NBSIR 73-156

A Study of the Strength Capabilities

of Children Ages Two Through Six

W. C. Brown

C. J. Buchanan

Consumer Product Systems Section

Measurement Engineering Division

Institute for Appiied Technology

and

J. Mandel

institute for Materials Research

August 7, 1973

This is a final Report

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

N BSIR 73-156

A STUDY OF THE STRENGTH CAPABILITIES

OF CHILDREN AGES TWO THROUGH SIX

W. C. Brown

C. J. Buchanan

Consumer Product Systems Section

Measurement Engineering Division

Institute for Applied Technology

and

J. Mandel

Institute for Materials Research

August 7, 1973

This is a final report

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Acknowledgements

We wish to acknowledge the valuable assistance rendered by

the following persons: Dr. Charles Fried, Behavioral Psychologist,

Technical Analysis Division, National Bureau of Standards; Dr. Robert

P. Klein and Dr. Frank A. Pedersen, Research Psychologists of the

Social and Behavioral Branch of the National Institute of Child Health

and Human Development; Miss Mary Nan Steel, Statistician, Institute

for Materials Research, National Bureau of Standards; Mr. Samuel D.

Toner, Chemist, Measurement Engineering Division, National Bureau of

Standards; and Dr. William W. Williams, Educational Psychologist,

Montgomery County Public Schools, Rockville, Maryland.

We wish to express our appreciation for the time and cooperation

afforded us by the following child institutes and to the many children

who so willingly participated in this study.

Adelphi Day Care Center Montrose Christian Center

Boyds Day Care Center Potomac Montessori School

Catholic Charities Model City Rockville Day Care Center

Day Care Center

Diamond Farms Day Care Center Sligo Day Nursery

Gaithersburg Day Care Center St. Joseph's Day Care Center

Greenwood Elementary Summit Hall Elementary

Londonderry Day Care Center Tumble Inn

Merriland Day Care Center Viers Mill Day Care Center

Montgomery Village Day Care Center

Introduction

"The little boy and his sister were playing with a metal

doll house. After several minutes, they began to fight over

it, each of them tugging at its sides. Suddenly the clamps

holding the structure opened and the doll house flew apart.

One piece struck the boy in his face, slashing him from ear to

mouth .

This incident, reported by Marlene Cimons in the

October 23, 1972, issue of the Los Angeles Times News Service,

is an example of the danger of children pushing, twisting, or

pulling apart toys that may not be hazardous initially but

that could be hazardous when broken. Incidents of this nature

have evoked the concern of Government officials as well as

parents across the nation for the safety of children when

playing with toys.

The Child Protection and Toy Safety Act of 1969 was

passed by Congress with the intention of eliminating hazards

associated with children's toys. However, in order to develop

reliable and realistic standards and test methods to deal with

this problem, one must first know, among many other characteristics, the strength capability of children. For this reason,

a study was conducted by the Product Evaluation Technology

Division, National Bureau of Standards, to gain some information

in this area.

The main objective of the child strength study was to

determine what the forces are that children 2 through 6 years
:
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old* are capable of exerting when pulling, pushing, twisting,

and squeezing. This study was conducted with 556 children in

the Washington Metropolitan area. A minimum of 50 males and

50 females in each of the 2 through 6 year old age groups

was tested. Each age group consisted of a miminum sample of

20% black children, and included children from widely varying

economic backgrounds. The children participating in the study

attended rural, suburban, and inner-city schools which were

selected at random from various child institutes in the

Washington-Metropolitan area.

Four test devices were used to conduct the child strength

study. Three of these devices, a push-pull tester and two twist

testers, were developed and constructed at the National Bureau

of Standards. A fourth device, which was used to measure

squeeze forces, was purchased commercially.

Prior to beginning the child strength study, consultations

were held with psychologists from the staff of the National

Institute of Child Health and Human Development, National

Institutes of Health, and the Technical Analysis Division,

National Bureau of Standards. The information obtained during

these discussions was instrumental in designing the test

procedures used in this study.

*The age groups tested are designated as:

2 year old - 24 months old through 35 months old

3 year old - 36 months old through 47 months old

4 year old - 48 months old through 59 months old

5 year old - 60 months old through 71 months old

6 year old - 72 months old through 83 months old

Summary and Conclusions

The present study was designed to provide objective

information that can serve as a basis for developing standards

and test methods for children's toys.

The study involved children 2 through 6 years old of

both sexes (at least 50 in each age and sex group) and four

specially constructed test instruments that could be operated

in a variety of configurations and modes, giving rise to

19 "tests."

The results of the study are exhibited in tables of:

a) The average strength values for each age and sex

group, for each test;

b) Measures of variability in strength among children

of the same group;

c) 95th percentiles for each of these groups.

A number of graphs are also included for a quick appraisal

of the results.

Contrary to what might be expected in a study involving

many uncontrollable variables, the results provided quantitatively precise and useful information on several points, the

most important of which are the following:

1. Quantitative measures were obtained for the effect

of age on the strength capability of children from

2 through 6 years old. An approximately linear

increase with age was observed for the strength of
i

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either sex, the rate of increase being higher for

boys than for girls in all tests. The rate of

increase was found to be a function of the particular

test

.

