study have been published.~ A summary of

Schaiets findings regarding adolescents with some

brief remarks regarding several other relevant

studies follows.

Schaiets study was designed to assess the

adequacy of the WRAT to predict actual grade

placement and to estimate achievement as measured by another comprehensive battery. Level

II of the WRAT was administered to 314 boys

and 319 girls attending secondary schools in

Monongalia County, West Virginia. The sample

consisted of approximately equal numbers of

youths in grades 7 through 12. To assess the

possibility of regional bias, an additional sample

of 596 subjects was selected from the 7th and

10th grades in Milwaukee County, Wisconsin,

the 8th and llth grades in Los Angeles, California, and the 9th and 12th grades in Fort

Collins, Colorado. The Stanford Achievement

Test (SAT) was administered to the junior high

school students (grades 7-9) and the Metropolitan

Achievement Tests (MAT) were given to students

in senior high school. In the junior high population

reasonably good concurrent validity was demonstrated by the correlation of WRAT scores

with those on the appropriate subtests of the SAT.

Among the three grade levels and the geographic

regions the coefficients ranged from .66 to .84

for arithmetic and from .47 to .80 for reading.

Likewise the high correlation of the appropriate

sections of the MAT with the two WRAT subtests

for the senior high school group further supported

the validity of the WRAT. These validity coef -

ficients ranged from .62 to .82 for arithmetic

and from .49 to .82 for reading. Schaie concluded

that, while there is a considerable range in the

magnitude of validity coefficients depending on

level and geographic region involved, there is

sufficient evidence of substantial correlation

with criterion measures at every age level

investigated to consider the WRAT a satisfactory

brief instrument for estimating school achievement. 7

In estimating grade level placement, the

WRAT was found to vary considerably, ranging

from close agreement to wide disagreement with

the various criteria applied. Level II tended to

underestimate actual grade level, but it rather

accurately predicted achievement levels on the

SAT and MAT arithmetic-related subtests. The

WRAT Level II reading test overestimated the

actual grade level of junior high students but

underestimated that of senior high students.

Performance on the SAT was underestimated,

while performance on the MAT criterion variables

was overestimated.

The latest edition of Buros’Mentil Measuvenwtts Yewbook 8 lists 64 references on the

WRAT which have been published since it was

first issued in 1936. The length of this list

attests to a more than narrow or limited interest

in the test, but a review of the articles reveals

that many have dealt with applications involving

small and special populations. For example, one

recent study g suggests that the WWT and the

California Achievement Tests (CAT) are highly

correlated when used with preschool children

and” early elementary school children. A median

correlation of .80 among all the subtests, with

a high of .89 between WRAT reading and total

CAT score, is reported for a sample of 96

children. Another study,lo again comparing the

WRAT and CAT, is more relevant to the present

report because the 98 test subjects were 7th

grade students. Correlation coefficients between

WRAT and total California reading and arithmetic

scores are reported to be .73 and .80, respectively. At least 20 of the 64 references cited

in Buros dealt with samples of retarded persons.

A brief report of a 1962 studyll illustrates the

use of the WRAT in such studies of mentally

retarded subjects. When the WRAT scores and

MAT scores of 25 institutionalized boys (ages

9-14) were compared, rank order correlation

coefficients were .87 for arithmetic and .76

for reading. Another study 12 that illustrates

the wide use of the WRAT with mentally retarded

persons also exemplifies a common procedure

initiated by Jastak, that of comparing WRAT

scores with intelligence test findings. For the

test results of 72 mentally retarded males aged

16-35, correlation of WRAT scores with StanfordBinet and Wechsler Adult Intelligence Scale

scores ranged from .47 to .78.

Although the foregoing comments are not

3
presented as a comprehensive review of the

literature on the WRAT, the studies cited are

representative of the evidence that supports

the reliability and validity of the two WRAT

subtests for the purposes of HES Cycle III.

FIELD TESTING

PROCEDURES

The WRAT subtests were administered during

individual testing sessions conducted by psychologists who had at least a master’s degree and

who had experience in test administration. There

were two psychologists on the examining team

at all times. The examiners were trained in

the special HES testing procedures and supervised by the advisory staff of the survey. During

the training and supervision, strong emphasis

was placed’ on uniform methods of test administration, scoring, and recording of data. Throughout this survey of adolescents 12 psychologists

worked in the field.

The arithmetic and reading subtests were

the first procedures administered in each testing session. They were given in accordance with

the WRAT Manual for the 1965 revised edition, G

with certain minor modifications to conform with

special forms and practices of the survey,

Only Level II tests were used, since all sample

youths were 12 years old or older.

Both tests were printed on the same twopage form in a format identical to Jastak’s

standard form. The arithmetic section was on

one page, which contained the 46 probIems of the

written part and 15 dots and five numbers, The

dots and numbers along with three orally presented

word problems compose the oral arithmetic

test, The opposing page had space for computation.

The page of arithmetic problems was shown to

each youth, and he or she was asked to work

in 10 minutes as many problems as possible. If the

youth did not correctly complete at least six

problems within the allotted time, the oral part

of the subtest was given. In the oral part the

youth was asked to count aloud the 15 dots on the

form, to read the five numbers, and to solve three

simple word problems. These tasks were worth

10 points, one point for counting five dots

correctly, another point for counting six through

15 dots, one point for reading each number, and

one for solving each problem. If the youth obtained

a score of six or more (one point for each problem) on the written problems, the 10-point

credit was given for the oral part. The highest

possible raw score for the arithmetic subtest is

56 points.

The reading test consists of 13 capital letters

and 76 words which are printed on one page in

order of increasing difficulty. A laminated copy

of this sheet was presented to the youth, who was

instructed to read aloud each of the words in the

sequence in which they appeared. On another test

form (the one on which the youth had done the

arithmetic), the examiner checked off each word

that was incorrectly pronounced until 12 consecutive words were missed. On the first mispronunciation of any one word, the youth was asked

to repeat the word, but from then on the first

response or spontaneously changed response was

scored. Approximately 10 seconds were allowed

for each word, with the examiner controlling

the speed by saying “next” or “go on to the next

word.” If the youth failed to score at least six

points on the word pronunciation (one point for

each correct word), he or she was asked to

read aloud the 13 capital letters and to read the

first two letters in his or her name after writing

it on the test form, The letter reading was worth

a total of 15 points. Anyone obtaining a score of .

11 or more on the word pronunciation was credited

with the 15 pojnts for the letters. A possible

maximum 89 points can be earned on the reading

test. The verbatim instructions used by the examiners for the arithmetic and reading subtests

are included in appendix 111,

The examiner recorded all right and wrong

answers on each test in specified spaces on the

test form. Scores were computed and recorded

on the front of the form. As part of the comprehensive quality control practices of the survey,

the two psychologists daily exchanged all test

forms and checked each other’s work for apparent

errors in administration or recording.

Once a week an entire testing session was

recorded on tape by each field psychologist. A

transcription of the taped session was reviewed

by a psychologist at headquarters, who noted

errors, commented on testing procedures if

necessary, and then returned the transcripts to

the examiners,

4
RESULTS

Reading Subtest-Raw Scores

On the reading subtest of the Wide Range

Achievement Test, youths 12-17 years of age in

the noninstitutionalized population of the United

States attained a mean raw score of 48.5 points

out of a possible 89 points (table 1). fie mean

reading score increased steadily with age, rising

from 42.1 points at 12 years to 53.7 at 17 years

(figure 1 and table 1). Mean scores for halfyear age intervals are also presented as a more

precise reflection of the growth patterns in

school achievement as ‘measured by the WRAT.

Gradually increasing mean scores also occurred

among the 6-month age groups (table 2). ‘The

variability as indicated by the standard deviations for each of the 6-month age groups tended

to increase with age, although not consistently.

The relative variation among the reading test

scores was, however, ‘quite constant throughout

the age range. This was determined by computing

coefficients of variation which allow comparisons

of dispersions of scores in different series

where the means vary.

As indicated in table 1 and figure 2, mean

scores increased steadily as the amount of

education increased, rising from 42.6 in the 7th

grade to 58.7 in the 12th. The increasing scores

from one grade level to the next can be observed

for youths’ at every single year of age. Within

the appropriate grade range for the population

(grades 7-12), there was a fairly consistent

increase of around three points from grade to

grade. “Those youths who were in grades belQw

the expected level for the ages of this population

performed substantially poorer. The mean score

of 6th graders was 6.4 points below t,hat of 7th

graders; the mean score of 5th graders was

8.3 points below that of the 6th graders.

High school graduates obtained about the

same s“cores as those in the 12th grade. Youths

who continued or plamed to continue their formal

education beyond high school obtained substantially higher scores than those who did not. This

difference probably reflects a phenomenon of

selection, wherein persons of greater ability

continue their education, while those with less

ability do not.

A few other observations regarding the data

in table 1 may be of interest. The youths, mostly

16- and 17- year- olds, who had left school before

graduating, that is, the small group of school

dropouts, generally achieved scores on the reading test comparable to those observed in the 6th

and 7th grades. The group of youths designated

as being in some kind of special class had a

mean score of 23.1, lower than the scores of

all educational placement categories except that

of grade 4 and below. This relatively small

60 —

.~”

g 40 40 –

$i

~

K

3!

= 20 - 20 –

Readingsubtest Arithmetm sub:est

o I I I I I o I I I I I

12 13 14 15 16 17 12 13 14 15 16 17

AGE IN YEARS AGE IN YEARS

Figure 1. Mean raw scores on the reading and arithmetic subtests of the Wide Range Achievement Test for ymsths, by age: United

Statas, 1966-70.

5
4 and High Left

below 5 6 7 8 9 10 11 12 #$&l hl&&ml school special

graduate education placmment

graduating

GRADE IN SCHOOL

4 and High Left

below 5 6 7 8 9 10 11 12 school #:fl;::l hlg~d);:l special

graduate education placement

GRADE IN SCHOOL

graduating

Figure 2, Mean raw scores on the reading and arithmetic subtests of the Wide Range Achievement Test for youths 12-17 years of age,

by grade@ school: United States, 1966-70.

group included individuals with major reading

problems, many complicated with serious mental

and physical handicaps. In observing the relationship between age and grade, it can be seen that

mean scores *of youths in the usual grade for

persons” of their age were higher than scores for

those who were older and a little lower than

those of youths who were younger. This finding

is expected since it is a reasonable assumption

that persons who are permitted to skip grades are

generally more advanced than the average and

that those who are retained in a grade are

slow learners or at least slower.

Girls performed better than boys on the reading subtest, averaging 2.5 raw score points higher.

Higher scores were achieved by the girls at all

ages, with differences being significant in all

but the 13- and 15- year-old groups (figure 3

and table 1). Among those youths in school and

within the appropriate grade range for the population, boys again obtained lower reading scores

than did girls at every grade level (figure 4

and table 1). These differences averaged about

two points but only for the 9th and 10th grades

were the differences significantly different.

Variability of the reading subtest raw scores

was consistently greater for boys than for girls in

all half- year age groups except for the 17 l/2-

year-olds. The differences were significant in all

but five of the groups (all 12- and 16- year-olds and

the 15 1/2-year-old group). The girls exhibited

significantly more variability than did boys in the

17 l/2-year-old group (table 2).

6
60 - 60-

Girls

# 40 - 40 -

~

~

~

j ~.

Boys

20 —

Girls

Reading subtest Arithmetic subtesi

o I I I I I o I I I I I

12 13 14 15 16 17 12 13 14 15 16 17

AGE IN YEARS AGE IN YEARS

Figure 3, Mean raw scores on the “readingand arithmetic subtests of the Wide Renge Achievement Test for boys and girls, by age:

United States, 1966-70.

7n ,_

4 and High More than

Left

below 5 6 7 6 9 10 11 12 ~gh ~hool high school Special

sshool before graduate education placement

graduating

GRADE IN SCHOOL

4 and High More than Left

below 5 6 7 8 9 10 11 12 school ~gh ~hool high school Special

before graduate education placement

graduating

GRADE IN SCHOOL

Figure 4, Mean raw scores on the reading and arithmetic subtests of the Wide Range Achievement Test for boys and girls 12-17

years of age, by gradd in school: United States, 1966-70.

