A Study of Accuracy of Direction in Motor Skills at Different Distances as Determined by the Relative Size of the Angle of Error

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a r m m or accuracy oFPfRsdTicf ;i$ motor skills at DIFFERENT DISTANCES AS JJgTEHKXHSD' BY THE RELATIVE SIZE OF THE'AMLfe'-OF ERROR

by Donovan Clifford Moffett

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, in the Department of Physical Education, in the Graduate College of the State University of lo^a May, 1942

ProQuest N um ber: 10831775

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uest ProQuest 10831775 Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

7/5 11 /

The writer Is deeply indebted to Dr* 0. H. MeCloy for the dirsetion and supervision of this study.

Mis advice and helpful sug­

gestions during the progress and completion of the study are gratefully acknowledged.

Hi

CQBTESTS

Page

Chapter Statement of Problem.

1 t

II Kevi m of the Literature

4

I

Introduction . . . . . .

III Procedure. . * . . . . . Selection of Subjects Description of Testa Administration of the feats .Computation of the Angles of Error. IY Analysis of the Data . . . . ....... Method of Analysis. . Results of Analysis . Tabulation of Significant Differences V

Conclusions. . . . . . . . . . . . . . .

Suggestions for Further Study . . . . Bibliography ............

......

Appendix Figures fables of Original Bata . .

8 8

5 13 13 17 17 04 65 70 76 78 81 82 86

Iv nawm FIgap# 1

Page Target Used for Throwing a Baseball*. Throwing a Football, and Shooting an Arrow . , . . . * ,

82

2 Target Used for Striking a Tennis Ball with a Raequet Using a Forehand Drive. . .

83

3 Target Used for Throwing a Basketball with a One-Handed Push Shot and a TwoHanded Push Shot . . . . . . . . . . . . .

84

4 Illustration of the Effect of an Increase in the lumber of Hits on the Vertical and the Horizontal Axes upon the Means of the Angle of Error ......... 88

V tables

fable 1

2

Fag© Mean© of the Angle ©f Error (In Minutes) for throwing a Baseball at a target from Biff©rest Distances . . . * * * . • * * •

19

Differences between Means (in Minutes) of the total Angle of Error for throwinga Baseball at a target from Different Distancee

19

3 Differences between Means (in Minutes) of the Angle of Error to the Left of the Vertical Axis of the target for Throwing a Baseball from Different Distances ** . 4

5

20

Differences between Means (in Minutes) of the Angle of Error to the Eight of the Vertical Axis of the target for throwing a Baseball from Different Distances .. *

21

Differences between Means (in Minutes) of the Angle of Error above the Horizontal Axis of the Target for Throwing a Base** ball fro© different Distances.........

22

6 Differences between Means (in Minutes) of the Angle of Error below the Horizontal Axis of the Target for Throwing a Baseball from Different Distances * * , ♦ * . , .

23

7 Means ©f the Angle of Error (in Minutes) for Throwing a Football at a Target fro© Different Distances

24

8

Differences between Means (in Mimatee5of the Total Angle of Error for Throwing a Football at a Target fro© Different Distances . , ...................

24

9 Differences between Means (in Minutes) of the Angle of Error to the Left of the Vertical Axis of the Target for Throwing a Football from Different Distances *.* •

25

vi TABLES (Continued) fable

Page

1© Differences between Means (in Minutes) of the Angle of Error to the Right of the Vertical Axis of the Target for Throwing a Football from Different Distances . . . 11

26

Differences between Means (In Minutes) of the Angle of Error above the Horizontal Axis of the Target for Throwing a Foot­ ball from Different Distances

27

12 Differences between Means (in Minutes) of the Angle of Error below the Horizontal Axis of the Target for Throwing a Football from Different Distances . . . . . .

26

13 Means of the Angle of Error (in Minutes) for Throwing a Basketball with a TwoHanded Rush Shot at a Target from Differ­ ent Distances . . . . . . . ..........

29

14

Differencesbetween Means (in Minutes) of the Total Angle of Error for Throwing a Basketball with a Two-Handed Push Shot at a Target from Different Distances . »

29

15 Differences between Means (in Minutes) of the Angle of Error to the Left of the Vertical Axis of the Target for Throwing a Basketball with a Two-Handed Push Shot from Different Distances. . . . . . . . .

30

16 Differences between Means (is Minutes) of the Angle of Error to the Right of the Vertical Axis of the Target for Throwing a Basketball with a Two-Handed Push Shot from Different Distances. . . . . . . . .

31

17 Differences between Means (In Minutes) of the Angle of ETror above the Horizontal Axis of the Target for Throwing a Basket­ ball with a Two-Handed Push Shot from Different Distances .......

32

rii CABLES (Continued) Page

Table IS

Differences between Meanstin Minutes)of the Angle of Error below the Horizontal Axis of the Target for Thawing a Basket­ ball with a Two-Handed Bush Shot from Afferent Distances

19 Means of the Angle of Error (in Minutes) for Throwing a Basketball with a One-Banded Bush Shot at a Target from Different Distances . .............. . 20

21

24

34

Differences betweenMeans (in Minutes} of the Total Angie of Error for Throwing a Basketball with a One-Handed Push Shot at a target fro® Different Distances * . . , .

34

Differences between Means (in Minutes) of the Angle of Error to the Left of the Vertical Axis of the target for Throwing a Basketball with a One-Handed Push Shot from Different Distances.......... . ,

35

22 Differences between Means (in Minutes) of the Angle of Error to the Bight of the Vertical Axis of the Target for Throwing a Basketball with a One-Handed Push Shot fro® Different Distances 23

33

36

Differences between Means(in Minutes) of the Angle of Efc*rorabove the Horizontal Axis of the Target for Throwing a Basket­ ball with a One-Handed Push Shot fro® Different Distances » . .

3?

Differences between Means(in Minutes) of the Angle of Error below the Horizontal Axis of the Target for Throwing a Basket­ ball with a One-Handed Push Shot from Different Distances , . .......... » .