2. Very high correlations (0.95 or better) were found

among all 19 tests.

3. Several of the tests gave almost identical results;

thus

a) The top twist tester and the front twist tester,

when used with the same knob size, gave very

similar results.

b) The push-pull tester gave almost identical results

whether used with the knob or with the rubber

sleeve

.

4. The size of the knob, in the front and top twisters,

was found to have an appreciable effect on the

strength measurement, the latter increasing as the

diameter of the knob increases.

5. In the squeeze test, the use of two hands markedly

increased, but did not quite double, the measured

strength of one hand.

All of these conclusions, and others of a more quantitative

nature, can readily be derived from two empirical equations,

one for the average strength, and the other for the 95th

percentiles, that were developed from the data. The equations

fit the data within experimental error.
I

••••••
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A secondary result of the study is the observation that

the differences in strength between white and black children

showed no consistent patterns in the age range tested.

The similarities in the results found for several tests

indicate that the number of tests to be used in future

studies may be appreciably reduced. The observation that,

in a few cases, the strength of some of the older children

exceeded the range of the instrument should lead to an

extension of this range in future studies.

-6-

Instrumentation Description

Push-Pull Tester

The push-pull tester, Figures 1, 2, and 3, was designed

to measure the force that children, in each of the ages two

through six years old, are capable of exerting when pushing

and pulling. This instrument utilizes a rotary variable

differential transformer and a set of compression springs

to produce a voltage output proportional to the amount of

force exerted on a pivotal vertical lever. A spherical knob,

cylindrical rubber sleeve, or a two and one-half foot chain can

be attached to the lever to measure forces exerted during different modes of manipulation. A series of colored lights, located

on a panel behind the vertical lever, was used as a motivational

tool to er.tice the child being tested to exert maximum effort.

These lights illuminate sequentially as the amount of force

being exerted on the lever is increased. The output from the

push-pull tester can be recorded on a strip chart recorder for

later reduction and analysis.

The strength ranges of the youngest and oldest children

in the two through six year old age groups varied appreciably,

based on the results of preliminary child performance tests.

These results also indicated that the ranges for the push and

pull directions accommodated both extremes of the forces exerted

by the children involved in the child strength study. A major

consideration in the selection of these ranges was the ability

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of a two year old child to light a sufficient number of lights

at the lower end of the force ranges to cause him to be

adequately motivated to perform to his maximum capability.

The measurement limits of the push-pull tester were fifty-five

pounds (244.6 newtons) in the push direction and sixty-six

and a half pounds (295.8 newtons) in the pull direction.

Top and Front Twist Testers

The top and front twist testers, Figures 4 and 5, were

designed to measure the amount of torque that children are

capable of exerting when twisting metal knobs of various sizes

in both a horizontal and vertical configuration. The detachable

knobs selected for use in the twist tests are one, one and a

half, and two inches in diameter, with grooved edges to

facilitate a better grip. These knobs are attached to a round,

slotted shaft. A flexible steel spring is inserted through

the slot in the shaft and securely anchored. When the knob

is rotated, the shaft rotation is approximately proportional

to the rotation of the knob. A rotary potentiometer, which

is attached to the opposite end of the shaft, provides an

electrical output which is directly proportional to the amount

of torque exerted on the knobs being twisted. This signal is

recorded on a strip chart recorder and then converted to

inch-pounds

.

-8-

In similar fashion to the push-pull tester, a series of

sequentially illuminating lights is used to aid in motivating

the child to twist as hard as possible.

Hand Dynamometer

A hand dynamometer, Figure 6, was purchased commercially

and used to obtain data on the squeeze forces that children,

ages two through six years old, are capable of exerting.

This device consists essentially of a mainframe, an adjustable

stirrup-shaped handle attached to an extension spring, a

calibrated needle and dial, and a clutch to hold the adjustable

handle in place. A rotary potentiometer is attached to the

indicator, and when attached to a small power supply, provides

an electrical output proportional to the force being exerted

on the dynamometer handle.

Calibration

Prior to beginning the child strength study, the four

test devices were calibrated and curves were constructed to

facilitate data conversion. The calibration of these devices

was checked periodically to insure that the data obtained

remained as accurate as possible [reading error not to exceed

2 pounds (approximately 9 newtons) for any measurement]

throughout the duration of the tests.

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Test Procedure

The four test devices were placed on a table, approximately

20 inches from the floor, and the push-pull tester, front

twist tester, and top twist tester were securely fastened to

the table. The test devices were arranged in the same order

during each testing period, i.e., the hand dynamometer,

followed by the front twist tester, the top twist tester, and

the push-pull tester, respectively.

For ease in demonstrating the operation of the test

devices and conducting the tests, the two and three year old

children were tested in separate groups of three; and the four,

five, and six year old children were tested in groups of four.

Prior to commencing any of the tests, a brief demonstration was

given by the test instructor for each group of children. First,

the instructor demonstrated the operation of the hand dynamometer

by squeezing on the lever three times with each hand and then

squeezing three times with both hands while pointing out how

the indicator recorded the amount of force being exerted.