7
Arithmetic Subtest-Raw Scores

Youths 12-17 years of age -in the noninstitu-

.ticmalized population of the United States had a

mean of 23.0 raw score points out of a possible

56 points on the arithmetic subtest of the WRAT

(table 3).

The mean raw score increased slightly with

age through age 16 and then leveled off (figure 1

and table 3). Mean scores are also reported for

half-year age groups, and a gradual increase can

again be observed from one age group to the

next (table 4). The variability as indicated by the

standard deviations for each half-year age group

also increased slightly with age. As on the reading

spbtest, the relative variation among the arithmetic scores was generally constant over all age

levels (table 4).

A steady increase in mean scores, reflecting

increasing skill in arithmetic computation, maybe

seen throughout the grade range. The mean raw

scores for grades 7 through 12, the appropriate

range of grades for this population, increased

from 19.6 to 28.1 (figure 2 and table 3). Increases

from one. grade to the next can be seen within

each single year of age. Observations regarding.

other grade placement categories are similar to

those made about the reading subtest. Youths in

grade 6 and under had lower scores than those in

the 7th grade and over. Means for the 5th and 6th

grades, however, were within the same gradually

increasing progression, rather than substantially

lower than those obtained by youths in the typical

grade range as found in the reading subtest.

Youths who were in special classes performed

similarly to those with less than 5th grade placement, and the dropouts again achieved scores at

the 6th or 7th grade level, Mean raw scores of 12th

graders and high school graduates were about the

same, Youths who had begun college or were preparing to begin college scored higher than all

others. As in the similar findings on the reading

subtest, the higher raw score means for students

with education above high school is probably a

result of the group’s composition (only the more

superior students being included) rather than a reflection of educational level. It is also of interest

that the modal age group in each grade showed

about the best performance on the arithmetic test.

Those youths who were younger than the modal age

for their grade did not do noticeably better than the

modal age group, as they did on the reading test.

Those who were older than the typical age for each

grade did achieve slightly lower scores. The

fact that there were not in the arithmetic test,

as in the reading test, striking differences between

the mean scores of the groups of youths who had

probably been accelerated or detained and the

scores of the modal age-@ grade groups suggests

that success in school is more dependent on

developing reading ability than on acquiring

arithmetic skills.

Overall there was no difference between the

performance of boys and girls on the arithmetic

subtest, the mean score being 23.0 for each.

There were no significant differences between

raw scores of boys and girls at single years

of age or at half-years of age (figure 3 and tables

3 and 4). Likewise, there were no significant

differences in arithmetic scores between boys and

girls at any grade level, although from 9th grade

on, the scores of boys were slightly higher than

those of girls at each educational” level (figure

4 and table 3).

Variability of arithmetic subtest raw scores

was greater among boys in all 6-month age groups

except three (the age groups 12 1/2, 15 1/2, and

17 1/2 years). The greater variability exhibited by

the scores of boys was significant for ages

12-0 to 12-5, 13-0 to 13-11, and 17-0 to 17-5

(table 4).

Percentiles and Standard Scores

For the majority of testing purposes, the

most satisfactory types of norms for achievement

tests are those showing the examinee’s position

within his own grade level. In the present report,

percentiles and T scores (normalized standard

scoyes with a mean of 50 and standard deviation

of 10) are employed for that purpose. Is In

addition, the same two measures are presented

for the six age levels of the population surveyed.

Grade-equivalent scores, which are often

used for achievement tests and are presented

for the WRAT in Jastak’s original work, are not

shown in this report. Basically, grade equivalent

tables have

the sample

by HES are

been omitted for two reasons: (1)

design and testing procedures used

such that the construction of grade

8
equivalents would incorporate unacceptably large

biases, and (2) shortcomings inherent in the grade

equivalent concept itself make the measure less

than desirable for grade norms, especially at

levels beyond the elementary school grades.

Elaboration on the two points follows.

The usual procedure for construction of grade

equivalents is to select samples from specific

grade populations and test them once or several

times during the course of the school year, Is

The sample design for the HES called for selection

of eligible youths from households. Examinations

were administered throughout the year, imd youths

were tested whether they were enrolled in school,

were on vacation, or had left school for any

reason. In addition, testing was done in a mobile

examination center, so seasonal variation in

weather was a consideration in scheduling the

40 sample locations. Examination sites during the

winter, approximately the middle of the school

year, tended to be in warmer climates, while

during warmer weather examinations took place

in the more northern regions of the country.

Grade equivalents like those constructed by Jastak

would therefore be subject to a regional bias

if developed from HES data. For example, if

WRAT scores of youths in the South should be

generally lower than those in the Northeast (an

actual finding from the Health Examination Survey

of children aged 6-11), then this difference would

be reflected in the midgrade grade equivalents

assigned to certain raw scores; that is, any

regional differences would be reflected in the

grade equivalents developed from raw scores

obtained during the course of each school year,

Conceptually, grade equivalents assume that

growth is uniform throughout the school year.

The inclusion of grade equivalents in this report

would require the assumption that learning is

roughly uniform for every youth throughout his

junior and senior high school years everywhere

in the United States. That is a difficult assumption

which would ignore both the planned and unplanned variation in the educational experiences

of youths throughout the country,

There is also a problem in interpreting grade

equivalents even” though superficially they may

appear quite simple. For example, an 8th grader’s

performance on the arithmetic test could result

in a grade equivalent of 10.8. This does not

necessarily mean that the person has mastered

most arithmetic taught in the 10th grade, but

more likely that he achieved a high score by

superior performance on arithmetic taught up

through the 8th grade.

Grade equivalents can be potentially misleading when used as a simple measure of

achievement if they are construed as “norms”

signifying satisfactory levels of achievement

without consideration of such factors as intelligence or curriculum emphasis of the youths

being evaluated. Grade equivalents generally

tend to exaggerate the significance of small

differences and to encourage the improper use of

test scores. In addition, grade equivalents do not

provide a good basis for Comparing an examineets

performance on several tests, nor are they a

better measure than other scales for assessing

changes in an individual’s achievement level.

There is general agreement among educational

psychologists that percentile rankings provide a

sounder basis for interpreting a student~s score

on a particular test and for comparing his standing on a number of tests.11

Any reader wishing to examine grade equivalents from the present report may do so by simply

using the mean raw scores for each grade as

presented in tables 1 and 3 as grade equivalents

for the midpoints of specific grades and then

interpolating intermediate grade equivalents to

represent fractions of grades. The school year

covers roughly 10 months; thus successive school

months can be expressed as decimal components

of a given grade. For example, a grade equivalent

of 12,0 indicates average achievement at the

beginning of the 12th grade (September testing)

and a grade equivalent of 12.5 indicates average

achievement at the midpoint of the school year

(February testing).

Percentiles have been derived from the raw

scores on both the reading and arithmetic subtests. Percentile ranks reported in the tables

represent the percentages of youths falling below

designated raw scores. Tables 5 and 6 present

reading test percentiles for the six age groups

and for grades 7-12 (the appropriate grade levels

for these ages). These percentiles are based on

all persons of the given age or in the given grade.

9
Similarpercentilesfor the arithmeticsubtest

are presentedforage andgradegroupsintables

7 and 8,respectively.

Comparison of the two subtestswitheach

other,withothermeasures ofacademicachievement, or with otherpsychologicaland physical

measures may bemisleadingifbasedonpercentile

ranks.Percentilesreflectboththerangeoftest

scores obtainedand the distributionof those

scoreswithinany categoryreported,inthiscase

age and grade levels.Completelysimilardistributionsof scores may not occur for each

subsample.Indeed,therangeofitemsattempted

on a testliketheW RAT would be expectedto

increaseover the successiveages and grades

inthepopulationunderdiscussion.

lnviewoftheprecedingdiscussion,thenorm

tablesin thisreportpresentstandardscores

computedfrom theraw scoredistributions ofeach

subtest.The standardscore equivalentsof raw

scores are based on a common scalewitha

mean of 50 and a standarddeviationof 10

Table A. Means and stand~rd deviations (SD) on the reading and arithmetic subtests of

the Wide Ramze Achievement Test for Jastak’s standardizationgroup and HES estimates

for the Unit&d States among

Age in years and months

12-0 to

12-6 to

13-0 to

13-6 to

14-0 to

14-6 to

15-0 to

15-6 to

16-0 to

17-0 to

12-0 to

12-6 to

13-0 to

13-6 to

14-0 to

14-6 to

15-0 to

15-6 to

16-0 to

17-0 to

12-5-----------------

12-11----------------

13-5-----------------

13-11----------------

14-5-----------------

14-11----------------

15-5-----------------

15-11----------------

16-11----------------

17-11----------------

12-5-----------------

12-11----------------

13-5-----------------

13-11----------------

14-5-----------------

14-11----------------

15-5-----------------

15-11----------------

16-11----------------

17-11----------------

-.

ouths in 1966-70

HES sample, 1966-702

Jastak’s

standardizationgroupl

Unsrnoothed Smootheds

Number Mean

I

SD Mean SD Mean SD

Reading subtest

314

336

321

325

340

351

324

265

558

485

301

323

305

309

328

345

314

248

544

480

43.92

45.64

46.40

48.73

51.14

52.29

54.31

54.93

55.76

57.29

23.71

25.22

26.31

27.63

28.30

29.48

29.50

29.65

29.85

30.60

11.78

11.81

11.75

11.92

11.87

12.06

12.13

12.20

12.72

41.67

42.41

44.52

46.21

47.85

48.52

49.18

50.48

52.85

11.37

11.61

12.62

12.49

12.98

12.67

13.22

13.40

13.19

42.04

42.87

44.38

46.19

47.53

48.52

49.39

50.84

52.33

12.761 53.671 14.551 53.26

Arithmetic subtest

5.46

5.70

6.08

6.10

6.15

6.38

6.37

6.63

6.91

7.25

18.82

19.57

20.79

21.39

22.60

23.43

23.56

24.39

25.58

25.74

4.76

5.30

6.04

6.04

6.33

6.68

6.55

6.80

7.f5

7.65

19.19

19.73

20.58

21.59

22.47

23.20

23.79

24.51

25.24

25.66

11.49

11.87

12.24

12.70

12.71

12.96

13.10

13.27

13.71

13.87

5.03

5.37

5.79

6.14

6.35

6.52

6.68

6.83

7.20

7.40

‘Jastak,J. F., and Jastak, S. R.: The Wide Ran e Achievement Test, Manual of InSl@, rev. ed. Wilmington, Del. Guidance Asso~iates, 19rj5

Eslzmates of means and standard deviations for the United ;tates based on the inflated HES sample. See appendfx I for a further explanation and for the number of examinees on which findings are based.

3Means and standard deviations smoothed by a three-pointmoving average. End points

estimated from two groups.

10
60

r

60

Jastak

: 40

,,,,,,t,,,,,,,,,,,,,,,,,,,,,8,,s,,,u''''nn'n'n','sns's,sn,sa's't'n,s':E,r',',,,,',','t

40

0

8

$

~ ,0

20

I Reading wbtw

o~ o

12 13 14 15 16 17

AGE IN YEARS

Jastak

,,,,,,, n,n, t,,, "'1`91'ln'';;~1 '11111111'11111n1'##,'

,,,, *,,,#,,,,*,,,,9 *n19B,~***’””

Arithmxic subtesr

I I I I I

13 14 15 16 17

AGE IN YEARS

Figure5, Mean rawscores onthereading andarithmetic subtestsofthe Wde Range Achievement Test for Jastak’s standardization

group (1965) and HES estimates for the United States among youths (1966-70), by age.

(2’ r3cores).14 Although this method deviates

from that used by Jastak and from the method

followed in the earlier report on the children

tested in HES, it provides standard scores

which can be compared both within and across

age and grade groups. Thus, the statement in the

Cycle H reportl counseling caution in the use

of standard scores for across-age comparisons

need not be included here. Subsequent reports

on the adolescent survey will employ T scores

in presenting results for other tests, such as

the Wechsler Intelligence Scale for Children and

the Goodenough-Harris Drawing Test.

Tables 9 and 10 present by single year of

age the T score equivalents for reading and

arithmetic raw scores, respectively. The T

scores for each age level were computed from the

test results for all persons of the age designated.

