WM 11 1 WWW | 1293 01058 5085 g PPLEMENTIQ g" Sl1AATERiAL 1% BACK OF 300:4 PLACE ll RETURN BOX to roman thin checkout 1mm your record. TO AVOID FINES return on or before date duo. DATE DUE DATE DUE DATE DUE Wall” 1 \ COLLEGE OF EDUCATION , - "9"?!“ t s a ' '1'.‘=‘.1“. I‘_L‘?_‘!)‘“"\ r1 1'“) m: E!.:1_SC,A§“L 1‘51" ” BUALP"”,n»rerDHcALuA COIIfLJ‘Z- ‘v‘ — " ' 1 ‘;Y , 1' 7' ’1:'~.1~"!"‘4' \fivz‘ ‘rH'..’~."3 01‘“ ‘- " I I. .I‘ '- ‘rA‘g'. 1A.“.“l‘4‘f3 AN INVESTIGATION OF THE RELATIONSHIP OF GRIP STRENGTH AND ACCURACY MEASURES TO BEGINNING BOWLING ACHIEVEMENT OF COLLEGE‘NOMEN By Joan Huff A THESES Submitted to the College of Education of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Health, Physical.Education, and Recreation 1958 ACKNGHDGEMDITS The author wishes to extend her thanks to Dr. Janet Weasel for her interest and guidance in the preparation of this thesis. Special thanks are also extended to Mr . Perry Johnson and Mr. Marvin Zuidema for their assistance in designing the accuracy measuring apparatus . The author is also indebted to Dr. Wayne Van Huss and Dr. Henry Montoye for their suggestions throughout the project. Appreciation is also extended to the faculty and students in the cooperating bowling classes which made this stuiy possible. J. H. TABLE OF CONTENTS Chapter I INTRCDUCTIW o o o o o o o o o o o 0 Purpose of the Study . . . . . . . . Definition of Terms. . . . . . . . . Limitations of the Study . . . . . . . II REVIEI OF THE LITERATURE . . . . . . . . Strength . . . . . . Hand-eye Coordination or Accuracy . . . . Baum. . O O O O O C C O O O C III METHODOLOGY . . . . . . . . . . . . IV ANALXSIS.AND PRESENTATION OF DATA . . . . . AnalysisofData. . . . . . . . . Presentation of Data . . . . . . . Ranges and Means. . Reliability of Measures of Variability Relationship of Accuracy, Grip Strength and Weight and their Relationship with Bowling Criteria . . . . . multiple Regression Analysis. . . . Analysis of Grip Strength, Accuracy and Strength Residuals and Letter Grade. v summer, RESULTS, CONCLUSIONS AND REOWATImS O O C O O O O O 0 Summary. . . Results. . . . Conclusions . . Recommendations . O O O O O O O O o 0 0 0 Q 0 O O O O O I O O O o O 0 O O O O O O O 0 Bmummo 0 o o e o o o o o o o o o o APPMH o o o o o o o o o o o o o o o 0 £5 Brim ox rue. H 30 30 31 Table II III VI VII VIII LIST OF TABLES Range and means of Grip Strength, Accuracy, ‘Weight and Bowling Average . . . . . Actual and Corrected Reliability Coefficients of Experimental Variables. . . . . . Correlations of Experimental Variables with Bowling Criteria and their Intercorrelations . . . . . . . . Actual and Attenuated Correlation Coefficients Between Grip Strength and Accuracy and Bowling Achievement. . . . . . . . Multiple Regression.Analysis Results'with Final Six Game Average as Bowling criteria 0 O O O O O O O O 0 0 Multiple Regression Analysis Results with Total Term Average as Bowling Criteria . . . . . . . . . . . Ranges and means of Strength and Accuracy Measures of Letter Grade Groups. . . . F Ratios of Letter Grade and Grip Strength, Accuracy and Grip Strength Residuals . . Page 21 22 2h 25 26 26 28 29 LIST a“ FIGURE Figure Page 1 Accuracy Measuring Equipment on the Bowling Alley O O O O O 0 O 0 O O O 0 1.6 CMWWI INTRODUCTION "Bowlers . . . come in all shapes, sizes and ages today," reports a proprietor of a bowling establishment in Chicago. Grandma and the 'whole family take part in America's number one participant sport. The figures for the current bowling boom indicate over 20 million bowlers spending ”250 million yearly in some 7,500 bowling establishments.1 And last year 16,000 participated in the American Bowling Congress championships.2 This upsurge has been attributed to the installation of auto- matic pin setters which allow twenty-four hour use of the alleys and to television which now devotes more time to bowling than to any other sport. In 1956 Chicago had seven bowling programs per week, New York had four and Detroit three.3 1957 saw 9,000 bowling hours on the air each'week.h Bowling leagues represent industry, social and fraternal clubs as well as business establishments. Country clubs are installing alleys. In many towns physically handicapped groups bowl.free and school children 11?. G. Houseman, “The Big Bowling Boom," Coronet, XLIII, (Dec- ember, 1957), 76. 