Next, the operation of the front and top twist testers were

demonstrated. The instructor placed one hand on the machine and

the other hand on the knob selected for demonstration. She

then twisted the knob three times in the counter clockwise

direction and three times in the clockwise direction. During

this period, the children were urged to observe the motivation

lights as they illuminated sequentially as the knobs were turned

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with an increasing amount of force. The children were reminded

that they could use only one hand at a time on the twist knobs.

The instructor demonstrated the operation of the push-pull

test device by placing one hand on the body of the device and

the other hand on the knob attached to the vertical lever.

She then pushed the knob forward three times and pulled the

knob back three times while calling the children's attention

to the sequentially illuminating motivation lights. The

children were told that they could use either one or both hands

when operating the push-pull device.

The children were usually so enthusiastic about playing

with the machines that there was relatively no problem with

respect to the fact that the instructor and child were not

familiar with one another. Referring to the child by name and

allowing a brief time for individual conversation helped to

develop a more personal relationship between child and instructor.

For those children who obviously did not understand the

mechanics of squeezing, twisting, pushing, and pulling, brief

games were played during the demonstration. Some examples of

the expressions used in the games are: (1) "Hold my two

fingers with one of your hands and squeeze or bring them

together;" (2) "Hold up one hand and pretend that you are

turning a circle in the air towards the window - now twist the

other way;" (3) "Place your hands against mine (fingers vertical)

and push them away from you;" and (4) "Hold my hand and pull

my body towards you."
.

-
The tests were conducted in three phases. A consideration

of the fatigue factor resulted in allowing children to complete

only one phase at a time. They rested approximately 10 minutes

between each phase. Phase one consisted of the one and two hand

squeeze test; twist tests on the front and top twist testers,

using the two inch diameter knob; and push and pull tests using

the round knob. Phase two consisted of twist tests on the

front and top twist testers, using the one and a half inch

diameter knobs; and push and pull tests with a rubber sleeve

over the vertical lever of the push-pull tester. The third

phase consisted of twist tests on the front and top twist

testers, with one inch diameter knobs; and pull tests with a

two and a half foot long chain attached to the lever of the

push-pull tester.

Each child was allowed a minimum of three trials in each

direction on any given test. The first trial was used by the

test instructor as a general indication of the amount of force

the child could be expected to exert for that particular test.

Through observation, the instructor could then sense the degree

of encouragement necessary to motivate the child to avoid frustrating him or making him feel a lack of adequate accomplishment.

The children were given signs of encouragement by the instructor

through gestures, facial and verbal expressions. In addition,

the colored lights located on the push-pull and twist test

devices were observed to be essential motivational tools.

-12-

Prior to conducting the squeeze tests, the size of each

child's hand was measured and the stirrup-shaped handle of the

hand dynamometer was adjusted (per manufacturer's instructions)

to yield the optimal squeeze force. This adjustment was approximately one-half the distance between the vertex of the angle

formed where the thumb joins the hand and the end of the child's

longest finger.

It was assumed that the child's hand of preference was

the hand with which the child was most likely to exert maximum

force. Since in most cases the identity of the hand of

preference was uncertain, the test instructor requested the

child to use the other hand at least once during each test.

Stricter controls on the test procedure were purposefully

omitted with regard to the performance of the tests previously

described. This allowed the children to use innovation,

intelligence, creativity, and ingenuity to achieve maximum

performance, thus approximating a more normal play condition.

A more rigidly controlled test procedure was attempted to

eliminate some of the variables inherent in tests of this

nature; however, this approach proved unsuccessful. Attempts

were made to record the methods used by the children to

manipulate the test devices during specific tests, such as one

hand, both hands, elbow leverage, and knees or feet. This

proved unsuccessful since the methods of manipulation changed

so rapidly that it was impossible to accurately annotate the

moving tape on the strip chart recorder. Attempts were also

-13-

made to restrict the child to one prescribed method of

performing a given test. This procedure also proved unsuccessful since the children insisted on using that method which

they felt would enable them to perform to their maximum

capability. An example of the different methods that one child

might use to manipulate a given test device during a specified

test is illustrated in Figure 7 of this report.

One could easily question whether or not weight and body

build iiave a direct correlation to a child's strength

performance. A search of the literature relating to child

strength revealed several interesting factors which were significant considerations in developing the test procedures used in

this study. Investigations by Jones (1947), and Smith and

Royce (1963), indicate that there is no sizable correlation

between an individual's strength performance and body weight.

Krogman and McCown (1971) concluded that there is no relation

between strength and the body build of children 3 through 6

years old. In addition, Ikai and Steinhaus (1961) found that,

"In every voluntarily executed, all-out maximal effort,

psychologic rather than physiologic factors determine the

limits of performance."

Test Results

A detailed statistical analysis of the data obtained

during the Child Strength Study is presented in the Appendix

of this report. In this section, some graphs and charts are

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presented, from which the major findings of this study can

readily be deduced.