In table 11, T score equivalents for reading raw

scores are presented by each of the six grade

levels appropriate to the age range of the population. Table 12 presents similar scores for the

arithmetic subtest. Since it was decided that

standards of performance at different educational

levels should be based on the “typical” performance in each grade, the T scores in tables 11

and 12 were computed from the raw scores of

only those youths who were at the modal age in

each grade.

COMPARISON OF HES FINDINGS

WITH OTHER DATA

As indicated previously, the Health Examination Survey sample was a highly representative

probability sample of the noninstitutionalized

population of the United States. It is of interest

to compare the results of this survey with the

data from the group on which Jastak standardized

the 1965 revision of the WRAT. Limited information on the standardization sample appears in the

WRAT Manual. The sample was drawn from

schooIs in seven States. Apparently some effort

was made to have various socioeconomic levels

represented. IQ scores were used to develop a

“mentally average” sample with representative

dispersions of scores above and below the mean,

but no attempt was made to obtain representative

national

present

timates

Jastak’s

As

average

sampling. 5 It should be noted that the

sample, on which the United States esare based, is nearly twice as large as

sample (appendix I).

indicated in table A and figure 5, the

raw scores attained in the Health Examination Survey on the reading subtest and the

arithmetic subtest were consistently lower than

those reported for standardization groups. The

differences were significant at every age level for

both subtests. Raw scores on the reading subtest

11
of youths in the present study, except for those of

12-year-olds, tended to be more variable than

were the scores of persons in the ,standardization

sample, The HES arithmetic scores were also

more variable except at ages 12 and 13.

The HES data can also be compared with

those obtained by Schaie in the study summarized

earlier.; In this case there is the opportunity to

compare raw score means for each grade level

obtained from a substantial sample of students

(about 200 in each grade) with the HES national

estimates of mean scores for each grade. As

indicated in table B, the United States estimates

are lower at every grade level for both the

reading and the arithmetic subtests. Differences

are significant in the 7th, 9th, and 10th grades for

reading and in all but the 1lth grade for arithmetic,

The standard deviations are slightly larger for the

national estimates in every case except reading

in the llth grade.

The most plausible explanation for the lower

raw score means and greater variability of the

scores obtained from the national sample of

adolescents lies in the sampling and examination

procedures used in HES, The previous studies,

Jastak’s standardization study and the study by

Schaie, made use of some variety of stratification

and quota sampling within school populations,

thus limiting the range of potential sample persons

far more than the sampling techniques employed

by HES. A great effort went into having every

person in the HES sample examined (leading to

the 90-percent response), which certainly resulted

in reaching some of the lower level and problem

cases who were probably “lost” in the smaller

scale efforts,

SUMMARY

This report presents national estimates of

school achievement as measured by the reading

and arithmetic subtests of the Wide Range Achievement Test for the noninstitutionalized population of the United States 12-17 years of age.

Data were obtained in the Health Examination

Survey of 1966-70. In the survey a probability

sample of 7,514 youths was selected to represent

the 23 million adolescents 12-17 years residing

in this country. A total of 6,768, or 90 percent,

of the sample youths were examined, Because

Table B. Means and standard deviations

(SD) on the reading and arithmetic subtests of the Wide Range Achievement Test

for the Schaie study sample and HES estimates for the United States for youths

in 1966-70

Grade in

school

Grade 7---

Grade 8---

Grade 9---

Grade 10--

Grade 11--

Grade 12--

Grade 7---

Grade 8---

Grade 9---

Grade 10--

Grade 11--

Grade 12--

Schaie samplel I

H;;6;anq#e,

--

1

I I I

wnl-

~er Mean SD I

Mean SD

I I I I

Reading subt es t

215 49.0 10.8 42.6 11.3

210 47.2 11.4 46.3 11,6

232 55.7 11.1 48.7 12.1

199 55,8 11.1 52.0 11*7

201 56,7 12.5 55.6 11.7

172 6001 10.8 58.7 11.3

Arithmetic subtest

2151 22.51 4.31 19.6 I 5.2

210 24.3 5.0 21.6 5.8

232 28.7 5.5 23.4 6.2

199 29.1 5.9 25.0 6.3

201 27.6 6.3 26.8 6,5

172 31.4 6.2 28,1 6.8

t I n 1

l~i~al a d Health Statistic, Series

2, t’jO. 24.

‘Estimates of means and standard deviations for the United States based on the

inflated HES sample. See appendix I for a

further explanation and for the number of

examinees wwhich the findings are based.

of the sample design, adjustment fornonresponse,

and weighting procedures used in the survey,

findings for these youths may be considered to

be representative of thetotalnoninstitutionalized

U.S. population of 12- through 17-year-olds with

respect to age, sex, race, region, and other

socioeconomic characteristics,

Test results have been presented by age,

sex, and educational level in their raw score

form to permit comparison with other studies

using the WRAT. Percentile ranks andnormalized

standard score (T score) equivalents of the raw

scores have also been included.

Findings on the two WRAT subtests have

been compared with the data from Jastakts

standardization sample and with the findings from

a recent study on the test done by Schaie. The

12
HEX estimates of raw score means for age and

grade levels are consistently lower than those

obtained in the two previous studies.

The Cycle HI HES data demonstrate a continued development of reading and arithmetic

skills through the adolescent years and as formal

education increases. A noteworthy finding is that

girls in the age range surveyed performed better

than boys on the word recognition and pronunciation task presented by the WRAT. It might be

pointed out that a similar finding came from the

HES Cycle 11 program when the Level I reading

subtest of the W RAT was administered to children

6-11 years old.1 No significant differences between

boys and girls in arithmetic computational skills

were found in either survey.

—’o 00

REFERENCES

~N:ltiont{l Ct.ntcr for Health Statistics: School achievenwnt uf children 6-11 years as measured by the reading and

arithmetic subtwts of the Wide Range Achievement Test,

United Sr:~tes. I’ital Cd Heakh Statistics. PHS Pub. No.

1~lOtHSwics 1 l-No. 103. Public Health Service.. Washington.

U.S. Gmwrnlncut Printing Office, June 1970.

2Natimml Center for Health Statistics: Plan, operation,

:In Li rcspunw results of a program of children’s examinations.

I ‘it,d aI~dH1,a/t/l St,Itistic.r. PHS Pub. No. 1000-Series l-No. 5.

Public Hc:iltb Service. Washington. U.S. Government Printing

(lflke, Oct. 1967.

~NLltiOll:i[ Ccrltcr for Hc:llth Statistics: plan and operation

of n Iluolth cxamirmt ion survc }, 0 f U.S. youths 12-17 years of

:Igc. I ‘it,tl {III({ He,IltlI St’~tistics. PHS Pub. No. 1000-Series

1-Nw X, Public Hcakh Service. Washington. U.S. Government

Printing Officu, Sept. 1969.

‘iN:lti”n,ll Center for Health Statistics: Evaluation of

Iwychologicol mc:lsurcs used in the Health Examination Survey

of children ages 6-11. Vital at~dHealth Statistics. PHS Pub. No.

1(ltl~LScrics 2-No, 15. public Health Service. Washington. U.S.

Guvcrrtmcnt Printing Office, Mar. 1966.

5 Jwta!i, J, F., and Bijou, S. W,: The Iuide Range AchierreI)IL+Itt‘l”t~.ft.Wihniugton, Del. C. L. Story Co., 1946.

t~~:lst;tk, J. F., :Ind Jasta!i, S. R.: The Wide Range AckieveItI1,IItTc,st, J1,III1{(I1of” 1}1.strl~ctions,rev. cd. Wilmington, Del.

Guidance Associates, 1965,

7Nation:~l Center for Health Statistics: A study of the

wbicvmcut test used in the Health Examination Surveys of

pcrsuns :Igcd 6-17 years. l’itul and Health Statistics. PHS pub.

No. 1000-Series 2-No. 24. Public Health Service. Washington.

U.S. Gcwernmcnt Printing Office, June 1967.

8 huros, (), K.: The Seuenth Mental Measurements Yeurhook, Vtd. 1. Highkmd Park, N.J. The Gryphon Press, 1972.

9Washington, E.’ D., and Teska, J. A.: Correlation betw~en

the Wide Range Achievement Test, the California Achievement

Tests, the Stanford-Binet and the Illinois Test of Psycholinguistic Abilities. Psyclzol. Rep. 26(1) :291-294, 1970.

10oldridge, O. A.: A congruent validity study of the Wide

Range Achievement Test at grade seven. Ecinc. Psych. Meas.

24(2):415-517, 1964.

11 Reger, R.: Brief tests of intelligence and academic

achievement. Psyclro~. Rep. 1 l(l) :82, 1962.

1 Zcochran, M. L., and Pedrini, D. T.: The concurrent

validity of the 1965 WRAT with adult retardates. Am. j. Merit.

De&. 73(4) :654-656, Jan. 1969.

13Anastasi, A.: Psychologkal Testing, 3d ed. New York.

The Macmillan Co., 1968.

14Angoff, W. H.: Scales, norms, and equivalent scores, in

R. L. Thorndike, editor, Educatiorral Measwernent, 2d edition.

Washington, D.C. American Council on Education, 1971.

15National Center for Health Statistics: Sample design and

estimation procedures for a national health examination survey

of children, Vital and Heakh Statistics. Series 2-No. 43.

DHEW pub. No. (HSM) 72-1005. Health Services and Mental

Health Administration. Washington. U.S. Government Printing

Office, Aug. 1971.,

16National Center for Health Statistics: Replication: An

approach to the analysis of data from complex surveYs. Vitaf and

Health Statistics. PHS pub. No. 1000-Series 2-No. 14. Public

Health Service. Washington. U.S. Government Printiqg Office,

Apr. 1966.

1 7National Center for Health Statistics: pseudoreplication: Further evaluation and application of the batanced

half-sample technique. Vital and Health Statistics. PHS pub.

No. 1000-Series 2-No. 31. Public Heidth Service. Washington,

U.S. Government Printing Office, Jan. 1969.

13
LIST OF DETAILED TABLES

Page

Table 1. Mean reading raw scores on the Wide Range Achievement Test for youths,

by sex, age, and educational level: United States, 1966-70-------------- 15

2. Means, standard deviations (SD), coefficients of variation (SD/mean), and

standard errors (SE) of means for raw scores on the reading subtest of

the Wide Range Achievement Test for youths,by age and sex:United States,

1966-70---------------------------------------------------------------- 15

3. Mean arithmetic raw scores on the Wide Range Achievement Test for youths,

by sex, age, and educational level: United States, 1966-70-------------- 16

4. Means, standard deviations (SD),coefficients of variation (SD/mean), and

standard errors (SE) of means for raw scores on the arithmetic subtest

of the Wide Range Achievement Test for youths,

States, 1966-70

by age and sex: United

-------- ---:---- -------- -------- -------- -------- -------- - 16

5. Percentile equivalents of raw scores on the reading subtest of the Wide

Range Achievement Test for youths, by sex and age: United States, 1966-

70------------------.-------------------------------------------------- 17

6. Percentile equivalents of raw scores on the reading subtest of the Wide

Range Achievement Test for youths 12-17 years,by sex and grade inschool:

United States, 1966-70-------------------------------------------------- 18

7. Percentile equivalents of raw scores on the arithmetic subtest of the

Wb& R#ge Achievement Test for youths, by sex and age: United States,

------- ---------.---- ------- -------------- ------- ---------------- 19

8. Percentile equivalents of raw scores on the arithmetic subtest of the

Wide Range Achievement Test for youths 12-17 years, by sex and grade in

school: United States, 1966-70 ------------------------------------------ 20

9. T score equivalents of raw scores on the reading subtest of the Wide

Range Achievement Test for youths, by age: United States, 1966-70------- 21

10. Tscore equivalents of raw scores on the arithmetic subtest of the Wide

Range Achievement Test for youths, by age: United States, 1966-70------- 22

11. Tscore equivalents of raw scores on the reading subtest of the Wide

Range Achievement Test for youths 12-17 years,by grade in school: United

States, 1966-70 --------------------------------------------------------- 23

12. T score equivalents of raw scores on the arithmetic subtest of the Wide

Range Achievement Test for youths 12-17 years,by grade in school: United

States, 1966-70 -------- ---------------- -------- -------- ---------------- - 24

14
Table 1, Mean reading raw scores on the Wide Range,Achievement Test for youths, by sex, age, and educational level:

United States, 1966-7U

Grade in school High

All

Levels

school

4 and

gradubelaw 5

6 7 8 9 10 11 12 ate

More

than

high

school

education

Left I

high

school Special

before P&+n:-

graduating

Sex and age

Both sexes

12-17 years----

12 years-------------

13 years-------------

14 years-------------

1~ y~~r~-.-..-------.