38

25 Means of the Angle of Error (is Minutes) for Shooting as Arrow at a Target from Different Distances . * * * * * * • . . ...........

39

viii tables

(Continued) Table

Pag©

26 Differences between Means tin Minutes) of the Total Angle of Error for Shooting an Arrow at a Target fro® Different Distances 39 ST Differences between Means (la Minutes) of the Angle of Error to the Left of the Vertical Axis of the Target for Shooting m Arrow fro® Different Distances * . . . MB

40

Differences between Means (in Minutes) of the Angle of ^*ror to the Right of the Vertical Axis of the Target for Shooting an Arrow fro® Different Distances . , . .

41

Differences between Means (la Minutes) of the Angle of Error above the Horizontal Axis of the Target for Shooting an Arrow fro® Different Distances* . . . . . . . .

42

Differences between Means (la Minutes) of the Angle of Ekror below the Horizontal Axis of the Target for Shooting an Arrow fro® Different Distances. . . . . . . . .

43

31 Means of the Angle of Error (in Minutes) for Driving a Tennis Ball at a Target fro® Different Distances. . . . . . . . .

44

29

30

32

Differences between Means (in Minutes) of the Total Angle of Error for Driving a Tennis Bali at a Target fro® Different Distances . . . . . . . . . . . . . . . .

44

33 Differences between Means (in Minutes) of the Angle of Error to the Left of the Vertical Axis of the Target for Driving a Tennis Ball fro® Different Distances. •

45

34 Differences between Keans (in Minutes) of the Angle of Error to the Bight of the Vertical Axis of the Target for Driving a Tennis Ball fro® Different Distances. .

46

i% tables

{Contimed) fable

Page

3$ Differences between Mease (in Minutes) of the Angle of ^c*ror above the Hori­ zontal Axis of the target for Driving a tennis Ball from Different Distances * 36

Differences between Means (In Minutes) of the Angle of Error below the Horizontal Axis of the target for Driving a tennis Ball fro® Different Distances . . * . .

47

46

37 Means of the Angle of Error (in Minutes) to the left and to the Bight of the Longitudinal Axis of the target, and the Means of the Yardage in Error beyond and short of the Lateral Axis of the target for “Pitching11 a Golf Ball from Differ­ ent Distances , . . , , , . . . . . . .

49

38 Differences between Means (in Minutes) of the fetal Angle of Error for “Pitching” a Oolf Ball at a target from Different Distances...............

49

39

40

41

42

Differences between Means (in Minutes) of the Angle of Error to the Left of the Longitudinal Axis of the Target for 11Pitching” a Dolf Ball from Different Distances

50

Differences between Means (in Minutes) of the Angle of Error to the Bight of the Longitudinal Axis of the Target for “Pitching” a CSolf Ball from Different Distances

51

Differences between Means (in Yards) of the Distance in Error beyond the Lateral Axis of the Target for “Pitching” a Golf Ball from Different Distances . * .* ,

52

Differences between Means (in Yards) of the Distance in Error short of the Lateral Axis of the Target for “Pitching1* aGolf Ball from Different Distances . ♦ *. *

53

X tabu® (Continued)

Table 43

44

Fag# Record of the Angle of Staror (In Minutes) for Throwing a Baseball ineluding On® Hundred Trials by Each of Fire Subjects fro® fire Different Distances........

86

Record of the Angle of Error (in Minutes) for Throwing a Football including One Hundred Trials by Each of Six Subjects fro® Five Different Distances* . . * * *

if

46 Record of the Angle of Error (in Minutes) for Throwing a Basketball with a TwoHanded Push Shot including One Hundred Trials by Each of Six Subjects fro® Six Different Distances

88

46 Record of the Angle of Error (in Minutes) for Throwing a Basketball with a One* Handed Push Shot including On© Hundred Trials by Bach of Six Subjects from Six Different Distances * . .

89

47 Record of the Angle of %ror (in Minutes) for Shooting an Arrow including On© Hundred Trials by Each of Five Subjects from Five ......... .. . * Different Distances

90

48

49

Record of the Angle of Error (In Minutes) for Driving a Tennis Ball with a Racquet including One Hundred Twenty Trials by Each of Six Subjects from Five Different Distances . * . ............. .. * .

91

Record of the Angle of Error (in Minutes) and the Yardage in Error for MPitching* a dolf Ball including One Hundred Trials by Each of Five Subjects from Five Differ­ ent Distances ♦ . . ........

92

1

Chapter 2

During the last twenty years professional workers in the field of physical education have contributed a tremendous amount of research that has been of great value in organising and promoting purposeful programs of physical education.

-4s a matter of fact, much of the improvement in

our programs may toe correctly attributed, either directly or indirectly, to the knowledge made available through the ®@dlum of this research.

As a result of many of these

Investigations, new problems have arisen which have been provocative ©f further research.

Only with knowledge of

the functional relationships that exist within certain areas ©an we proceed with reasonable assurance in de­ veloping and maintaining progressive programs of physical education. In 1899, Woodworth {25} wrote as follows:

MIt

is the accuracy of a movement that makes it purposive.* Since then many attempt® have been made to analyse motor skills in order to acquire a more thorough understanding of the synthesis of various factors in specific types of neuromuscular performance.

The results of some of these

studies, as suggested above, have indicated the necessity of further research for a toetter understanding of skill technique.

McCloy (19) has suggested a relationship between the accuracy of direction, as determined by the size of the angle of error, and the distance from the target as one of the factors In motor educability.