In terms of the ultimate purpose of this study, the

distinction between top and front twist, as well as between

twisting in the clockwise and counterclockwise directions is

of secondary importance. So is the distinction between the

use of a knob or a rubber sleeve in the push and pull tests.

Therefore, the data were condensed in the following way. For

each child, the maximum value was selected for all twist tests

using a given knob size. Similarly, for each child the

maximum value was selected for both pull tests (excepting the

chain), and for both push tests. However, for the squeeze

test, both the two-hands and one-hand results were considered.

This reduced the number of "tests" to eight: twist for three

sizes of knobs, push, pull, chain-pull, and squeeze (one and

two hands). Figures 8 through 13 show the average results, as

well as the 5th and 95th percentiles*, for these eight tests

for each age and sex group. A quick appraisal of the data can

be made from Table 1 (reproduced in metric units in Table la)

,

which lists the 95th percentiles, averages, and 5th percentiles

for four tests from the condensed data for all age and sex

groups tested.

*For a definition of the 95th percentile, refer to the Appendix

(p. 18). The definition of the 5th percentile is determined

by interchanging the numbers 95 and 5 in that definition.

Estimates of these quantities were obtained, in this study,

by taking the third largest (95th percentile) and the third

smallest (5th percentile) value in each group.

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At the basis of this study was the belief that all tests

conducted were valid measures of the same basic characteristic,

namely, the physical strength capability of a child. The

correlation matrix presented in Table 5 of the Appendix can be

used to test this assumption. These results show that the

correlation between tests was quite high and support the

hypothesis that, to a considerable extent, all tests measure

the same basic characteristic.

As previously stated, each age and sex group consisted of

at least 20% black children. This mix afforded an opportunity

to study any difference that might exist between the strength

capability of black and white children. Table 2 summarizes

the information gained from analyzing the data acquired on

the strength performance of these two groups. It is seen

from the table that in spite of apparently significant differences between the two races for some age and sex groups, no

overall pattern emerges in regard to this point.

-16-

References

Cimons, Marlene. Los Angeles Times News Service , October 23

1972.

Ikai, Michio, and Steinhaus, A. H. : "Some Factors

Modifying the Expression of Human Strength," Journal of

Applied Physiology, 16 (1), 157-163 (1961).

Jones, H. E.: "The Relationship of Strength to Physique,"

American Journal of Physical Anthropology, 5_:29 (March 1947)

Krogman, W. M. : "The Manual and Oral Strengths of

American White and Negro Children, Ages 3-6 Years,"

Philadelphia Center for Research in Child Growth, p. 14

(Sept. 1, 1971).

Mandel, John: "A New Analysis of Variance Model for NonAdditive Data," Technometrics, 13_, 1-18 (1971).

Royce, J., and Smith, Leon: "Muscular Strength in Relation

to Body Composition, " Annals of the New York Academy of

Sciences, 10_:809 (Sept. 26, 1963).

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FIGURE 7. Motivation lights on the Push-Pull Tester encourage the test

suhject to apply maximum force. Note that various body positions

are assumed by the subject, resulting in varying degrees of

leverage.

Table 1. Condensed Force Values for Twist,

Push, Pull and Squeeze Tests

95th Percentiles

(years)

Twist (2

M knob) Push Lever Pull Lever Squeeze (2 hands)

Female Male Female Male Female Male Female Male

2 14.4 15.6 19.8 23.5 37.5 38.5 22.0 19.8

3 18.4 19.5 29.5 28.0 39.5 43.0 26.4 25.3

4 26.2 24.8 45.3 56.7* 58.0 60.5 34.1 37.4

5 30.0 30.5 52.8 60.5* 60.5 63.5 44.0 48.4

6 31.6 32.2 57.7* 63.1* 63.5 66.5 46.2 52.8

Averages

(years)

Twist (2" knob) Push Lever Pull Lever Squeeze (2 hands)

Female Male Female Male Female Male Female Male

2 9.1 10.1 10.9 13.9 20.2 23.1 12.8 13.8

3 12.6 13.2 16.7 18.2 27.2 27.4 15.8 16.9

4 17.2 18.7 26.4 32.5 36.0 40.4 24.1 26.6

5 26.4 22.4 34.3 39.5 45.8 49.4 31.8 32.8

6 23.2 25.8 39.3 46.9 50.3 56.3 35.0 40.3

5th Percentiles

Twist (2" knob) Push Lever Pull Lever Squeeze (2 hands)

Age (years) Female Male Female Male Female Male Female Male

2 5.5 6.0 6.8 6.8 12.0 9.0 . 4.4 6.6

3 7.5 7.5 4.0 10.5 17.5 12.5 6.6 8.8

4 10.8 13.0 12.5 16.0 19.0 24.0 13.2 14.3

5 13.6 15.5 21.3 20.5 24.0 28.0 19.8 18.7

6 17.6 19.2 25.0 29.5 32.5 38.5 20.9 26.4

Note: 1. Values in this table are based on a minimum of 50 children in each

age and sex group.

2. Push, pull and squeeze values are expressed in pounds; twist values

are expressed in inch pounds.