16 years-------------

17 y(l~~~-.....-.--..--

Boys

12-17 years----

12 years-------------

13 years -------------

14 years-------------

15 years-------------

16 years-------------

17 yeare-------------

Girls

12-17 years----

12 years-------------

13 yQ~~~..-.-.------

14 ycar9-------------

15 yuars-------------

16 ycvm-s------------

17 yOars-------------

Mean raw score

48.5 22.0 27,9

42.1 21.4 29.2

45,3 * 25,5

48.2 $: ;~

49.8 - ;’~

52.8 >,? >,<

53,7 - -

47.2 22.5 26.9

41.1 20.4 27.4

44.6 ~’~25,4

47.0 $C ~~

48.9 - -

51,3 - -

51.6 - -

49.7 21.5 29.3

43.1 21.9 31.9

46,0 $~ 25.6

49.4 * -

50.8 - ;’:

54.4 >,? ;,<

55.8 - -,

36.2 42.6 46.3 148.7 52.0 55.6 58.7 58.2 66.2 39.4 23.1

38.0

30,1

30.3

.*

35.3

~

42.0

36.5

28.2

>,<

>!

41.8

48.8 *

~ 51.8

43.8 ~

35.2 44.9

37.6 39.5

$< 30.3

45.6 47.7

22.1

20.2

23.0

.,.,.

>,,

>k

22.7

,,,.

55.0

~

50,0

42.8

51.0

>,,

.,,:

58.6

56.7

51.6

54.8

.:

.A.

58.2

59.1

>k

.:

>,,

66,0

64.4

37.1

29.8

28.1

>?

37.4

39.1

30.6

35.6

,,,

43

41.7

36.8

27,4

>?

$,

43.5

4-

42.3

36.1

31.0

>,:

>,<

:

49.2 >~

~ 50.4

42.9 ~

34.5 44,6

38.3 39.1

~~ 28.6

46.9 49.8

48.5 -

Q._2 53.1

45.1 ~

36.3 45.3

34.5 40.2

- 37.9

22.1

19.5

23.1

>,<

,,.

,,<

23.8

22.1

21.6

$:

>:-

>,:

,,:

,~

55.1

~

47,8

41.0

53.1

,!..

54.9

~

52.2

46.8

59.1

~

50.6

56.4

;.,

>k

58.2

~

52.7

,,<

59.0

57.8

.:.

.,.>.

57.9

>’(

64.3

67.7

,,>.

67.4

,?

>k

36.2

39.5

40,7

>)<

,:-

45.6

38.8

NOTE: Ncan raw scores for the modal age-in-grade groups are underlined.

Tnblo 2, Ffeans,standard deviations (SD)j coefficients of variation (SD/mean), and standard errors (SE) of means for

raw scares cm the reading subtest of the Wide Range Achievement Test for vouths.bv age and sex: United States. 1966-70

Age in

years and monthe

Both sexes Boys Girls

SD

13.18

11.04

11.02

11.86

11.76

12.08

11.86

12.47

12.87

12.08

13.31

12.78

15.49

SE of IIMean

nean

SE o: SE of

mean Mean SD SD/mean SD 3D/mean Mean SD/mean

0.42 47.25

0.46 40.52

0.58 41.58

0.49 44.07

0.64 45.25

0.69 46.62

0.66 47.38

0.65 48.03

1.04 49.86

0.64 51.52

0.75 51.03

0.90 51,23

0.91 51.95

3.2-oto 17-11-------

12-0 ta 12-5--------------

12-6 to 12-Ll-------------

13-0 ta 13-5--------------

13-6 tcl13-11-------------

L4-O tcl14-5--------------

14-G to 14-11-------------

15-0 to 15-5--------------

15-6 to 15-11-------------

16-0 to 16-5--------------

16-6 to 16-11-------------

17-0 to 17-5--------------

17-6 to 17-11-------------

48.47 13.61 .281 13.92 .295 0,50 49.72 .265 0.40

41,67

42.41

44.52

46.21

47.85

48.52

49.18

50.48

52.78

52,92

53.05

54.30

11.37

11.61

12.62

12.49

12.98

12.67

13.22

13.40

12.73

L3.66

14.42

14.67

.273

.274

.284

.270

.271

.261

.269

.266

.241

.258

.272

.270

11.59

12.08

13.29

13.10

13.72

13.29

13.76

13.92

13.18

13.77

15.68

13.40

.286

.290

.302

.290

.294

.280

.286

.279

.256

.270

.306

.258

0.63

0.84

0.59

1.05

1.06

0.83

0.92

1.12

0.92

0.94

1.40

1.12

42.80

43.31

45.01

47.19

49.07

49.71

50.44

51.07

54.15

54.73

54.86

56.69

.258

.254

.264

,249

.246

.239

.247

.252

.223

.243

.233

.273

0.83

0.55

0.68

0.68

0.85

0.64

0.82

1.11

0.84

0,98

0.91

1.33

15
Table 3. Mean arithmetic raw s,coreson the Wide Range Achievement Test for youths,by sex, age, and educational level:

United States, 1966-70

Grade.in school More Left

All

High than

. . I I I I I I I

School h$gh- &$l Special

.evels 4 and school before p~n:-

below 5 6 7 8 9 10 11 12

gradUate educa- gradution ating

Sex and age

Both sexes

12-17 years----

12 yeara-------------

13 years-------------

14 years-------------

15 years-------------

16 years-------------

17 years-------------

Boys

12-17 yeara----

12 years-------------

13 years-------------

14 years-------------

15 years-------------

16 years-------------

17 years-------------

Girls

12-17 years----

12 years-------------

13 years-------------

14 years-------------

15 years-------------

16 years-------------

17 years-------------

Mean raw score

23.0 10.3 19.6 121.6

19.2 11.3

21.1 *

23.0 *

24.0 *

25.6 *

25.7

23.0 9.7

19.1 11.6

21.1 *

23.0 *

24.1 *

25.8

25.6

23.0 11.0

19.3 11.7

21.1 *

23.0 *

23.9 -

25.3 *

25.8

13.8 17.4 23.4 125.0 26.8 28.1 27.3 32.0 17.9 11.4

14.5

12.7

*

*

*

13.2

17.9

15.6

16.4

*

*

17.6

18.0

16.1

16.2

*

.

17.2

19.9 22.0

G ~

18.2 21.2

15.9 17.8

* 18.4

* *

19.5 21.6

Q& 22.0

19.7 ~

18.3 21.2

15.8 17.6

* *

* *

19.6 21.6

lJQ 22.0

19.8 ~

17.9 21.3

16.4 18.2

* *

* -

* -

23.8 *

24.6 25.8

22.2 25.5

19.3 24.3

18.0 21.0

23.6 25.2

* -

24.5 *

25.1 26.8

z 26.2

19.6 24.2

* 20.6

23.2 24.6

- -

23.3 *

24.1 25.0

G ~

18.7 24.4

* 21.7

10.8

10.5

11.4

*

*

*

11.4

*

*

27.4

~

25.2

27.3

*

*

28.9

~

28.6

*

*

27.4

28.1

*

31.8

33.8

*

*

18.7

17,8

17.9

13.9

11.7

*

-

14.5

10.6

11.0

*

*

*

*

11.4

27.3

2~

25.8

26.3

*

*

30.3

28.2

27.7

*

28.1

26.9

*

33.6

30.5

-

*

*

16.8

18.6

18.0

15.4

14.7

*

*

17.7

15.0

*

*

11.2

9.4

*

*

*

*

*

*

27.4

26.7

%

*

27.8

27.7

*

*

27.1

*

30.3

-

*

*

20.4

16.9

NOTE: Mean raw scores for the modal age-in-grade groups are underlined.

Table 4. Means, standard deviations (SD), coefficients of variation (SD/mean), and standard errors (SE) of means for

raw scores On the arithmetic subtest of the Wide Range Achievement Test for youths,

1966-70

by age and sex: United States,

Both sexes

i=

SE of Mean nean

Boys

--t

;E of Mean

Bean

Girls

Age in

years and months

;D/mean

.310

.271

.264

.308

.300

.286

.295

.283

.270

.282

.290

.318

.289

SD

6.76

4.40

5.45

5.57

5.65

6.26

6.32

6.38

6.98

6.59

7.15

7.31

7.70

;E of

mean

0.27

0.33

0.38

0.42

0.53

0.48

0.52

0.42

0.54

0.54

0.45

0.61

0.51

SD

6.95

4.76

5.30

6.04

6.04

6.33

6.68

6.55

6.80

6.91

7.40

7.77

7.53

Mean SDlmean

23.00

SD ;D/mean

.294

.233

.276

.269

.263

.274

,272

.272

.287

.262

.281

.282

.299

0.27 22.98

0.33 18.86

0.38 19.72

0.42 20.70

0.53 21.47

0.48 22.89

0.52 23.21

0,42 23.46

0.54 24.29

0.54 25,13

0.45 25.43

0.61 25.90 I 0.51 25.79

0.26 23.02

0.27 18.78

0.33 19.43

0.31 20.89

0.34 21.33

0.38 22.30

0.40 23.66

0.29 23.66

0.51 24.51

0.49 25.47

0.41 26.28

0.50 25.84

0.43 25.44

12-0 to 17-11------- .302 7.13

5.09

5.14

6.44

6.40

6.38

6.99

6.69

6.61

7.18

7.62

8.21

7.36

12-0 to 12-5--------------

12-6 to 12-11-------------

13-0 to 13-5--------------

13-6 to 13-11-------------

14-0 to 14-5--------------

14-6 to 14-11-------------

15-0 to 15-5--------------

15-6 to 15-11-------------

16-0 to 16-5--------------

16-6 to 16-11-------------

17-0 to 17-5--------------

17-6 to 17-11-------------

.253

.271

.290

.282

.280

.285

.278

.279

.273

.286

.300

.294

18.82

19.57

20.79

21.39

22.60

23.43

23.56

24,39

25.31

25.85

25.87

25.61

16
Table 5. Percentileequivalentsof raw scores on the reading subtest of the Wide Range Achievement Test for youths, by sex and age: United States, 1966-70

Sex and

percentile

Both sexes

99--------------

98--------------

-----------..-

%-------------

95--------------

90--------------

85--------------

80--------------

75--------------

70--------------

--------- -----

%--------------

55--------------

--------------

&-------------

jg--------------

---------- ----

30--------------

25--------------

20--------------

--------- ----- L---------- ---------..--

:---------------

3.......--------

2---------------

1......---------

Boys

. . . . . . . . . -..--

%--------------

97=-------------

96--------------

95--------------

90--------------

85--------------

80--------------

75--------------

70--------------

. . . . . . . . . . . . . .

K...---------

55--------------

50--------------

II

II Age in years

Total

13 14 15 16 17

Raw scorel

77

74

72

71

70

66

62

60

58

56

22

19

65

62

60

57

55

67

~~

61

57

55

52

:;

47

46

44

42

40

39

37

35

33

31

29

27

24

23

22

20

17

66

65

64

63

61

57

54

%

48

::

42

41

/

%

66

65

64

61

58

57

%

%

48

46

45

43

41

38

36

33

30

28

;:

22

21

19

69

67

65

65

64

61

59

57

55

53

52

;;

46

74

72

:$

68

64

61

59

58

56

%

%

48

46

44

42

39

36

33

30

26

25

24

22

20

%

::

67

63

61

59

57

55

53

%

49

75:

-73

72

%

67

64

:!