2"Prosperous and Proper," Time, LKIX (April 22, 1957), 87. 3Houseman,‘gp, cit., p. 76. h"Prosperous and Proper," 32; Citg: p. 87- receive special rates. The American Junior Bowling Congress, estab- lished in 1938, now numbers 130,000 youngsters. The sport is being added to many school physical education curricula. On the nation's campuses over 200 colleges and universities sponsor intramural and inter— collegiate contests in the sport.5 With so many people learning and participating in this sport it 'would be valuable to understand the relationship of different factors to successful performance and methodology of teaching. ,Generally, it is believed that a larger, stronger person will be more successful in sports. However, in the early forties a siquear old girl, TWinkle ‘Watts, was the talk of the bowling'worhi. Rolling a ten and one—half pound ball which was one-quarter of her forty-two pound weight, she toured the country, demonstrating her ability and often averaging 150 in a three—game exhibition.6 Later that year it was reported that she had beaten the world's women's champion, Floretta McCutcheon, and'was carrying an average of 200 and a 250 top game. TIinkle had picked up the game herself in an alley where her father worked. Her first game scored 126, and she could bowl ten strings before tiring.7 This un- usual performance would seem to suggest that more than strength, per se, is important to bowling achievement. Strength is needed in holding the ball and in putting the bowling ball in.motion. Iniaddition it would seem that other factors, e.g., balance, coordination and accuracy are related to achievement. From empirical evidence it is clear that ac- S"Houseman, 2p_._cit., pp. 76-79. 6"Twinkle's Gold," Time, mm (January 19, 19h2),55. 7"Twinkle,” American Easine, chII (June, 191m), 78. curacy of aim for knocking down the pins plays an important part. Rirpose 93 the Study The purpose of the study was to determine the relationship of grip strength and accuracy measures to beginning bowling achievement of college women. This study consisted of the following determinations: 1) the intercorrelations of grip strength, accuracy and weight and the correlation of these variables with selected bowling criteria (last six game bowling scores and total term bowling average), 2) the relation- ship of strength, accuracy and strength residuals to letter grade in the bourling course, and 3) the percentage of contribution of grip strength and accuracy to the achievement of beginning bowling achieve- ment of college women. Definition 2f_ Terms Hand Dynamometer. The Narrogansett Hand Dynamometer apparatus is a spring scale device which measures the amount of pressure exerted by the hand grip. Beginnin‘g‘ Bowlers. Those women students who were registered for the beginning bowling classes and were classified beginners either by their experience and/or score. M 33111 Avergg . The individual bowling average computed for each student and based upon the total number of games rolled during the course. 2313 115 9593 Average. The individual bowling average computed for each student and based upon the last six games bowled in the course. 1:. Accuracy. The ability to roll a bowling ball over a designated spot on the alley a certain number of times. Residuals. The difference, plus or minus, between actual strength and predicted strength, using weight as the basis of predic- tion. Limitations 3f_ the _S_t_u£1_y 1. The bases upon which the letter grades were determined were not identical. In general they included final average, improvement, bowling form, written tests, and attendance. The weighting of these factors varied with the five instructors from whose classes the sub- jects were drawn. 2. Reliability of accuracy tests increases with the number of trials given. Time limited the number of trials in this study, but re- liability coefficients of .309, .119, and .195 for an'average of .208 were found between the three tests. Lack of time prevented a retesting of students on thirty more throws. 