*Estimated values computed by adding 2 standard deviations to the average

value

Table la. Condensed Force Values for Twist,

Push, Pull and Squeeze Tests

95th Percentiles

Twist (2" knob) Push Lever Pull Lever Squeeze (2 hands)

Age (years) Female Male Female Male Female Male Female Male

2 1.62 1.76 88 105 167 171 98 88

3 2.08 2.20 131 125 176 191 117 113

4 2.96 2.80 202 252* 258 269 152 166

5 3.39 3.44 235 269* 269 282 196 215

6 3.57 3.63 357''' 281* 282 296 206 235

Averages

Twist (2" knob) Push Lever Pull Lever Squeeze (2 hands)

Age (years) Female Male Female Male Female Male Female Male

2 1.03 1.14 49 62 90 103 57 61

3 1.42 1.49 74 81 121 122 70 75

4 1.94 2.11 117 145 160 180 107 118

5 2.98 2.53 153 176 204 220 141 146

6 2.62 2.91 175 209 224 250 156 179

5th Percentiles

Twist (2" knob)

Age (years) Female Male

2 .62 .68

3 .85 .85

4 1.22 1.47

5 1.54 1.75

6 1.99 2.17

Push Lever Pull

Female Male Female

30 30 53

118 47 78

56 71 85

95 91 107

11 131 145

Lever Squeeze (2 hands)

Male Female Male

40 20 29

56 29 39

107 59 64

126 88 83

171 93 117

Note: 1. Values in this table are based on a minimum of 50 children in each

age and sex group.

2. Push, pull and squeeze values are expressed in newtons, rounded off to

the nearest newton; twist values are expressed in newton meters, rounded

off to the nearest .01 newton meter.

^Estimated values computed by adding 2 standard deviations to the average value.

Table 2. Effect of Race*

Number of tests for which

kge Sex white is stronger black is i

2 F 1 18

M 3 16

3 F 9 10

M 18 1

4 F 14 5

M 16 3

5 J. ?£m 17

M 4 15

6 F 18 1

M 9 10

Total 94 96

*Based on averages of 50 children in each age and sex group, of which at least 20% are black children.

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APPENDIX

Statistical Analysis of Data

Scope

In the preceeding sections, the main results of this

study have been presented partly in graphic and partly in

tabular form. To facilitate the drawing of practical

conclusions, the data were "condensed," in the sense that

for each child, only the maximum strength of several similar

tests was considered. The present section covers the data

in much greater detail. First, the results of all nineteen

tests are examined, rather than just the condensed data.

Secondly, measures of variability (standard deviation and

coefficients of variation) among children of any given age and

sex group are given for all tests. Thirdly, histograms are

presented for a selected number of tests, and finally, a

detailed analysis is presented of the interrelationships among

the results for all nineteen tests, as well as among the

results for the ten age and sex groups. This analysis led to

two empirical equations which provide very useful summaries

of the entire set of data obtained in this study. The

statistical analysis outlined in the four points above will

also help in establishing the overall validity of our study.

-18-

Basic Results

The results of all tests conducted are presented in

Tables 1 through 4, in the form of two-way tables 1 of 19 rows,

representing the nineteen tests, and ten columns, representing

the 10 age and sex combinations. Table 1 contains the averages

of each age and sex group for each test. Table 2 contains the

standard deviation measuring the variability among children

within each such group. In Table 3 these standard deviations

have been converted to coefficients of variation. Finally,

Table 4 lists the 95th percentiles for all groups. This is a

value such that 95 percent of the entire population of

children in a particular age and sex group, when measured by

a particular test, will have a strength capability less than

or equal to this value. In other words, 5 percent of the

entire population of children in each group will exceed the

95th percentile of that group. Since all groups consisted of

from fifty to sixty children, an acceptable estimate of the

95th percentile is obtained by taking the third largest result

in each group. This procedure, which has the advantage of

being non-parametric (independent of the nature of the

frequency distribution), was used in the present case.

A comparison of Tables 2 and 3 shows that the coefficients

of variation vary over an appreciably smaller range than the

''"More significant figures are given in the tables than are warranted by the precision of the data. This is done to allow

the reader to further examine the data, if he so wishes,

without being handicapped by rounding errors.

-19-

standard deviations. In fact, the coefficients of variation

for the various tests, when averaged over all ten age and sex

groups, vary by a ratio of less than two to one. The value

%CV = 30% is a reasonably good approximation for all cases,

with the exception of the two year olds (for which it is

higher) and the six year olds for some of the tests (for which

it is lower)

.

It should be remembered that these coefficients of

variation are measures of the relative variability among the

results for children in the same age and sex group when

performing the same test.

Histograms

Figures 1 through 5 present histograms for five selected

tests, for all five age groups. The results for both sexes

are combined in each histogram. The figures are presented

mainly for information; no attempt was made to fit any particular statistical distribution curve to the data. For purposes

of uniformity of presentation, the same class interval, of

two pounds, was used in all cases, in spite of the fact that

in some cases this led to too many intervals. The interested

reader can, of course, derive histograms with fewer class

intervals from these figures.