58

X

53

51

50

:;

43

40

38

35

30

26

::

22

20

75

72

72

;:

67

64

62

60

58

;:

52

50

80

;;

73

73

69

$J

60

59

57

56

54

52

::

47

45

42

39

%

27

25

23

22

E

74

73

72

68

65

63

62

59

57

55

53

52

—

Sex and

percentile

Boys-Con.

45-----------

40-----------

35-----------

30-----------

25-----------

20-----------

-----------

&----------

3------------

2------------

1-.----------

Girls

99-----------

-----------

%----------

96-----------

95-----------

90------------

85-----------

80-----------

75-------.-o.-

65-----------

60-----------

55-----------

50-----------

45-----------

40-----------

35-----------

30-----------

2------------

2. ,.‘---------

15-----------

1o-----------

------------

;------------

---------...

2------------

1------------

rotal

lScorebelow which the given percentageof the”populationfalls.

46

44

42

j?

::

28

24

23

22

20

18

78

75

73

72

71

67

63

61

59

57

56

%

:;

47

::

40

38

35

31

27

;;

23

21

Age in years

I I I I I

12113114115116117

39

X

34

32

30

28

25

2;

20

19

18

67

65

62

62

61

57

55

52

51

50

48

47

46

44

41

40

38

37

35

32

;:

$:

23

22

20

—

Raw scorel

44

42

40

37

35

32

29

26

22

21

20

19

18

68

%

65

64

60

58

57

;:

52

:;

47

45

44

42

40

37

34

31

;:

26

24

22

20

46

45

43

:?

33

31

28

24

24

22

21

18

73

72

;:

68

64

61

60

58

57

55

54

52

;:

47

45

43

41

38

36

32

28

27

26

24

21

48

46

::

39

36

32

29

25

24

23

21

19

76

73

72

;:

67

64

62

60

58

2<

54

;:

49

47

45

42

40

37

:;

;;

24

22

—

i!

47

45

44

;;

32

27

26

24

22

20

80

78

76

75

73

:;

X

61

6-;

57

56

54

52

:;

47

44

&

:;

27

25

23

—

17
Table 6. Percentileequivalentsof raw scores on the reading subtest of the Wide Range Achievement Test for youths 12-17 years, by sex and grade in school: United States, 1966-70

Sex and

percentile

.BOth sex~s

99----------------

98----------------

96----------------

95----------------

90----------------

80------------------

75----------------

70----------------

65----------------

60----------------

................

%---------------

45----------------

40--------*-------

35----------------

----------------

L------------

20----------------

15----------------

1o----------------

-----------------

:-----------------

3.......----------

-----------------

:----.----.=

Bovs

----------------

%---------------

97----------------

96----------------

95----------------

90----------------

85----------------

;(&-------------

----------------

70----------------

65----------------

60----------------

55----------------

50----------------

Grade in school

7 8 9 10 11 12

Raw scorel

66

64

63

62

61

57

55

53

51

50

48

46

45

:?

39

37

36

34

32

30

28

24

:~

21

19

65

63

63

62

61

57

55

52

;$

47

45

44

42

f%

66

65

64

61

59

#

52

::

47

46

44

42

40

38

35

%

27

;;

23

21

u

%

64

61

59

57

55

53

52

::

46

73

&

68

67

63

61

59

57

56

54

53

51

::

47

45

43

::

35

31

;:

25

24

22

74

%

68

67

63

61

59

57

55

%

::

75

73

;:

70

67

65

62

61

59

58

%

53

51

::

46

:;

39

36

31

;?

26

23

75

73

72

71

70

:;

62

61

59

57

55

%

79

78

76

75

74

::

65

64

62

61

59

58

56

55

53

%

::

44

40

35

32

31

27

25

79

77

76

75

74

%

64

63

62

60

58

56

55

82

81

79

77

77

73

:;

67

65

64

62

60

58

57

56

%

i!%

47

45

$:

36

33

30

81

79

77

75

75

72

:!

66

64

63

61

59

58

Sex and

percentile

Boys-Con.

40---------------

35---------------

30---------------

25---------------

20---------------

15---------------

1o---------------

5......----------

3.......---------

2----------------

1---------.......

Girls

99---------------

98---------------

97--------*------

95---------------

90---------------

80---------------

75---------------

70---------------

65---------------

60---------------

---------------

iL-------------

40---------------

--------.-.--.-

%-.--.---d ------

25---------------

20---------------

15---------------

1o---------------

5...... ..- -------

3----------------

2----------------

1--------- -------

Grade in school

7 8 9 10 11 12

41

38

36

35

33

30

28

26

23

23

22

:;

2;

%

61

X!

54

51

50

48

:;

44

42

g

37

35

33

31

29

;;

25

23

20

Raw scorel

45

43

41

38

36

34

31

29

26

25

24

22

20

69

%

65

64

60

2;

55

53

52

g

46

45

43

41

39

37

;;

27

26

25

23

47

45

44

41

39

36

34

30

27

25

24

23

22

72

71

;:

67

64

62

60

58

57

56

54

53

51

50

48

46

44

$;

:5

29

28

27

26

24

49

48

46

45

43

:;

34

28

26

25

;;

76

74

72

71

70

67

64

62

60

59

58

56

55

%

51

;:

46

44

40

38

35

34

31

29

27

54

52

:;

47

45

43

40

34

31

30

26

24

80

78

76

74

73

&

66

64

62

61

60

59

57

56

54

%

::

45

41

35

34

32

%

57

55

55

54

52

:;

45

40

39

36

%

82

82

80

79

78

75

72

:;

66

%

60

59

58

56

2:‘

:;

48

45

40

37

35

34

32

%core below which the given percentageof the populationfalls.

18
Table 7. Percentile equivalents ofraw scores on the arithmetic subtest of the Wide Range Achievement Test for youths, by sex and age: United States, 1966-70

*

Sex and

percentile

Both sexes

99--------------

98--------------

97--------------

96--------------

95--------------

90--” -----------

85--------------

;y------------

--------- -----

70---------”----

65--------------

. ......-------

%--------”----

.-------- -----

:L-------------

&-------------

--------- --.--

;;--------------

---------- -----

20--------------

15--------------

1o--------------

--------- .-----

&----------

“...-.-... ------

2 --.--,..- .,------

1 ---------------

~

99--------------

98--------------

97--------------

96--------------

95--------------

.------- ------

&------------

80--------------

75-------”-----”

70--------------

65--------------

60--------------

55------------”-

50--------------

II II

40

38

37

36

35

32

31

29

28

26

H

;:

22

21

20

19

18

17

16

14

12

12

12

11

10

40

38

37

36

35

32

31

;:

27

;;

24

23

Raw scorel

33

31

29

28

27

26

24

23

22

21

21

20

19

19

18

18

17

16

::

14

13

12

12

11

10

9

34

31

29

29

28

26

24

23

22

21

21

20

19

19

36

33

32

32

31

30

28

26

25

24

23

22

22

21

20

19

18

17

17

16

15

14

12

12

11

10

9

37

34

33

32

32

30

28

26

25

25

?3

!3

!2

!l

38

37

36

35

34

32

30

29

28

26

25

24

24

23

22

21

20

19

18

18

16

15

13

12

11

10

9

37

:;

34

34

32

30

29

28

27

?5

?4

i4

~3

40

37

36

35

34

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

15

13

12

11

10

9

:;

36

35

35

32

31

30

29

28

?7

~6

~5

24

41

39

38

38

37

35

33

32

31

29

28

H

$!

24

23

22

20

19

18

16

14

13

12

11

10

41

40

39

38

38

36

34

32

31

30

29

28

~7

26

44

43

41

g

36

33

32

31

30

29

27

;:

25

24

23

22

21

19

18

16

14

13

12

11

10

:$

41

40

39

36

34

32

31

30

29

28

27

26

Boys—con.

45------------

40------------

35------------

30------------

25------------

20------------

15------------

1o------------

5 ------- ------

4 --- - -- ----- --

3 -----.-- -----

2 ---.---- -----

1 ------- ------

Girls

99------------

98----:-------

------- -----

u------------

95------------

90------------

85------------

80------------

75------------

70------------

65------------

60------------

------------

H------------

45------------

40------------

35------------

30------------

25------------

20------------

15------------

1o------------

5 ---- .. -- -. --

4 ---- --- --- --

3 -------- ----

2 -------- ----

1 -------- ----

naw .L”.c

22

21

20

19

18

17

15

H

12

11

11

9

40

38

37

36

35

32

31

29

27

26

25

24

23

22

22

21

20

19

18

17

H

13

12

12

11

10

18

17

17

16

15

15

14

13

12

11

11

;

32

31

29

:;

26

24

23

22

21

21

20

20

19

18

18

17

17

16

15

14

13

12

12

11

10

9

:;

18

17

16

15

14

13

12

11

11

:

34

32

32

31

31

29

27

26

25

24

23

H

21

20

19

18

18

17

16

15

H

H

LO

9

—

:: ~

20

19

18

::

H

12

11

10

8

38

37

36

35

35

32

30

::

25

24

23

22

22

21

20

19

18

18

17

15

13

13

12

11

10

—

24

23

22

21

20

18

16

15

12

12

12

10

9

41

38

37

36

35

33

31

30

28

27

26

25

24

23

23

22

21

20

19

18

17

15

13

13

12

11

10

25

24

23

22

21

i9

17

16

13

13

12

11

10

41

39

38

37

36

::

31

30

29

28

27

26

25

24

23

;:

20

19

18

i:

13

13

12

11

25

24

23

22

21

19

18

H

13

12

11

10

44

43

;;

38

36

34

32

31

30

28

27

26

25

24

24

23

22

21

20

18

17

15

14

13

12

11

lscore below which the given percentage of the population falls.

19
Table 8. Percentile

ment Test for

Sex and

percentile

Both sexes

99----------------

98----------------

----------------

K---------------

95----------------

-------- --.----- EL---------------

80----------------

75----------------

70----------------

-------- --------

%----------------

55----------------

------.--..-.---

z)---------------

40----------------

35----------------

30----------------

-------------.--

K-------------

-------- -------- R---------------

5-----------------

4-.---------------

3-----------------

2--------.--------

1-------------.---

Boys

. . . . . . . . . -------

;: --------- .--..--

97----------------

96----------------

95----------------

. . . . . . . . . . . . . . . . x----------------

80----------------

75----------------

70----------------

65----------------

----------------

k--------------

50----------------

equivalentsofraw scores on the arithmeticsubtest of the Wide Ran e Achieveyouths 12-17 years, by sex and grade in school:United States, 196%-70

Grade in school

7 8 9 10 11 12

Raw score’

2

31

30

29

26

25

24

23

22

21

%

19

19

18

17

17

;:

14

H

12

11

11

10

34

:?

30

29

x

24

23

22

::

20

19

36

:;

32

32

30

28

26

25

24

24

;;

21

21

20

19

18

17

17

16

14

13

13

12

12

10

36

34

33

32

32

30

28

26

;:

24

H

21

—

::

35

:;

31

30

29

%!

25

25

24

23

22

22

21

20

19

18

17

15

::

12

12

12

38

36

35

34

34

32

30

29

28

27

$:

24

23

—

39

:;

36

35

33

32

31

29

28

27

26

25

25

24

23

22

21

21

20

19

17

15

14

L3

13

12

%

37

37

35

33

32

31

30

29

H

;;

::

g

38

35

34

32

31

30

29

28

27

;:

25

24

%

21

20

18

16

16

15

14

13

41

40

:;

38

36

34

32

;;

30

29

$;

45

43

41

40

40

37

36

34

32

31

31

29

::

27

26

25

%

22

21

20

17

::

15

13

46

:;

%

38

x

33

32

31

30

29

28

Sex and

percentile

Boys-Con.

45--------------

40--------------

35--------------

----------.-.-

%-------------

-----------..-

&-------------

1o--------------

---------------

2---------------

3---------------

2---------------

1----.----------

Girls

99--------------

--------------

;;--------------

96--------------

95--------------

90--------------

--------------

R--------------

75--------------

70--------------

65--------------

60--------------

55--------------

--------------

2!i’--------------

40--------------

35--------------

30--------------

--------......

%L------------

----.---------

R-------------

5---------------

4.-------------.