If there is a relation­

ship between the distance from a target and the size of the angle of error, knowledge of that relationship should certainly b© pertinent to the field of physical education, A review of the literature seems to Indicate that there are certain relationships existing between accuracy of direction and the distance from the target,

This study

is mad© in the hope that further knowledge may be added to this phase of motor skill analysis. Statement of the Problem the purpose of this study is to determine by the use of the relative size of the angle of error as a basis of discrimination, whether or not there are significant differences in accuracy of direction in certain motor skills at different distances. The problem, as pursued, resolves Itself into the determination of the relative size of the angle of error at different distances in the following motor skills: Throwing a baseball Throwing a football Throwing a basketball with a two-handed push shot

Throwing a basketball with a one-handed push shot Shooting an arrow Striking a tennis ball with & racquet, using a forehand drive HPitching* a golf ball with an iron club The relative sis# of the angle of error at different distances from the target was determined for de­ viations to the left and to the right of a vertical axis through the center of the target, for deviations above and below a horizontal axis passing through the center of the target, and for the total deviation from the center of the

Chapter II REVIEW

or

THE LXTEMT0HE

The use of many types of targets Is found re­ corded In studies that have been made for various purposes. Young and Moser (26) used a moving target as a test item In construsting a short battery of tests to predict play­ ing ability in women*s basketball.

Hicks (12) also used

a moving target to study the effects of practice in throw­ ing at a moving target with subjects ranging from three to six years of age. Stationary targets have often been used to de­ termine accuracy in various motor skills.

Targets used

to measure accuracy In throwing are generally placed la such a manner that the face of the target is perpendicular to the plane on which the subject stands.

Targets used

by Glevett (3) and by Edgren and Robinson (8) to measure accuracy in “pitch* shots and in putting In golf were placed in a horizontal position on the same plane as that upon which the subject stood.

Targets with concentric

circles have been used most frequently, although the rectangular type of marking has been used by Johnson (16) and by others. In an experiment with a light gun, Voigt (24) found, by having an assistant stand behind a target of ground glass to ©ark the point at which the beam of light

5 struck the target* that the angle of error decreased* with­ in limits* as the subject moved farther away from the target*

When the gun was held at breast height he found

that the angle of error at a distance of six meters from the target was on© hundred seventy-nine minutes, at a distance of fifteen meters from the target the angle of error was one hundred thirty-on© minutes* and at twentyfive meters the angle of error was only one hundred twelve minutes.

In his experiment the sights of the gun were not

used in aiming the gun.

Me found that from thirty meters

on out there was no substantial decrease in the sis© of the angle of error.

H© also found in shooting from hip

height with one hand, that the angle of error two meters from the target was two hundred fifty-one minutes, and at a distance of eight meters from the target the angle of error was only one hundred twenty-five meters. Shooting with two hands from the same height* the angle of error was found to decrease from one hundred seventythree minutes at two meters from the target* to eightyseven minutes at eight meters from the target.

He

further found that with upward shooting the angle of error decreased from one hundred seventy-three minutes to one hundred fifty minutes when the distance from the target was increased from two meters to twelve meters. It was also found that the distance between the eye and the hand in which the gun was held could be increased to

6 a magnitude of seventy centimeters without influencing the tendency of the angle of error to decrease when the distance from the target was increased* MeCloy (21) found that In shooting baskets in basket ball* the percentage of errors at a distance of twenty feet from the basket was greater than the percent­ age of errors made from a distance of thirty-five feet from the basket*

Oliphant (23) found that the twenty-

foot distance from the basket yielded a greater percent­ age of successful shots in basketball games than either the ten-foot or the fifteen-foot distances*

He also found

approximately the same percentage of successful shots from the thirty-foot distance as he found under similar circum­ stances from the ten-foot distance* Griffith (11) found in a study of free throws* fifteen feet fro® the basket* that approximately twice as many errors were made with reference to the distance as were made in the direction of the throw,

this finding is

supported by Oliphant (23) as being true for shots from other areas of the playing court. In experimenting with children from three to six years of age* who threw at a moving target, Hicks (12) found that there were approximately twice as many throws below the center of the target as there were above the center of the target.

In reporting an experiment in which he used two classes of men* to study the acquisition of skill in archery L&shley (1?) suggests that a large number of shots are necessary for satisfactory reliability*

He

states; *fhe average of any smell number of shots does not give a fair measure of the skill of the individual, and the use of such averages as a measure of the initial and final accuracy and amount of improvement does not lead to trustworthy results. *

Chapter III PROCEDURE g e le o tiQ ii o f O uM ectg

After preliminary experimentation it was de­ cided to make use of a relatively mall number of sub­ jects In who® the specific motor skills were developed to a high degree of proficiency. This procedure should tend to reduce the variability of the angle of error in the selected skills and tend also to reduce the varia­ bility due to the practice element Inasmuch as each of the subjects had attained a relatively high degree of pro­ ficiency.

In each of the activities either five or six

men were used, and all of the subjects were right handed. In order to maintain a satisfactory degree of reliability a minimum of one hundred trials for each subject at each distance was exacted.* Description of feats fhe targets used in measuring the angles of error In throwing a baseball, in throwing a football, In 1 1''^nxri"

Studies by Brophy (£}, Cosens (5), Young and Moser (26) and Johnson (16) show that reliability for throwing a baseball, a football and a basketball at a target will range approximately from .905 to .984 when one hundred trials are taken. Co sens (5) has also shown that within limits reliability ©an be increased by en­ larging the target and increasing the number of divisions on the face of the target.

shooting an arrow, and in striking a tennis ball with a racquet using a forehand drive, were rectangular, approxi­ mately nine feet by ten feet.

(Figs. 1 and 2, Appendix,

pp. 82-83. ) bines, one-half Inch in width, were painted horizontally and vertically on the targets.

These lines

were six inches apart, that is, the distance from the center of one line to the centers of the lines parallel to it was six inches.

The entire target was, by this lin­

ing, cross-sectioned with six-inch squares.

The center

square of each target was painted the color of the lines except for a circle two inches in diameter in Its center, which was left the same color as that of the background of the target.