Interrelationships Among The Data

A glance at Tables 1 and 4 shows that the group averages,

as well as the 95th percentiles, are not just a random assembly

-20-

of results. In each of these tables, definite patterns are

present, resulting from the interrelationships among the

various tests. The existence of these relationships is not

unexpected, since the nineteen tests all measure, in various

ways, the same basic characteristic, namely, the physical

strength capability of the children tested.

A first appraisal of the relation among tests is obtained

by calculating the correlation coefficient between any pair of

tests. There are 171 such pairs. Rather than compute the correlations for the individual results obtained for each child,

they were computed over the ten age and sex groups . Thus , each

of the 171 correlations was calculated for 10 "points," i.e.,

10 pairs of values. The correlations are listed in the correlation matrix shown in Table 5. All correlation coefficients

exceeded 0.95, and 106 of the 171 pairs had a correlation

coefficient of 0.99 or higher. These results support the

hypothesis that to a very considerable extent all 19 tests

measure the same basic characteristic. Nevertheless, some of

the tests may be superior to others in ability to detect smaller

differences in strength capability. The sensitivity of a test

is directly proportional to its rate of change (slope) with

increasing strength and inversely proportional to its

experimental scatter. Applying this criterion to the 19 tests,

it appeared that all four push and pull tests (knob and rubber

sleeve) showed high sensitivity, whereas the top and front

twisters were not consistently high in sensitivity. This

-21-

would indicate a slight superiority for the push and pull

tests, but it must be understood that the sensitivity of any

of the other tests is not appreciably different from that of

these four tests.

Empirical Equations

Let A represent age, S sex, and T test (instrument,

configuration, and mode of use); and let Y represent the test

result for a particular child. Then, Y is a mathematical

function of the form:

Y = f(A,S,T) + e (1)

The quantity e is a random fluctuation measuring the

amount by which the strength of a particular child differs

from the average of all children in his age and sex group.

Similarly, if Z represents the 95th percentile for any

particular age, sex, and test combination, it is expected

that a relation exists of the form:

Z = <KA,S,T) (2)

We now wish to find explicit expressions for the

functions f and The function f(A,S,T), occurring in

equation (1) is to be derived from the averages Y; and the

function <j>(A,S,T) shown in equation (2) is to be derived from

the 95th percentiles.*

*The values in Table 4 are subject to the following shortcoming:

in a given age and sex group, the third largest value for any

two tests may or may not be associated with the same child. In

fact, such associations do occur in the table. This would

create difficulties if the values were to be the basis for tests

of significance because of correlations between the data.

However, for our purpose, which is one of estimation rather than

hypothesis testing, these correlations are of no importance.
-
The empirical derivation of these functions followed the

procedure described in reference (5)

.

Empirical Equations for Group Averages

It was found that the function f(A,S,T) (see equation 1)

could be satisfactorily approximated by the following expression

f(A,S,T) = Y

0

+ P (AfS)

• Q (T) (3)

where YQ is a constant, g-j is a quantity that depends

only on age and sex, and Q(t) i- s a quantity that depends

only on the "test" (instrument, configuration, and mode of use).

The value of P is in all cases larger for the males than for

the females. The value of Y

Q

= 0.52, and the values for

^(A S) anc^ ^(T) are shown in Table 6. The values of P^ g-j

are also shown in graphical form in Figure 6, as a function

of age, using different symbols for the two sexes. The degree

to which equation (3) fits the experimental data was examined

in terms of the variability among children of the same age

and sex group, and was found to be consistent with this

variability.

The values of Q(t) are a ls° instructive, showing the

effect of the size of the knob and of direction (counterclockwise vs. clockwise) in the front and top twisters, the

similarity between the results obtained by these two instruments and the almost identical results obtained for "knob" and

"rubber sleeve" in the push and pull tests.

By inserting in equation (3) the value Y

Q

= 0.52, and

the appropriate values of P and Q, it is possible to predict

the average result for any combination of age (2 through 6)

,

sex, and "test."

Empirical Equation for 95th Percentiles

Similarly to the results for averages, it was found that

the 95th percentiles could also be represented by a simple

empirical function:

<HA,S,T) = Z Q

+ P[A)S) • QjT) (4)

i i i where Z 0

= -0.92, and the values of P and Q are shown in

Table 7.

Observations similar to those made for the averages can

be made on the basis of the results shown in Table 7 and

0 illustrated in Figure 6.

Key for Tables 1-5

mmTT Top twist tester

Oil FT Front twist tester

PSH Push

PUL Pull

/~, x_i Ln Lnam

K Knob

K Rubber Sleeve

SQZ1 Squeeze, one hand

SQZ2 Squeeze, two hands

LL T /* A M "\ 1 . 1 1 _ C i J • i * Large (2") knob, left direction

LR Large (2") knob, right direction

ML Medium (1 1/2") knob, left direction

MR \ K J * /* 1 1 / ^ t 1 "\ 1 1_ • 1 . 1* | * Medium (1 1/2") knob, right direction

SL Small (1") knob, left direction

SR Small (1") knob, right direction

F Female

M Male

Note: In the tables and graphs presented in the Appendix,

push, pull, and squeeze values have been expressed in

pounds-force, and torque values have been expressed

in inch-pounds. To convert these values to newtons

and newton meters, multiply the values expressed in

pounds-force by 4.448 and the values expressed in

inch-pounds by .1129.