3-----.---------

---------------

:---------------

Grade in school

ZIIEEEE

Raw score]

19

18

17

16

15

::

:;

12

11

11

10

33

32

31

29

28

26

24

23

;;

21

20

20

:;

H

17

16

16

H

12

12

12

11

9

—

20

H

18

17

H

14

13

13

12

12

10

34

;:

32

31

29

28

26

25

24

23

22

22

21

21

20

i:

H

::

13

13

12

12

11

23

22

21

20

19

18

H

H

13

?$

38

;:

35

34

31

%

27

26

25

24

23

23

22

21

20

19

19

18

H

14

H

12

11

24

;2

22

21

;;

17

15

14

13

&

:;

36

36

35

33

31

30

29

28

27

26

25

24

23

23

22

21

;8

:?

15

15

14

13

12

27

26

25

24

23

22

21

19

16

15

::

13

41

41

40

38

37

35

34

32

:;

28

28

27

26

25

24

23

22

;:

19

18

17

16

15

14

13

—

1

Score below which the given percentageof the population falls.

20
Table 9. T score equivalents of raw scores on the reading snbtest of the Wide Range Achievement Test

for youths, by age: United States, 1966-70

75------

74------

73------

72------

71------

70------

69------

68------

67------

66------

65------

64------

63------

62------

61------

60------

59------

58------

57------

56------

55------

.54------

53------

52------

51------

Raw score

69-89 171-89 176-89 178-89 ]82-89 I 84-89

1 I 1 1 1

65 72 I 74 78 80

64 67 71 73 77 79

63 66 70 72 76 78

62 65 69 71 74-75 77

61 68 70 73 76

60 64 67 69 75

59 63 66 68 72 74

58 62 65 71 73

57 61 64 67 70 72

56 60 63 66 68-69 71

55 59 62 64-65 67 70

.54 58 61 63 66 68-69

53 57 60 62 65 67

52 56 59 61 63-64 66

51 55 58 60 62 65

49-50 54 57 59 61 63-64

48 53 55-56 58 60 61-62

47 52 54 57 59 60

46 51 53 55-56 57-58 59

45 49-50 52 54 56 57-58

43-44 48 51 52-53 55 56

50----

49----

48----

47----

46----

45----

44----

43----

42----

41----

40----

39----

38----

37----

36----

35----

34----

33----

32----

31----

30----

29----

28----

27----

26----

25----

Raw score

42 146-47149-501 51 153-54 I 55

41 45 48 50 52 53-54

40 44 46-47 48-49 51 52

38-39 42-43 45 46-47 49-50 51

37 40-41 44 45 48 49-50

36 38-39 42-43 43-44 46-47 48

34-35 36-37 40-41 41-42 45 46-47

33 35 38-39 40 44 45

32 34 36-37 39 43 44

30-31 32-33 35 38 41-42 42-43

29 31 34 37 40 41

28 30 33 36 39 40

27 29 32 35 38 39

26 28 31 34 36-37 38

25 27 30 33 35 37

23-24 26 29 31-32 34 36

22 25 28 30 33 35

21 24 27 29 32 34

20 23 26 27-28 ‘ 30-31 33

19 22 24-25 26 29 31-32

17-18 20-21 23 25 28 30

16 19 22 24 26-27 29

15 18 20-21 22-23 25 27-28

14 17 19 21 24 26

13 16 18 20 23 25

00-12 00-15 00-17 00-19 00-22 00-24

21
Table 10. T score equivalents of raw scores on the arithmetic subtest of the Wide Range Achievement

Test for youths, by age: United States, 1966-70

Age in years

T score

12 13 14 15 16 17

Raw score

75------ 34-56 37-56 40-56 41-56 ,42-56 46-56

74------ 33 36 39 40 41 45

73------- 35 38 39 44

72------ 32 34 38 40

71------- 37 43

70------ 31 33 37 39 42

69------ 30 36 36 41

68------ 29 32 35 38 40

67------ 28 35 39

66------ 31 34 37

65------ 27 33 34 38

64------ 36 37 ~

63------ 26 30 32 33 35 36

62------ 25 29 31 32 35

61------ 28 34 34

60------ 24 27 30 31 33 33

59------ 29 32

58------ 23 26 30 32

57------ 28 29 31 31

56------ 22 25 27 28 30

55------ 24 26 29 30

54------ 21 27 29

53------ I I 231 251 261 281 28/

52------ 20 22 24 25 27 27

51------ 23

I

Age in years

T score

12 13 14 15 16 17

I Raw score

50------ 19 2.1 24 26 26

49------ 20 22 23 25 25

48------ 18 24 24

47------ 19 21 22 23 23

46------ 17 18 20 21

45------ 22 22

44------ 16 17 19 20 21 21

43------ 18 19 20

42------ 16 20

41------ 15 17 18 19 19

40------ I 141 151 I 171 181 18

39------ 16 16 17

38------ 13 14 15 17

37------ 15 16 16

36------ 12 13 14 14 15 15

35------ 12 13 14 1.4

34------ 11 13

33------ 10 11 12 12 13 13

32------ 11 12 12

31------ 09 10 10 11 11 11

27------1 I 071 071 081 081 08

26------ I 061 061 06106-07[ 07/ 07

25------ 00-05 00-05 00-05 00-05 00-06 I

00-06

.

22
Table 11. T score equivalents of raw scores on the reading subtest of the Wide Range Achievement Test

for youths 12-17 years, by grade in school: United States, 1966-70

Grade in schooll Grade in schooll

T score T score

7 8 9 10 11 12 7 8 9 10 11 12

Raw score Raw score

75------ 68-89 70-89 76-89 7,7-89 82-89 84-89 50----- 45 49 52 54 57 59

74------ 67 69 75 76 81 83 49----- 43-44 48 51 53 56 58

73------ 66 74 75 80 82 48----- 42 46-47 50 52 55 57

72------ 68 47----- 41 45 49 51 54 56

71------ 65 73 74 79 46----- 40 44 48 50 53 55

70------ .64 67 72 73 78 81 45----- 39 43 47 48-49 52 54

69------ 63 66 71 72 77 80 44----- 38 42 46 47 51 53

68------ 62 70 71 76 , 79 43----- 37 41 45 46 50 51-52

67------ 65 69 70 75 78 42----- 36 39-40 44 44-45 49 50

66------ 61 68 74 77 41----- 35 38 42-43 43 47-48 49

65------ 60 64 67 69 73 75-76 40----- 33-34 36-37 41 41-42 46 48

64------ 59 63 66 68 72 74 39----- 32 35 39-40 40 45 46-47

63------ 58 62 65 71 73 38----- 31 34 38 39 44 45

62------ 57 61 64 67 69-70 72 37----- 30 33 36-37 38 42-43 44

61------ 56 60 63 66 68 71 36----- 29 32 35 37 41 42-43

60------ 55 59 62 65 67 70 35----- 28 31 34 36 39-40 41

59------ 54 58 64 66 69 34----- 30 33 35 37-38 40

58------ 53 57 61 63 65 68 33----- 27 29 32 34 36 38-39

57------ 52 56 60 62 64 67 32----- 26 31 32-33 35 36-37

56------ 51 55 59 61 63 66 31----- 28 30 31 33-34 35

55------ 50 54 58 60 62 65 30----- 25 27 29 30 32 34

54------ 49 53 56-57 59 61 64 29----- 24 27-28 29 30-31 33

53------ 48 52 55 58 60 62-63 28----- 23 26 28 28-29 32

52------ 47 51 54 57 59 61 27----- 26 27 27 31

51------ 46 50 53 55-56 58 60 26----- 22 25 25 26 26 30

25----- 00-21 00-24 00-24 00-25 00-25 00-29

lT scores for each grade level are computed from the test results of only those youths who were the

modal age in each grade, for example, only the 12-year-olds in the 7th grade and the 13-year-olds in

the 8th.

23
Table 12. T score equivalents of raw scores on the arithmetic subtest of the Wide Range Achievement

Test for youths 12-17 years, by grade in school: United States, 1966-70

Grade in schooll

T score

7 8 9 10 11 12

I

Raw score

75------ 34-56 137-56 139-56140-561 42-56 146-56

, , 1 I

74------ 33 39

73------ 36 38 41 45

72------ 32 35 38

71------ 34 37 44

70------ 31 33 37 40 43

69------ 30 36 42

68------ 29 32 36 39 41

67------ 35 38 40

66------ 28 35

65------ 27 31 34 37 39

64------ 33 34

63------ 26 30 33* 36 38

62------ 32 37

1 ! , ,

61------ 25 29 I 321 35 36

60------ 28 31 34 35

59------ 24 27 30 34

.

58------ 31 33 33

57------ 23 26 29 30 32

56------ 28 29 31 32

55------ 22 25

54------ 24 27 28 30 31

53------ 21 26 27 29 30

52------ 23 29

51------ 20 25 26 28 28

Grade in school*

T score

7 8 9 10 11 12

Raw score

50----- 22 24 27 27

49----- 19 25

48----- 21 23 24 26 26

47----- 25 25

46----- 18 20 22 23

45----- 19 24 24

44----- 17 21 22 23

43----- 18 20 21 23

42----- 16 22 22

41----- 17 19

40----- 20 21 21

39----- 15 18 20

38----- 16 19 20

37----- 14 18 19

36----- 15 17 17 19

35----- 18 18

34----- 13 16 16

33----- 14 15 17 17

32----- 15

31----- 13 14 16 16

30----- 12 14 15 15

29----- 13

28----- 12 13 14 14

27----- 13 13

26----- 11 12 12

25----- 00-10 00-11 00-11 00-11 00-12 00-12

IT scores for each grade level are computed from the test results of only those youths who were the

modal age in each grade, for example, only-the 12-year-olds in the 7th grade

the 8th.

and the 13-year-olds in

24
APPENDIX I

DEFINITIONS

Age.—The age recorded for each youth was age at

last birthday as of the date of examination. Age was confirmed by comparison with the date of birth on the

youth’s birth certificate. The age criterion for inclusion

in the sample was the age at the time of the first interview. Since the examination usually took place 2 to 4

weeks after the interview, some youths who were 17

years old at the time of interview became 18 years old

by the time of examination. There were 58 such cases.

In the adjustment and weighting procedures and in the

tmalyai~, these youths were included in the 17-yearold ~OUp.

Gvade. —The grade placement of sample youths was

obtained from the questionnaire sent to the schools they

attended. If educational level was not available from the

school questionnaire, grade placement or the fact of

having completed or left school was determined from

information noted by examiners on one of the psychological test record forms. For youths on summer vacation, the grade placement recorded was the grade the

youth would enter in the fall. Those included in the “more

than high school education” category are youths who

were enrolled in colleges or training programs beyond

high school level or youths on summer vacation after

high school graduation who planned to continue their education in the fall.

—000

25
APPENDIX II

TECHNICAL NOTES

The Survey Design

The sample designs for’the first three programs,

Cycles I-III, of the Health Examination Survey were

essentially similar in that each was a multistage,

stratified probability sample of clusters of households

in land-based segments. The successive elements for

this sample design are primary sampling unit (PSU),

census enumeration district (ED), segment (a cluster of

households), household, eligible youth, and finally, the

sample youth.

The 40 sample areas and the segments utilized in

the design of Cycle III were the same as those used in

Cycle II. Previous reports describe in detail the sample

design used for Cycle II and in addition discuss the

problems and considerations given to other types of

sampling frames anodl~whether or not to control the

selection of siblings.”’

Requirements and limitations placed on the design

for Cycle III were similar to those for the design for

Cycle II.

1. The target population was defined as the civilian,

noninstitutionalized population of the United

States (including Alaska and Hawaii) in the age

range of 12-17 years with the special exclusion

of children residing on reservation lands of the

American Indians, an exclusion adopted as a

result of operational problems encountered on

these lands in Cycle I.

2. The time period of data collection was limited

to about 3 years, and the length of the individual

examination within the specially constructed

mobile examination center was between 2 and 3

hours.

3. Ancillary data was collected on specially designed household, medical history, and school

questionnaires and from copies of birth certificates.

4. Examination objectives were related primarily

to factors of physical and intellectual growth

and development.