The targets for each of the

above mentioned motor skills were erected with their faces perpendicular to the plane of the floor or ground. The center of the target for the baseball and the football throws was raised to a height of seventy-one Inches, which was the mean height of the subjects used In each of these skills* The center of the tennis target was placed at a height of thirty-four inches.

This height was selected

after the average height was determined at which each of the six subjects hit the ball with the racquet as the ball rebounded from the floor,

A high jumping standard was

placed alongside each subject, and the height of the re­

bound from the floor was marked and measured approximate­ ly twenty times for each subject.

The average height of

the rebound for the six subjects used was thirty-four Inches, with a range from thirty-three inches to thirtyfive inches. Before each series of trials by any one of the subjects the center of the archery target was adjusted to the height at which the subject held the point of the arrow in the shooting position. The target for both the two-handed and the onehanded basketball throws was a five-elghths-inch piece of plywood, five feet by six feet.

It was cross-sectioned

Into six-inch squares, as were the targets mentioned above, and in the center of the target a circular hole twelve inches in diameter was cut.

(Fig, 3, Appendix, p. 84. ).

The target was then placed at a forty-five degree angle with the floor, and the center of the target was raised to a height of one hundred thirty and one-half Inches, which was five feet plus the mean height of the group of six subjects,

A study of slow motion pictures showed that

the average point of release for the two-handed shots was approximately two inches below the height of the sub­ ject, while the average point of release for the onehanded shots was approximately three inches above the height of the subject.

These differences, however,

* -I .ljL should b® Inconsequential as far as the results in the measurement of the angle of error are concerned, the target for “pitching’* a golf ball with an Iron club was a 1st el portion of a playing field. It was a rectangle, seventeen yards by twenty-five yards, cross-sectioned with cord string at intervals of one yard. In the center of the center square, a metal container eight and one-half inches In diameter was countersunk in the ground with its open end six inches above the level of the target.

This container was clearly visible at a distance

of sixty yards. In all cases the subject was Instructed to at­ tempt to hit that part of the target designated as the center by the markings as described above. Hestraining lines for each of the skills were established at distances from the center of each of the targets as- follows: For throwing a baseball 15 feet, 30 feet, 45 feet, 60 feet, and 75 feet For throwing a football 16 feet, 30 feet, 45 feet, 60 feet, and 75 feet For throwing a basketball with a one-handed push shot 10 feet, 15 feet, 20 feet, 25 feet, 30 feet, and 35 feet

For throwing a basketball with a two-handed push shot 10 feet, 15 feet, 20 feet, 25 feet, 30 feet, and 35 feet For shooting an arrow 10 yards, 20 yards, 30 yards, 40 yards, and 50 yards For striking a tennis ball with a racquet, using forehand drive 15 feet, 25 feet, 35 feet, 45 feet, and 55 feet For “pitching* a golf ball with an iron club 20 yards,

30 yards, 40 yards, 50 yards,

and 60 yards For golf, these lines were one inch wide and four inches long, and intersected a line drawn from the center of the target and perpendicular to the horizontal axis of thetarget.

Restraining lines for the other skills were

of the samesize and intersected a line drawn from the center of the target, projected upon the plane on which the subject stood while taking his trials, and which was perpendicular to a plane formed by the projected point and the horizontal axis passing through the center of the target,

Care was taken in each case that the point of

release (or impact in the case of tennis and golf) was over this established restraining line.

MmXnlstmtXQn of Tests In all eases subjects were permitted a “warm­ ing-up* period.

After this preliminary practice they

were permitted two or three practice trials, but not at the distance at which they were to start that day* After the trials were started, no practice was per­ mitted between trials. In all Instances, except In the ease of tennis, twenty trials were taken each day at each distance. In the administration of the trials each subject started on the first day at the distance nearest the target with ten trials.

He then moved back to the next distance for ten

trials, and so on until he reached the distance farthest away from the target.

At the distance farthest from the

target he took twenty trials and then proceeded to move in toward the target, taking ten trials from each distance until he had completed hi® ten trials at the distance at which he started.

On the second day he proceeded in a

similar fashion, except that he started with ten trials at the second nearest distance, then moved back as before, taking ten trial® at each distance, until he reached the distance farthest away from the target where he took only ten trials.

He then went to the distance nearest the target,

where he took twenty trial®.

From here he went to the

distance farthest away fro® the target, taking ten trials there, and then moved in toward the target, tak­ ing ten trials at each distance, until he had completed his last ten trials at the distance where he started, this procedure was followed throughout the experiment, the subject being required to start at a distance one restraining line farther back than he did on the last previous trial. The subjects in tennis took forty trials each day at each distance, requiring three days to complete their trials.

They followed the same general method used

in the collection of the data for the other skills, except that they took twenty trials at each distance before mov­ ing on t© the next restraining line.

On the first day

they were started at fifteen feet, the second day at thirty-five feet, and on the third day at fifty-five feet. In the various motor skills each subject com­ pleted on© hundred trials at each distance, except those subjects in tennis, each of whom completed one hundred twenty trials at each distance. With each attempt by a subject to hit the center of the target, the point on the target which was actually hit was observed and recorded on a chart corresponding to the outline of the target.

Hits made upon division

lines of the target were recorded as having been made in

those squares lying nearest the center of the target. Commutation of Angles of Error For the purpose of this study the angle of error is defined as the number of minutes between two lines, one of which is determined by the point of re­ lease of the hall (or arrow) and the point on the target which the subject attempted to hit.

The other line is

determined by the point of release of the ball (or arrow) and the point on the target vihieh Is actually hit. Angles of error were computed upon the assumption that any hit within a square was made upon the center of that square, and the distance of the hit from the center of the target was determined by the distance from the center of the builds ©y© to the center of the square in which the hit was made.