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TABLE 6

Empirical Fit for Averages of Group

Y = 0.52 + P (A,S) • Q(T)

1. Values of P (A,S)

Sex Age 2 Age 3 Age 4 Age 5 Age 6

F .456 .661 .972 1.232 1.381

M .543 .697 1.081 1.363 1.620

2. Values of Q(T )

Top Twister Front Twister

Counterclockwise

Small

6.31

Medium

10.72

Large

13.30

Small Medium Large

8.33 10.86 12.52

Clockwise 8 .04 11 .63 14 . 82 9.69 12.39 15.02

Knob Rubber Sleeve Chain

Push 25.11 25 .35

Pull 34.10 34 .88 30.46

Squeeze

1 hand 14. 24

2 hands 24. 46

TABLE 7

Empirical Fit for 95th Percentiles of Groups

Z = -0.92 + P(AjS )

* Q(T)

1. Values of P (A,S)

Sex Age 2 Age 3 Age 4 Aire 5 A*;e 6

F .584 .754 1 .041 1. 185 1.,280

M .636 .772 1.118 1. 263 1

,

,376

2. Values of Q(T)

Counterclockwise

Clockwise

Top Twister

Small Medium Large

12.97 18.77 21.43

14.73 19.44 22.82

Front Twister

Small Medium Large

15 . 14

16.01

18.23 20.49

21.15 24.16

Push

Pull

Knob Rubber Sleeve

41.73 40.75

52.35 52.52

Chain

46.48

1 hand

2 hands

Squeeze

23.91

36.56

NEWTONS

44.48 133.40 222.40 311.36

J I

I I L

T

10 30 50

SQUEEZE -2HANDS (LBF)

FIGURE I. FREQUENCY DISTRIBUTION OF CHILDREN'S STRENGTH

FOR SELECTED TESTS.

2 YEAR OLD GROUP

(INCLUDES BOTH FEMALE AND

MALE CHILDREN)

NEWTONS

44.48 133.40 222.40 311.36 J I

I I L

10 30 50

RUBBER PULL, (LBF)

NEWTONS

44.48 133.40 222.40

J I I I I L

CHAIN PULL, (LBF)

44.48 133.40 J I L 222.40 311.36

J I L

NEWTON METERS

44.48 133.40 222.40 31 J. 36

J I I I I L

RUBBER PUSH, (LBF) FRONT TWIST, (LBF- IN)

NOTE*. A VALUE OCCURRING AT THE END OF A FORCE INTERVAL IS COUNTED IN THE NEXT HIGHER INTERVAL-

40 -+

ec3 30 - I

o

u. 20 H o

ac. £ 10 z

3

44.48

i i

NEWTONS

133.40 222.40 311.36

I I l I

4 _o_ 0 10 30 50

SQUEEZE -2 HANDS, (LBS)

70

FIGURE 2. FREQUENCY DISTRIBUTION OF CHILDREN'S STRENGTH

FOR SELECTED TESTS.

3 YEAR OLD GROUP

(INCLUDES BOTH FEMALE AND

MALE CHILDREN)

NEWTONS

44.48 133.40 222.40 311.36 J I I I I L

0 10 30 50 70

RUBBER PULL, (LBS)

NEWTONS

44.48 133.40 222.40 311.36 J I I I L

0 10 30

CHAIN PULL, (LBS)

NEWTONS

44.48 133.40 222.40 311.36

-1 1 1 L

i r 0 10 30 50

RUBBER PUSH, (LBS)

40

<r3 30 x

<j

u. 20 o

Km 10

2

NEWTON METERS

44.48 133-40 222.40 311-36

i i

i

i i i r

2in KNOB, CLOCKWISE

l

1 r~

10 30 50

FRONT TWIST, (IN-LBS)

70

NOTE'. A VALUE OCCURRING AT THE END OF A FORCE INTERVAL IS COUNTED IN THE NEXT HIGHER INTERVAL.

NEWTONS

44.48 133.40 222.40 311.36 J I I L

10 30 30

SQUEEZE -2 HANDS (LBS)

FIGURE 3. FREQUENCY DISTRIBUTION OF CHILDREN'S STRENGTH

FOR SELECTED TESTS.