5. The sample was sufficiently large to yield reliable findings within broad geographic regions

and population density groups as well as within

age, sex, and limited socioeconomic groups for

the total sample,

The sample was drawn jointly with the U.S. Bureau

of the Census, beginning with the 1960 decennial census

list of addresses and the nearly 1,900 PSU’S into which

the entire United States was divided. Each PSU is either

a standard metropolitan statistical arpa, a county, or a

group of two or three contiguous counties. These PSUIS

were grouped into 40 strata so that each stratum had

an average size of about 4.5 million persons, and the

grouping was done so as to maximize the degree of

homogeneity within strata with regard to the population

size of the PSI-J’S, degree of urbanization, geographic

proximity, and degree of industrialization, The 40

strata were then classified into four broad geographic

regions of 10 strata each and next cross-classified

within each region by four population density classes

and classes of rate of population change from 1950 to

1960. Using a modified Goodman-Kish controlled-selection technique, one PSU was drawn from each of the

40 strata.

Generally, within each PSU, 20 EDIS were selected

with the probability of selection of a particular ED

proportional to its population in the age group 5-9

years in the 1960 Census, which by 1966 approximated

the target population for Cycle III. A similar method

was used for selecting one segment (a smaller cluster

of households) in each ED. Because of the approximately 3-year time interval between Cycle II and Cycle

III, the Cycle 111sampling frame was updated for new

construction and to compensate for segments where

housing was partially or totally demolished to make

room for highway construction or urban redevelopment.

Each of the resulting 20 segments within a PSU was

either a bounded area or a cluster of households (or

addresses). All the youths in the appropriate age range

who resided at the address visited were eligible youths,

i.e., those eligible for inclusion in the sample. Operational considerations made it necessary to reduce the

number of prospective examinees at any one location to

a maximum of 200. When the number of eligible youths

26
in a particular location exceeded this number, the ‘‘excess” eligible youths were deleted from the sample

through a systematic sampling technique. Youths who

were not selected as sample persons in the Cycle III

sample but who had previously been examined in Cycle

II were scheduled for examination if time permitted

and will be included in special longitudinal analyses.

Individual twins who were deleted from the Cycle III

sample were also scheduled for examination, as in

Cycle 11, to provide data on pairs of twins for future

analysis. These data are not included in this report as

part of the national probability sample of youths.

The sample was selected in Cycle III, as it had

been for the children in Cycle II, so as to contain proportional representation of youths from families having

only one eligible youth, two eligible youth’s, and so on,

thus making the sample representative of the total target population. However, since households were one of

the elements in the sample frame, the number of related

youths in the resulting sample was greater than would

result from a design which sampled youths 12-17 years

without regard to household. The resulting estimated

mean measurements or rates should be unbiased, but

their sampling variabilities are somewhat greater than

those from a more costly, time-consuming, systematic

sample design in which every kth youth would be selected.

The total probability sample for Cycle III included

7,514 youths representative of the approximately 22.7

million noninstitutionalized U.S. youths of 12-17 years.

The sample contained youths from 25 different States,

with approximately 1,000 in each single year of age.

Table 1. Number of examiqees who were scored on the Wide Ran e Achiev_ent Teat and estimated

frequencies for the normnstitutionalized population of the Un!?ted States, by age and sex: Health

Exatninatf.on Survey, 1966-70

Age in yeara

and months

12-0 to

17-11 -----

12-0 tO 12-5---

12-6 to 12-11 --

13-0 to 13-5---

13-6 to 13-11 --

14-0 to 14-5---

14-6 to 14-11 --

15-0 to 15-5---

15-6 tO 15-11 --

16-0 to 16-5---

16-6 tO 16-11 --

17-0 to 17-5---

17-6 to 17-11 --

lf;ol:o

.----

12-0 tO 12-5---

12-6 tO 12-11 --

13-0 to 13-5---

13-6 to 13-11 --

14-0 to 14-5---

14-6 tO 14-11 --

15-0 to 15-5---

15-6 tO 15-11 --

16-0 to 16-5---

16-6 to 16-11 --

17-0 to 17-5---

17-6 to 17-11 --

Both sexes I

Boya I

Girls

Total Scoredl acg:d2 Total Scoredl ‘ot 2 Total Scoredl Not

scored scored2

Number of examinees in sample

1‘

~

6,768 6,756 12

::$ ::;

637 636 i

571 :;;

611 $

593 591

562 561 1

554 553 1

566 566

526 526

473 473

485 483 51[

3,545 3,538

287 287

356 356

327 326

299 299

305 303

313 312

321 320

292 292

295 295

261 261

242 242

247 245

257

290

i 310

272

i 306

1 280

1 241

262

. 271

265

231

i 238

51 22’652!40

. n,n II . _._l

Population estimates in thousands

1. .34L ! II 1,842

2ji60 2.160 1:

2,100

1,852

1,950

1,902

1,860

1,891

1,914

1,711

1,759

1,75

-7—..

2,097

1,849

1,933

1,896

1,857

1,888

1,914

1,711

1.759 Ir

11,489 11,464

911 911

1,121 1,121

1,075 1,072

931 931

974 963

977 974

985 982

915 915

997 997

839 839

879 879

885 880

3,218

257

290

310

271

304

279

241

261

271

265

231

238

25 111,203

I 11====- 11,188

lIncludea estimates for missing data ahown in table II.

2N0 estimates made. since teata were not done because of factors attributable to the sample

youtha (blindness, physical disability, etc.).

27
The response rate in Cycle III was 90 percent, with

6,768 youths examined out of the total sample. These

examinees were closely representative of those in the

population from which the sample was drawn with respect to age, sex, race, region, and population density

and growth in area of residence, Hence it appears unlikely that nonresponse could bias the findings appreciably.

Reliability

While measurement processes in the surveyswere

carefully standardized and closely controlled, the correspondence between true population figures andsurvey results cannot be expected to be exact. Survey data

are imperfect for three major reasons: (1) results are

subject to sampling error, (2) the actual conduct of a

survey never agrees perfectly with the design, and(3)

the measurement processes themselves are inexact

even though standardized and controlled.

Data recorded for each sample youth are inflated

in the estimation process to characterize the larger

universe of which the sample youths are representative.

The weights used in this inflation process area prcduct

of the reciprocal of the probability of selecting the

youth, an’ adjustment for nonresponse cases, and a

poststratified ratio adjustment which increases precision by bringing survey results into closer alignment

with known U.S. population figures by color and sex

within single years of age 12-17.

In the third cycle of the Health Examination Survey

(as in Cycle II) the sample was the result of three

principal stages of selection—the single PSU from each

stratum, the 20 segments from each sample PSU, and

the sample youth from the eligible youths. The probability of selecting an individual youth is the product of

the probability of selection at each stage.

Since the strata are roughly equal in population

size and a nearly equal number of sample youths were

examined in each of the sample PSU’s, the sample design is essentially self-weighting with respect to the

target population; that is, each youth 12-17 years of age

had about the same probability of being drawn into the

sample.

The adjustment upward for nonresponse is intended

to minimize the impact of nonresponse on final estimates by imputing to nonrespondents the characteristics

of “similar” respondents. Here “similar” respondents

are judged to be examined youths in a sample PSU

having the same age in years and sex as youths not examined in that sample PSU.

The poststratified ratio adjustment used in the

third cycle achieved most of the gains in precision which

would have been attained if the sample had been drawn

@om a population stratified by age, color, and sex and

makes the final sample estimates of population agree

exactly with independent controls prepared by the U.S.

Bureau of the Census for the noninstitutionalized popuTable II. Number of missing or unusable reading

and arithmetic subtests of the Wide Range

Achievement Test, by age and sex of examinee:

Health Examination Survey, 1966-70

Age

12-17 years -------

12 years ----------------

13 years ----------------

14 years ----------------

15 years ----------------

16 years ----------------

17 years ----------------

12-17 years -------

12 years ----------------

13 years ----------------

14 years ----------------

15 years ----------------

16 years ----------------

17 years ----------------

w

Reading

36 25 11

32 18 ;;

36 24

28 21 17

20 13

29 1; 15

Arithmetic

I

198 123

41 29

34 21

43 30

28 19

24 10

28 14

75

12

13

13

12

14

lation as of March 9, 1968 (approximate midsurvey

point for Cycle III) by color and sex for each single

year of age 12-17. The weight of every responding

sample youth i~ each of the 24 age, color, and sex

classes is adjusted upward or downward so that the

weighted total within the class equals the independent

population control. Final sample frequencies and estimated population frequencies as of the approximate

midsurvey point are presented intableIbyage and sex.

Extent of Missing Test Results

and Imputation Procedures

In addition to youths who were selected for the

sample but, for various reasons, not examined, there

were some whose examination was incomplete inone

procedure or another. The extent of missing data for

theWRAT is shown in table IIaccordingto sex and age.

For 181 youths, or 2.7 percent of all those examined,

the WRAT reading subtest results were not available.

The WRAT arithmetic subtest results were not available for 198 youths, or 2.9 percent of all those examined. There were a numbr of reasons for this

missing data, primarily operational and logistical survey problems such as lost records or lack of time to

complete the examination. Since the reason formissing

test results in most cases wasnotdirectly related to

the characteristic being measured, raw scores were

imputed for ahnost all of these examinees. In certain

infrequent instances imputation was not considered ap28
,,

propriate, as for example the imputation of reading

scores for a blind youth or for a foreign-language

speaking youth who could not understand English well

enough to take any of the psychological tests.

Imputation was accomplished in the following manner. An intercorrelation niatrix of data collected during the survey, including all psychological test scores

and selected socioeconomic items, was derived to

identify those variables which were most highly associated with each raw test score. As a result, five

variables were chosen for the imputation of reading

and arithmetic raw scores: other available test scores,

educational level of the head of the household (four

categories), age, and two control variables—race and

sex. Imputation of a missing test result for an examinee

was accomplished by randomly selecting a match among

the group of examinees with the same age in years,

parental level of education, race, sex, and available

raw score test results most highly correlated with the

scores to be imputed. The raw score of this “matched”

cxaminee was then imputed to the examinee with the

missing score. When data for any of these variables

were not available, a match was selected using information on as many of the variables as were available

in the youth’s record.

Sampling and Measurement Error

In the present report, reference has been made to

efforts to minimize bias and variability of measurement

techniques. The probability design of the survey makes

possible the calculation of sampling errors. The sampling error is used here to determine how imprecise

the survey test results may be because they result

from a sample rather than from the measurement of

all elements in the population. The estimation of sampling errors for a study of the type of the Health Examination Survey is difficult for at least three reasons: (1) measurement error and “pure” sampling

error are confounded in the data, and it is difficult to

find a procedure which will either completely include

both or treat one or the other separately, (2) the survey design and estimation procedure are complex and

accordingly require computationally involved techniques

Table 111,. Standard errors of mean reading scores on the Wide Range Achievement Test for youths, by sex,

age, and educational level: United States, 1966-70

More

than

high

school

educa -

tion

Left

high

school

before

graduating

Grade in school High

school

graduate

All

levels

;pecial

)lacement

Sex and

age 4 and

below 5 6 7 8 9

0.54

10 11 12

~

SCxl?s

12-17

years - 0.42 4.08 1.42 1.10 0.53 0.40 0.53

1.2:

0.66

1.20

1.72

0.67

0.42 0.63

*

1.4;

0.63

0.78

1.68 2.71 1.03 1.12

1.24

1.54

3.66

?r

>k

*

1.43

1.94

2.84

6.58

*

;k

-*

1.39

12 years --

13 yuars --

14 years--

15 ycvms--

16 years --

17 yctms --

0.37

0.44

0.58

0.66

0,41

0,71

0.50

4.97

>k

>’r

>Y

-

6.02

1.18

3.87

>’r

*

>k

1.55

L.21

L.12

3.31

*

.

L.19

0.46

1.68

1.27

2.88

>V

+$

0.79

1.23

0.47

1.05

2.18

2.73

*

0.55

0.9;

0.52

1.18

1.18

2.02

0.57

*

1.5:

0.44

1.13

0.61

*

1.7;

1.85

*

$r

2.8;

1.85

*

,,<

1.86

0.89

1.67

BOVG

12-17

years -

12 years --

13 years --

14 yOars --

15 years --

16 years --

17 years --

0.56

0.64

0.78

0.73

0.76

0.91

0.40

6.46

%

>k

4.98

1.43

$.74

*

2.11

L.30

L.92

2.90

?k

L.25

0.68

2.23

1.62

2.40

>k

:?