Angles of error to the left and

the right of the vertical axis of the target, and above and below the horizontal axis of the target, were determined by the distance between the center of the square that was hit and the centers of the squares lying on the vertical and the horizontal axes nearest the hit, that is, the perpendicular distance to the vertical and the horizontal axes, respectively. In the baseball* the football* the archery, and the tennis trials the line determined by the point

of release ana the point on the target which the subject Is attempting to hit, is perpendicular to the plane of the target, and consequently the angle of error was ascertained by the computation of the tangent of the angle. In golf, the angle of error was also ascer­ tained by the computation of the tangent of the angle, inasmuch as the shot was made from the same plane as the location of the face of the target.

Deviations to the

left or the right eould be determined in minutes, but deviations due to the shortness or the excess in length of shots were recorded In the study in yards. In basketball, the angle of error was de­ termined by applying the formula for the determlnation of an angle upon the basis of three known sides of a triangle The formula used was: tan §& -

ill 1

m

.

(e - a)

^

, in which

*0- ( a e l

, and

s

m i(a + b + o); a, b,and e, being the

known sides of the triangle, EesuXts of the collection of original data are listed in the Appendix, Table© 43 to 49, Inclusive, pages 86-92.

Chapter IV ANALYSIS OF THE DATA Method ,of_Analysis. Because the number of subjects for each of the motor skills was small and because the subjects were not se­ lected at random* an analysis of variance was made accord­ ing to the principle of ^Interaction* variance and the X test for significance outlined by Lindquist (5, pp. 60 and 112-119).

The use of this analysis permits the application

of the standard error of a difference between angle of error, means, at different distances for any one of the groups of subjects* as a test of significance. At each distance the means were determined* in minute®, for deviations to the left and to the right of the vertical axis of the target* for deviations above and below the horizontal axis of the target* and for the total angle of error®. *

It should be noted that hits upon either of the axes show a total angle of error equal to the distance from the center of the target* but deviation from only one of the axes. Consequently* a hit upon the vertical axis of the target above the center of the target would be figured as a perfect hit as far as deviation to the right or the left Is concerned*but would of course show a deviation in the total angle of error, and in the angle of error above the hori­ zontal axis of the target. In computing the average angle of error for each of the above observed deviations* the square of the average total angle of error will always ex­ ceed the sum of the squares of the averages for angles of error to the left and the right of the vertical axis and squares of the averages for angles of error above and below the horizontal axis. This excess will be observed to Increase as the number of successful hits upon the axes of the target Increases. (Fig. 4, Appendix* p. 85)

For each group of means* that Is, the total angle of error, the angle of error to the left of the vertical axis, the angle of error to the right of the vertical axis, the angle of error above the horizontal axis, and the angle of error below the horizontal axis, differences in the means at different distances were de­ termined.

the standard error of a difference between

means was computed in each case, and also the maximum error, at both the five-per-cent and the one-per-cent levels of confidence, In the differences between all combinations of pairs of means in each motor skill, for the application of the X tost for significance. the following forty-two tables list the re­ sults of this analysis.

fable 1 Keans of the Angle of Error Expressed in Minutes For Throwing a Baseball at a Target from Different Distances Distance from fagftfift

...

To the left of the vertical axis To the right of the vertical axis Above the horizontal axis Below the horizontal axis Total angle of error

IB,....................................

ULisA

22.00

41.60

35.93

39.81

38.02

34.16

40.28

36.43

41.23

42.67

22.51

28.03

28.93

29.02

29.66

34.70

35.42

41.05

45.49

46.24

__ &SLM __ ■J5.8.4JL.

64.37

fable 2 Differences between Means of the Total Angle of Error (In Minutes) for fhrowing a Baseball at a Target frora Different Distances

SQfeet 15 30 45 60

feet feet feet feet

10.04

4ft S m ± 8.59 1.65

6Qfeet 10.96** .92 2.57

*1 Denotes a statistically significant Increase in of the angle of error The standard error of a difference between two means The maximum error at the five per cent level of confidence in the difference between two means The maximum error at the one percent level of confidence in the difference between two means

75fegt 12.92* 2.88 4,53 1.96

the size 4.76 10.09 12.90

20

table 3 Differences between Means (in Minutes) of the Angle of Sm>? to the Left of the Vertical Axis of the Target for Throwing a Baseball from Different Distances

30 feet 45 feet IS feet

U) (B) (0) (D)

30 feet

(A) (B) (0 (d |

45 feet

(A) (B) to} im

60 feet

(A) (B) to) (D)

19,SG^1 $.71 i b ,ii 16.68

6© feet 75 feet

13.93**1 5.66 i2,oo 16.53

X7.8X*1 16.02** 5.73 S.9S 12.57 12.15 17.32 16.74

5.67 $.6$ 11.77 16.21

1.79 5.62 11.91 16.42

3.58 5.81 12.32 16.97

3.88 5.57 11.81 16.27

2.09 5.77 12.23 16.85 1,79 5.84 12.38 17.06

♦i Denotes a statistically significant Increase in the site of the angle of error (A) Th m (0) CP)

60 feet

(A)

(A)

45 feet

W (G)

m 60 feet

(») } The maximum error attheone per cent level of confidence in the difference between means

33 fame 18 Differences between Means {%n Minutes) of the Angle of Error below the Horizontal Axis of the Target for Throwing a Basketball with a Two-Handed Bush Shot frost Different Distances

m 10 m feet cc) Cfl) (A) 18 (B) feet (G) (B) {*|

(C) (B)

30 yards

(A) m CC) CB)

40 yards

(a ) (B) (0) C£)

SO yards

U) (B) (0) m

r30 [email protected] 40 yards IB*0B 15*39 44.95

50 yards 30.yards...