4 YEAR OLD GROUP

(INCLUDES BOTH FEMALE AND

MALE CHILDREN)

40 zU

at3 3 - xu

^ 20 H o

ce£ 10

CD2

NEWTONS

44.48 133.40 222.40

1 1 I I I L

311.36

0 10 30 50

RUBBER PULL, (LBS)

70

40

30 - x

u

u. 20-(

o

ce£ io H

23

NEWTONS

44.48 133.40 222-40 311.36

I I 1 1 1 1

10 30 50

CHAIN PULL , (LBS)

70

40

EC3 30-

Xo

u. 20 H o

ce& 10-

32 0

44.48 133.40 222.40 311.36

1 I I I I I

fTfVrjr^

0 10 30 50

RUBBER PUSH.(LBS)

70

44.48 133.40 222.40 311.36

40 -I 1 I I 1 1 L

3 30 H

u. 20 - o

a.£ io z

z 0

2 in KNOB, CLOCKWISE

1 OH T 1 10 30 50

FRONT TWIST.(IN-LBS)

70

* 4 CHILDREN EXCEEDED 55 lb. TESTER UMIT.

NOTE*. A VALUE OCCURRING AT THE END OF A FORCE INTERVAL IS COUNTED IN THE NEXT HIGHER INTERVAL.

NEWTONS

44.48 133.40 222.40 311.36

_1 I I I I L

T

10 30 50

SQUEEZE -2 HANDS, (LBS.)

70

FIGURE 4. FREQUENCY DISTRIBUTION OF CHILDREN'S STRENGTH

FOR SELECTED TESTS.

5 YEAR OLD GROUP

(INCLUDES BOTH FEMALE AND

MALE CHILDREN)

NEWTONS

44.48 133.40 222.40

J I I I L

311.36

0 10 30 50

RUBBER PULL , (LBS.)

NEWTONS

44.48 133.40 222,40 311.36 J 1 I I L

0 10 30 50

CHAIN PULL, (LBS.)

TO

40 z

u

IEq 30H

20-

xo

u.o

K

in io H CD2z 0

NEWTONS

44.48 133.40 222.40 311.36

J_ J L

T

10 30 50

RUBBER PUSH. (LBS.)

70

NEWTON METERS

44.48 133.40 2 22.40 311.36

40

30

20

Ui

ID I 0

1 1 1 1 1 1

2 in KNOB, CLOCKWISE

-fflu , ,

"

FRONT TWIST, (IN -LBS.)

^ 8 CHILDREN EXCEEDED 551b. TESTER LIMIT NOTE! A VALUE OCCURRING AT THE END OF A FORCE INTERVAL IS COUNTED IN THE NEXT HIGHER INTERVAL.

NEWTONS

44.48 133.40 222.40

i I i i l_ 311.36

10 SQUEEZE-2 HANDS (LBS)

FIGURE 5. FREQUENCY DISTRIBUTION OF CHILDREN'S STRENGTH

FOR SELECTED TESTS.

6 YEAR OLD GROUP

(INCLUDES BOTH FEMALE AND

MALE CHILDREN)

NEWTONS

44.48 133.40 222.40 311.36 J I 1 I L

0 10 30 50 70

RUBBER PULL, (LBS)

NEWTONS

44.48 133.40 222.40 311.36

J I I

1 I L

i r 0 10 30 50

CHAIN PULL, (LBS)

NEWTONS

44.48 133.40 222.40 311-36

10 30 50 70

RUBBER PUSH, (LBS)

40

5 30

X

<_> £ 20 o

ec

ui

«a 10 2

3

NEWTON METERS

44.48 133.40 222.40 311.36

I 1 1 1 1 I

2 in KNOB, CLOCKWISE

i r

0 10 30 50

FRONT TWIST, (IN-LBS)

70

* I CHILD EXCEEDED 55 lbs. TESTER LIMIT. ** 19 CHILDREN EXCEEDED 55 lb. TESTER LIMIT- NOTE 1

. A VALUE OCCURRING AT THE END OF A FORCE INTERVAL IS COUNTED IN THE NEXT HIGHER INTERVAL.

FIGURE 6. EFFECT OF AGE AND SEX

C/i <

Cl

1.6

1.2 -

.8 —

A — O

J L

AVERGES

• MALE

O FEMALE

1.6

1.21— O

to<

a

.8

A

95th PERCENTILES

J I

1 I I 4 5

AGE (YEARS)

NOTE! FOR MEANING OF PLOTTED VALUES,

EQUATIONS IN THE APPENDIX.

SEE EMPIRICAL

form NBS-114A d-71)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 73-1562. Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A Study of the Strength Capabilities of Children

Ages Two through Six

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S) 8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4460142

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

National Bureau of Standards

Department of Commerce

Washington, D.C. 20234

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The Child Strength Study was conducted to provide information which can

be used to develop reliable and realistic standards and test methods for

children's toys. The study was conducted on over 550 children in the

Washington Metropolitan area, and included both black and white children with

varying economic and social backgrounds.

Four test devices were used to measure the forces exerted by children

when pushing, pulling, twisting, and squeezing. Quantitative relationships were found to exist between these four types of measurements. The study also

provided quantitatively precise and useful information about the effects of

age and sex on the strength capability of children two through six years old.

The results of the study are exhibited in tables of averages, standard deviations, coefficients of variation, and 95th percentiles for each age and sex

group tested. A number of graphs are also included for a quick appraisal of

the test results.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Children; Children's Strength; Pull; Push; Safety; Strength; Squeeze; Test

Methods; Toys; Toy Safety; Twist

18. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Price

USCOMM-DC 66244-P71