0.54

1.51

0.65

1.26

2.07

2.84

‘*

0.54

1.1;

0.58

0.96

1.72

1.33

0.72

l.zi

0.72

1.87

2.21

15.50

*

1.83

0.78

1.27

1.91

0.60

2.2;

0.73

1.38

0.61

*

1.5;

0.80

0.96

*

1.9;

2.35

2.1:

4.25

->

2.9;

1.40

1.09

Girls

12-17

years -

12 years --

13 years --

14 years --

15 ymms --

16 years --

17 years --

0.50

0.50

0.59

0.76

0.48

0.81

7.72

:V

*

>!

L.37

L.17

3.45

*

0.56

1.43

1.60

L1.62

*

$C

1.87

0.53

1.10

3.79

U3.30

1.70

5.21

*

*

*

*

29,

1.2;

0.68

1.62

3.78

*

1.1;

0.62

1.52

1.9i

0.95

*

*

2.50 4.2;

.*

*

2.02

1.76
Table IV. Standard errors of mean arithmetic scores on the Wide Range Achievement Test for youths, by sex,

age, and educational level: United States, 1966-70

I 11 More

than

high

]chool

:duca -

tion

Left

high

~chool

oefore

3radus.ting

;pecial

jlace -

ment

0.50

0.45

1.16

1.86

*

*

*

0.63

Sex and All

age levels

t--

4 and

below

Grade in school

+

High

school

gradu12 ate

t

0.29 1.33

8 9

0.28 0.29

5 6

0.55

7

+

10 11

0.32 0,27

Both

=s

12-17

- lJL

years - 0.26 1.48 0,76

~

0.71

2.21

*

9r

>’r

0.64

3.14

7.34

*

1.29

0,34 1.10

-

1,1;

2.41

0,44

*

0.9:

0,52

0.91

*

0.5:

0.39

*

1,3:

12 years --- 0.23 2.17

13 years --- 0.29 *

14 yeara --- 0.35 *

15 years --- 0.33 *

16 years --- 0,31 *

17 years --- 0.36 -

0.52

1.04

1.36

*

0.60

0.57

1.30

1.84

*

0.58

0.25

0.87

0.46

1.77

*

*

0.40

0.31

1.07

0.55

1.64

*

*

0.34

0.61

0.23 0.4;

p: 0.33

0.68

1:45 0,86

* 1,62

0,36 0.27

0.61

0.35 0.6;

0.88 0.43

1,14 0.55

* 1.10

* *

0.33 0.41

0.96

0.29 0.4;

0.70 0.43

2.71 1.01

* 1.44

*

L

0.6;

0.30 0,7:

*

0.73 0.30

0,71 0.51

0.40 0.27

Boys

12-17

‘1

years- 0.27

12 years --- 0.30

13 yeara --- 0.38

14 years --- 0.42

15 years --- 0.32

16 years --- 0.39

17 years --- 0.44

1.84 0.45 1.57

3.14

*

*

*

0.79

1,52

*

*

*

*

0,90

1.0: :

0.37 1.02

0.76 0.36

1.06 0.67

*

*

2.5;

1.61

*

1.1:

0.80

0.52

1.07

0.56

12-17

K

years- 0.27 2.22

12 years --- 0.23 3.07

13 years --- 0.32 *

14 years --- 0.39 *

15 years --- 0.42 -

16 years --- 0.32 *

17 years --- 0.46 - T_0.32 0.47

7.7;

0.92 10.7;

0.32 0.87

0.89 0.52

* 0.85

0.40 1.46

1.47

5.52

*

*

0.61

0.81

*

*

0.31

;.;;

6:70

*

*

1.00

3.01

*

*

*

*

*

1.5:

*

1.5;

-

*

1.2;

1.02

0.79

0,46

for the calculation of variances, and (3) thousands of 68-percent confidence and the rangewithin twostandard

statistics are derived from the survey, many for subclasses of the population for which the number of sam -

ple cases is small. Estimates of sampling error are

obtained from the sample data andare themselves subject to sampling error, which may be large when the

number of cases in a cell is small or occasionally even

when the number of cases is substantial.

Estimates of approximate sampling variability for

selected statistics used in this report are included in the

detailed tables and in tables HIand IV. These estimates,

called standard errors, have been prepared bya replication technique which yields overall variability through

observation of variability among random subsamplesof

the total sample. The method reflects both’’pure’’sampling variance and apart of themeasurement variance,

and is described in previously published reports.l’; ,17

Hypothesis Testing

In accordance with usual practice, the interval estimate for any statistic was considered to be the range

within one standard error of thetabulated statistic with

30

errors of the tabulated statistic with 95-percent confidence. The latter is used as the level of statistical

significance in this report.

An approximation of the standard error of a difference d = x - y of two statistics x and y is given by the

formula sd = (,s~ + s:)% where SXand S, are the sampling

errors, respectively, of x and y . Of course, where the

two groups or measures are positively or negatively

correlated, this formula will give an overestimate or

underestimate of the actual standard error.

Thus the procedure used in this report for testing

the significance of difference between means consisted

of dividing the difference between the two means by the

standard error of the difference as computed above,. If

the magnitude of t was greater than 2.00, the difference

was considered statistically significant at approximately the 5-percent confidence level. For example, the

mean reading raw score for 12-year-old boys was 41,1,

while the mean for 12-year-old girls was 43.1 —a

difference of 2.0. The approximate standard error of

the difference between means was .75. Since the dif-
ferencc between the means was 2.7 times the standard standard error may exceed .25, a generally accepted

error, the difference was considered significant beyond standard for NCHS publications. Such statistics are

the S-percent confidence level. included in this report along with their corresponding

standard errors in the belief that theinformation, while

Small Categories not meeting strict standards of precision, may lend an

In some tables averages are shown for cells for overall impression of the survey findings andmaybe of

which the sample size is so small that the relative interest to subject matter specialists.

000

31
APPENDIX Ill

INSTRUCTIONS FOR ADMINISTRATION OF THE WIDE RANGE ACHIEVEMENT TEST

FOR THE HEALTH EXAMINATION SURVEY, CYCLE Ill

WIDE RANGE ACHIEVEMENT TEST

ARITHMETIC INSTRUCTIONS

LOOK AT EACH PROBLEM CAREFULLY TO SEE WHAT YOU ARE SUPPOSED

TO Ml -ADO, SUBTRACT, MULTIPLY OR DIVIDE. YOU MAY DO YOUR

FIGURING IN THIS SPACE (point), BUT BE SURE TO PUT YOUR ANSWERS

ON OR BELOW THE LINES (point). SKIP ANY PROBLEMS THAT ARE TOO

HARD FOR YOU. YOU HAVE TEN MINUTES. BEGIN NOW. ‘

If the S is unable to correctly solve at least any five problems, administer the oral

parts according to the instructions outlined below.

COUNTING: With the page turned so that the &ts are closest to the S, point.to the

&ts and say:

POINT WITH YOUR FINGER AND COUNT THESE DOTS ONE BY ONE

BEGINNING HERE (Examiner’s right). COUNT THEM OUT LOUD AND

TELL ME HOW MANY THERE ARE.

Occasionally a S will read the numbers below and begin counting the dots. To

avoid confusion, cover the digits (3, 5, etc.) while the S counts the dots.

READING: Point to the numbers (right side up to the S) and soy:

READ THESE NUMBERS. WHAT IS THIS? (pOinting * the 3) AND THIS? etc.

SOLVING:

IF YOU HAVE THREE PENNIES ANO SPEND ONE OF THEM, HOW MANY

HAVE YOU LEFT?

HOW MANY ARE THREE APPLES AND FOUR APPLES?

JACK HAD NINE MARBLES. HE LOST THREE OF THEM. HOW MANY

WERE LEFT?

Scoring:

Oral port -CO.nts l-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l point

Counts 6-15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l point

Reads 5numbers, lpointeoch . . . . . . . . . . . . . 5 points

Solves 3problems, l point each.. . . . . . . . . . . . . . . 3 points

Written part - Score 1 point for ●ach correct answer, use the scoring Key-Level 11,

as the guide. In order for an answer to be correct it must match

this key.

WRAT - READING

LOOK AT EACH WORD CAREFULLY AND SAY [T ALOUD. BEGIN HERE

(point) AND READ THE WORDS ACROSS THE PAGE SD I CAN HEAR YOU

WHEN YOU FINISH THE FIRST LINE, GO ON TO THE NEXT.

If the Su~ect obtains a score of 10 points or less in the regular reading part, he

should be asked to name the 13 capital letters printed above the word list and

to name 2 letters in his name. Each letter is equal to one point.

READ THESE LETTERS ALOUD, WHAT IS THIS? (or) WHAT DO YOU CALL

THIS?

The examiner controls speed of reading by saying NEXT, or GO ON TO THE

NEXT WORD at the end of 10 second time limit.

32

Testing limits: 12 consecutive failures.

* U. 8. GOV33~ PR7NTJNG OFFICE :1974 543-8 Bl/48
VITAL AND HEALTH STATISTICS PUBLICATION SERIES

Originally Riblic Halth Service I%blication No. 1000

I

I

.1

‘1

Series 1.

Series 2.

Series 3.

Series 4.

Series 10.

Series 11.

Series 12.

Sm”es 13.

Series 14.

Serzes 20.

Series 21.

Sm’es 22.

*

Programs and collection #rocedures. —Reports which describe the general programs of the National

Center for Health Statistics and its offices and divisions, data collection methods used, definitions,

and other material necessary for understanding the data.

Dab evaluation and methods research. —Studfes of new statistical methodology including: experimental tests of new survey methods, studies of vital statistics collection methods, new analytical

techniques, 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 the expository types of reports in the other series.

Documents and committee reports. —Final reports of major committees concerned with vitaI and

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

birth and death certificates.

Dati porn the Health Interview Survev.— Statistics on illness, accidental injuries, disability, use

of hospital, medical, dental, and other services, and other health-related topics, based on data

collected in a continuing national household interview survey.

Data from the Health Examination Survey. —Data from direct examination, testing, and measurement of national samples of the civilian, noninstitutional population provide the basis for two types

of reports: (1) estimates of the medically defined prevalence of specific diseases in the United

States and the distributions of the population with respect to physical, physiological, and psychological characteristics; and (2) analysis of relationships among the various measurements without

reference to an explicit finite universe of persons.

Data from the Institutional Population Surveys —Statistics relating to the health characteristics of

persons in institutions, and their medical, nursing, and personal care received, based on national

samples of establishments providing these services and samples of the residents or patients.

Data from the Hospital Discharge Survey. —Statistics relating to discharged patients in short-stay

hospitals, based on a sample of patient records in a national sample of hospitals.

Da&a on health resources: manpower and facilities. —Statistics on the numbers, geographic distribution, and characteristics of health resources including physicians, dentists, nurses, other health

occupations, hospitals, nursing homes, and outpatient facilities.

Data on mortality. —Various statistics on mortali~ other than as included in regular annual or

monthly reports— special analyses by cause of death, age, and other demographic variables, also

geographic and time series analyses.

Data on natality, mawiage, and divorce. —Various statistics on natality, marriage, and divorce

other than as included in regular annual or monthly reprts+pecial analyses by demographic

variables, also geographic and time series analyses, studies of fertility.

Data from the National Nakdity and Mortality Surveys.— Statistics on characteristics of births

and deaths not available from the vital records, based on sample surveys stemmfng from these

records, including such topics as mortality by socioeconomic class, hospital experience in the

last year of life, medical care during pregnancy, health insurance coverage, etc.

For a list of titles of reports published in these series, write to: Office of Information

Nat ional Center for HeaIth Statistics

Public Health Service, HRA

Rockville, Md. 20852

/’”
U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE

PUBLIC HEALTH SERVICE

Health Resources Administration

5600 Fishers Lane POSTAGE AND FEES PAID

Rockvillc, Maryland 20852 U.S. DEPARTMENT OF HEW

OFFICIAL BUSINESS HEW 390

Penalty for Private Use $300

*

US.MNL

THIRD CLASS

BLK. RT.