20.37 15,85 33.82 46,33

28*91 15.79 33.47 46.12

40.74#i 15.31 32.46 44.72

4.34 15.90 33.71 46.44

12.88 15.83 33.56 48.24

24.71 15.34 32.52 44.81

8*54 16.29 34*53 47.58

20.37 15,82 33.54 46.21 11.83 15.75 33.39 46.0i

*1 Denotes a statistically significant increase in the sis© of the angle of error (A) The difference between the two means (B) The standard error of a difference between ©cans CO) The maximum error at the five per cent level of confidence its the difference between means (D) The maximum error at the one per cent level of confidence in the difference between

Table 40 Differences between Means (in Minutes) of the Angle of Error to the Bight of the Longitudinal Axis of the Target for HPi tching9 a dolf Ball fro® Different Distances

.30yarcl. 40 yards

m

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Target Used for Throwing a Baseball, Throwing Football, and Shooting an Arrow

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Figure 1.

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4. Illustrative diagram of the effeet of an increased num­ ber of hits upon the vertical and horizontal axes of the target -■aw one hit in eaoh numbered square, average deviations are as follows: to left, 4»6j to 4.b ; above, 4.S: below, 4.5; total, 7.24. the sum of■*&**** for averages to the right and left, ana an^ og is 40.SO, and the square of the total is 52.42, or 29.8* one hit in squares 1, 5, 5, and 7, and two hits In squares 2, 4 , 6, and 8, average tovlatlons are t o i f T l l % h f sum^f s q ^ s ’fof averages’t o the’ ’ l e l f a n t' rl gh tl Ld f o v e a n d h ^ o u i s 32, and the square

of the total is 46.38 or 44.9$ greater.

Table 45 Record of the Angle of Error (in Minutes) for Throwing a baseball including One Hundred Trials by Each of Five Subjects from Five Different Distances JSb haft of the Vertical Axis of the Target ^ Subject Mj&am*. .. 1 .2 . .5 4 _5 . ___ Total 1265 1150 5060 30 ft. 2916 ?4g 10380 2689 2719 1314 45 ft. 2554 2130 1786 1562 9251 1219 SO ft. 3416 9733 2411 1178 1407 1321 75 ft. 8155 1654 755 1218 tv,

To the 15 30 45 60 75

f% ft. ft. ft. ft.

3793 216© 1478 2039

2348 2516 1838

of the Vertical Axis of the TarggjL "SuBJeof JL 9221 10090 2290 1456 182? 140? 111? 2323 8835 10534 £8?0 1838 1949 3059 13JL Subject

15 ft'. 30 ft. 46 ft. SO ft. - 7 1 f t . .-

Srt® 1830 209? 8526 1815

'

1496 " Sb5 230 1770 342 1030 684 1859 722 1349 1064 779 713 -JUJ8L.. 889

1 1657 1295 1522 1961

ftjgSo 6629 6437 7240 6674

Below the Hordsontal Axis of the Target Subject 4 5 1 1 Total _ Distance. .....2 2530 3561 9196 1610 ioaS 460 15 ft. 2633 1773 2351 9333 1720 858 30 ft. 2380 2061 11391 8359 2513 2098 45 ft. 1750 11394 1839 2296 2870 2639 80 ft. 2465 .1&7.16 _ 3172 J.868.. 2300 2917 75 ft. '

Distance 1 5479 is ft. 7599 30 ft. 8187 45 ft. 8260 60 ft. 75 f t . _ 7545

Total Ansle Subject . 2_ . 3600 6470 5209 4741 6147 4748 6963 5023 6552 5677

of Error 4 4145 5650 4951 5122 5156

. . . ..... ..JL~ 5830 7550 5886 5838 7254

. Total. ... 25724 30749 29919 31206 32184

fable 44 Record of the Angle of Error (la Minutea)for Throwing a Football including One Hundred Trials by Each of Six Subjects fro* Fire Different Distances

To the Left of Vertical Axis of the Target Subject 15 30 45 60

15 30 45 60 ?§

15 30 46 60 75

ft. ft. ft. ft.

1830 1820 2632 2603 2594

'1^4 687 1752 1982 2090

345 1259 S37 1032 _.2483

1035 856 1523 833 2206

4248 3779 8863 2669 3459

9995 11556 12430 11360 14990

ft. ft. ft. ft. ft.

To laiiglt of the Vertical Subject 1 2 3 4 8643 1149 920 690 5385 3968 4009 1196 2286 3205 3726 4361 4210 3585 2383 3642 4866 4082 1906 2274

Axis of the Tarset 6 2230 2576 3354 2607 3344

Total 10043 23496 23896 22844 22289.

ft. ft. ft. ft, ft.

Above the Horizontal Axis of the Tarccet Subject 6 1 5 2 ..._ - 3 .. 4 li49 690 124 24l5 2987 1033 2691 3664 3547 2200 2803 2921 3779 3208 3164 2820 4316 3702 2927 2870 1434 2925 2362 3009 4247 2594 1172 2546 __ 1648 2042

Total 9536 17916 20987 15S17 14249...

5 2409 6360 6974 6417 5817

Below the Horizontal Axis of the Subject 5 4 3 2 1 Distance 2526 1380 1720 2&40 13&0 15 ft, 4237 2061 1030 2061 4200 30 ft. 4083 2784 3206 1128 3205 45 ft. 4414 4015 4329 2122 4096 60 ft. 4015 3122 3687 4655 76 ft.

Distance 15 ft. 30 ft. 45 ft. 60 ft, ..

1265 3146 2823 2151 M m

1 8§X4 11006 11580 10677 11052

Target 6 3675 4009 4621 2440 3461

Total 13321 17688 19027 21416 J8kV>±~,

Total Ansle of Error Subject 6 5 4 3 2. 8416 8048 3481 3564 4174 8061 14563 10068 5431 83m 8729 13450 11358 6107 9802 8126 8285 13213 6049 10352 12747 9152 7659 9001 _ 7084

Total 36597 57540 60826 57602 56695

Table 45 Kecord of the Angle of Error (in Minutes) for Throwing a Basketball with a Two-handed Push Shot ineluding One Hundred Trials by Each of Six Subjects from Six Different Distances

Distance 10 ft, 15 ft, 20 ft. 25 ft. 50 ft. 35 ft.

i^eft of the Vertical Axis Subject 2 4 ... 1 3 2812 5088 5845 4728 1984 1195 2975 2619 2291 1854 5194 2270 1855 2075 2524 5067 2595 964 2418 3931 2815 -JUUOL. . 3690 -

_

.

.

of the Target 5 3318 3370 4012 3167 2112 3026

Total 20072 14410 15049 15879 12724 14543

6 2305 2289 1428 1211 866 1324

— ~

To the Right Of the Vertical Axis of the Target Subject Ms_taper 1 2 5 4 5_____6 10 ft. 4081 2298 1530 l40¥ r 5820 2499 15 ft. 3512 2607 1750 2628 2960 2761 20 ft. 3292 2764 1858 2194 2352 2847 25 ft. 2023 3882 2931 2085 379© 4081 30 ft. 2922 3034 3779 2046 3600 4812 .35 ft. 2559 .2931. 2466 3434 3027 3892 Above the Horizontal Axis of the Target Subject 6 . Distance 2 3 4 .... 5 1 1370 1102 10 ft. 920 414 1280 282 598 1104 1058 2158 15 ft, 848 782 798 756 588 1372 714 588 20 ft. 576 936 790 576 216 @28 25 ft. 512 736 924 608 384 416 30 ft. 377 87 1064 840 406 783 35 ft. Below the Horizontal Axis of the Target _ _ Subject 6 2 3 .. 4 _ Distance 1 -4a 175& 2262 1662 1662 2250 io ft. 24^2 1972 2512 2820 1902 1300 2370 15 ft, 2578 2214 2626 3070 2306 4088 20 ft. 2550 2936 2240 3858 3064 3980 25 ft. 3108 3596 2820 4130 3584 3714 30 ft. 2312 2470 ft. 4160 3220_ 4162 4550 -

1 Distance 8548 10 ft. 7619 15 ft. 8840 20 ft. 8015 25 ft. 7693 30 ft. 8073 65 ft.

...

Tntal Anecle of Error . Subject 5 3 4 2 1047T 7086 7502 7532 8860 5353 7357 6819 8542 6402 7129 6796 8539 6092 8164 7141 7715 9016 7128 6594 7862 9383 7904 6421

6 7240 7332 6201 7288 8132 7169

Total 17437 16218 15307 18197 20193 18309

Total 53&8 6548 4816 3922 3580 3557

Total 12054 12876 16782 18628

Total 48465 43320 43910 45239 46278 46812

fable 46

Heccrd of the Angle of Error (in Minutes) fop Throwing a Basketball with a One-Handed Pash Shot including One Hundred Trials by Each of Six Subjects froa Six Different Distances •mBm

To the Left of the Vertical Axis of the Target Subject 1 10 ft. 2105 1532 2®' 3515 4190 5412 19213 15 ft. 2433 2280 2080 3708 2404 3526 16428 20 ft. 2014 2849 3115 3519 3421 3559 18477 25 ft. 2521 3056 4378 3370 3763 4481 21569 3079 3896 3539 3508 5326 4704 24052 30 ft. 38 ft*... 3735 4046 4736 4121 7070 5810 ,29518 To the Bierht ©f the Vertical Axis of the Target Subject 6 Total4 3 Distance 2 1 .5 . 3791 660f 378? 5628 40&S 2159 26049 10 ft. 4089 5469 4669 3079 3081 2886 23273 15 ft. 4378 4791 4459 2602 3451 4071 23752 20 ft. 4582 4423 3305 242? 3323 3552 21612 25 ft. 2717 3264 3090 3601 2930 3234 18836 30 ft. 35.ft.--- 2907 3820 3552 JSUUL. 2149 .m . 19756 Above the Horizontal Axis of the Target, Subject 5 506 736 ?8& '' 276 1286” 552 10 ft. 736 552 706 414 1150 1104 15 ft. 966 420 840 840 382 798 80 ft. 720 550 970 432 612 540 25 ft. 668 576 544 1084 800 916 30 ft. 993 403 433— 1320 546 1Q36 ^ the Horizontal Axis, of the Target Subject 6 4 2 1 Pistance 1950 2486 1706 1406 3380 10 ft. 1952 2006 3114 2912 1552 15 ft. 2576 2126 4768 2996 2256 2734 20 ft. 2852 5134 2534 3450 4810 2860 25 ft. 3896 5702 2492 2928 3384 §296 30 ft. , 3108 „62644S2 & §356 m m 35 ft. Totai Angle of Error Subject 5 6 3 Pistance 9560 8588 10240 8430 9474 9079 6045 7021 9699 10 ft. 8819 8392 8940 15 ft. 8410 10127 9521 7857 8508 9233 20 ft. 9116 11096 7770 10373 9842 9008 9538 25 ft. 11714 8406 6871 9833 9179 11934 10003 10777 13025 30 ft. 10047 9732 35 ft.

4138 4662 4746 3824 4588 4731

- ■

...

l2|SL. 13876 14354 17456 21440 23696 szaai ffp.lfiJL.

55991 50296 53656 56370 56376 65518

Table 4? Record of the Angle of Error (In Minutes) for Shooting an including One Hundred Trials by Each of Five Subjects fro® Five Different Distances

ffo the Left of the Vertical Axis of the Subject ....Distance 2 3 5 4 - .1. „ 10 yards 855 2458 1033 1425 2684 SO yards 1572 1971 1610 2842 980 30 yards 1238 1938 2587 1634 1919 40 yards 1164 1467 2089 1730 2236 50 yards 1166 2106 1413 2600 1610

Target Total 8452 8775 9313 9576 8895

To J&® Risht of the Vertical Axis .of...tbie...Target.._ Subject Distance Total 5 3 4 2 _JL , 10 yards 1596 456 798 171 87 114 20 yards 3X63 405 749 878 740 894 30 yards 456 437 2660 456 741 870 40 yards 787 527 2984 470 342 858 830 ..jai__ 942 1087 3940 -J5Q..JUO&S.. 600 Distance 10 yards 20 yards 30 yards 40 yards 50 yards

...Distance 10 yards 20 yards 30 yards 40 yards x 50 yards

Distance 10 yards 20 yards 30 yards 40 yards 50 yards

Above the ftolgpntal Axis Subject 3 4 .. 1 -.2. .. 1083 1714 3726 2169 2214 1686 1295 3728 1368 1843 1668 1331 888 1176 1264 243 1345 1028 602 m 2. Below the Horizontal Axis Subject 2 .r.3 .r r r X - r - ......A 1085 ll4 342 85$ 1178 405 1812 550 1216 2016 627 1938 3205 2796 £535 1638 2697 3076 3078 1483

of the Target 5 142$ 2184 1026 1376 1278

of the Target Total S 13538 n4i 5495 1550 7605 1808 1734 11908 220.2— 12530

___________ ...

1 1077 3286 3061 3793

. JZZffiL.

fetal Ansle of Error Subject 4 3 -2 4957 6595 4600 3796 6611 4607 4070 6453 4756 4754 6094 5061 5151 5739

...

_

Total 10118 11105 7236 4947 4608

.

......_

........

...

___ 5 4558 4974 3955 4431 4732

Total 22687 23274 22295 24133 24570

,—

---------

01

Table 48 Record of the Angle of Error (In Minutes) for Driving a Tennis Ball with a Baequet including One Hundred Twenty Trials by Each of Six Subjects from Five Biff©rent Distances

15 25 35 45 55

feet feet feet feet feet

To the heft of the Vertical Axis of the Subject --- -*u. 8142 9861 6881 3792 575 1610 7963 8032 5972 3989 1927 4944 6321 8820 2205 5190 7399 4116 5801 2895 ”=716 7598 6822 4845 6298 5768 5207 3619 3563 8018

..to the Bight of the Vertical Subject Distance 1 -.. 2 . 4 3 15 feet 4359 2525 2070 1836 25 feet 2134 2202 6244 4183 35 feet 3528 8401 3038 7845 45 feet 3394 2550 4884 8669 55 feet 3489 5618 8520 3619

Distance 15 feet 25 feet 35 feet 45 feet 55 feet

... -1. 9729 6413 3528 4312 2556

30861 32827 34051 31277 32473

Axis of the Target 8 . TotaJL _ 5630 21368 ©423 24048 3773 23804 3511 26885 1901 23578

5 4942 3802 3479 3277 4431

Above the H .Distance 15 feet 25 feet 35 feet 45 feet 55 feet

Target

;al Axis of the Subject 2 ... 3. 4 5 3670 rr585'2 n'-3w " ¥225 5496 6003 3990 4535 5007 3577 6713 3479 4657 4678 2440 3269 3219 3244 1183 1340

Below the Horizontal Axis of the Subject 2 5 4 5 1 2984 3101 3789 5620 7675 5016 2405 2544 4397 7415 4782 3724 4165 2989 6615 6836 3204 8422 5039 3190 6706 4828 4338 6456 7330

Total Ansle ofError Subject 5 4 3 Distance 1 2 10945 12333 15384 22016 18638 15 feet 25 feet 18807 18423 18646 10827 10530 22140 11329 10010 35 feet 15916 16870 18547 10562 11733 45 feet 16985 15026 12677 11296 16677 55 feet 14299 13380

Target 6 Total 344& 33374 5837 32274 0762 29066 3741 23097 3528 15070 Target 6 Total ... 6197 29366 5221 26998 3528 25803 5458 29149 4735 34393

Total 6 14590 93906 17374 94607 15601 91866 16348 89201 14496 82825

Table 49 Record of the Angie of Error (in Minutes) ana the Yardage in &a?ror for Pitching** a golf ball including One Hundred Trials by Each of Five Subjects from Five Different Distances Angle of Error (in Minutes) to the heft of the .tudlnal Axis Subject Distance Jt EO yards 3544 8503 §594 1755 2180 30 yards 5935 352? 6663 6214 2911 40 yards §050 3961 3664 7292 3470 50 yards 8279 2980 3944 7345 3146 _ 60 yards 11940 5396 5613 4615 .4388

Longi-

21574 25250 23437 25694 31962

Angle of Error (in Minutes) to the Right of Longi-- -- ---- ---.■ tu&inal Axis of.Target.... .........__ ___ Subject 5 . Total.... - Distance .. 1.....2 3 4 3537 26191 SO yards 8^06 2646 7395 4407 30 yards 29081 3987 6426 4252 7454 6962 38978 8445 5947 15860 4918 3808 40 yards 50 yards 37273 5985 8448 12808 4662 5372 31639 2474 5889 3555 10765 8966 do yards Yardage in Error for Shots Beyond Lateral Axis of ... .. ..... ...... ......... Target. ............. _._ ...... Subject Distance ...X .. 2 . Total 5 3 4 252 SO yards 102 41 31 30 48 ' 417 57 84 43 68 30 yard# 165 117 621 68 121 190 125 40 yards 726 136 98 147 184 50 yards 161 774 180 121 M X 84.... 178 60 yards far&age in Error for Shots Short of Lateral Axi# Of ....... -..... ... ... Target.._ Subject Total 5 Distance .1 .... 2__ 830 185 222 167 86 170 20 yards 1140 209 362 246 217 30 yards 107 1149 203 385 271 40 yards 121 169 1403 202 410 371 230 190 50 yards 193 546 326 „ i m ... 415 181._ 60 vard#

M atAnoe 20 yards 30 yards 40 yards 50 yards 60 yards

1 11750 9922 13495 14262 14414

Total Anede of Error Subject 3 4 2 12989 6160 11149 13176 9953 14117 12210 9908 19524 16752 12717 11428 16368 13581 11285

--5 5717 7163 7278 7808 7953

Total 47765 54331 62415 62967 63601