3. In setting up the devised accuracy apparatus a one-sixteenth inch tolerance in the distance of the marker from the alley floor was allowed. While the accuracy apparatus was constructed so that no ball could roll over the designated sport without moving any marker, it was possible that a ball could occasionally move two markers. This was compensated for by awarding an intermediate value of two points for such an occurrence, while three points were given for a perfect roll and only one for a slight deviation. )4. There was no way to measure the reliability of the observer. S. An attempt was made to control this limitation by having only one ob- server record for all accuracy testing. 5. Strength reliability was determined by comparing the first trial with the second. Time did not allow a retesting of two more trials which might have resulted in a higher reliability rating. 6. ‘Women may not be as highly motivated to exert maximum effort on strength tests, and thus the reliability figures for such tests are not as high as have been obtained in strength testing of men. Horwood8 got a reliability coefficient of .976 and Tinkle9 found a reliability of .802 and .838 for grip strength. 7. Weight readings were taken upon completion of the original measures. It was not possible to obtain the weight of all participating students, so the correlation of grip strength and weight and the sub- sequent analysis of grip strength residuals and letter grade were lim- ited to fewer subjects. 8Uilliam A. Horwood, ”The Relationship of Selected Wrist and Grip Strength Measures to Beginning Bowling Performance,“ (Unpublished Master's thesis, Michigan State University, East lensing, 1957), 16. 9layne F . Tinkle, "An Investigation of the Relationship Between Grip Strength and Achievement in Physical Education," (Unpublished Master's thesis, Michigan State University, East Lansing, 1956), 39. 01%me II REV IE” OF THE LITERATURE There have been many studies of the relationship of strength to performance in physical activities. Accuracy research in pmsical ed- ucation has been limited to developing valid tests and to discovering relationship of accuracy to performance. Specific investigations on the sport of bowling have not been numerous. Most of them have been con- cerned with the methodology in teaching bowling. Streggth Curetonl defined strength as the "capacity of the body to exert force on some external resistance." He believed that athletes have great need of strength in vigorous activities and that it is a funda- mental aspect of motor fitness .2 Espenchade stated in her sunnnary of the organic and neuro- muscular development of children that "muscular activity leads to mus- cular development; so that it is not surprising to find a relationship between the strength and activity."3 Lrhomas K. Cureton, ical Fitness Appraisal and Guidance (St. Louis: The C.V. Hosby mparw, I957), 3567 2mm, p. 391. 3Anna Espenchade, ”Organic and Neuromscular Development ," Children in Focus (Washington: American Association for Health, FifisicaI mucatIon and Recreation, 1951:), 56. 7. Clarkeh reported that competition in feats of strength and en- durance dates from the days of savage tribes, and similar contests have been handed down through the ages. For a time it was thought that the size of a mscle was inlicative of its power. However, Dr. Dudley Sargent found that a test of. ability to work was a better appraisal of a muscle 's power. He shifted his emphasis from the tape measure to testing strength;5 and, in 1880, he proposed a battery of tests to measure athletic ability .6 Rogers? postulated that there can be no physical activity without strength. His Plvsical Fitness Index contained a battery of strength tests . Furthermore, he concluded that ”grip strength alone responds re- markably well to changes in general physical condition.” Grip strength testing had a reliability above .90 and its validity has been estab- lished as a measure of capacity for pmrsical activity .8 From his investigations of athletic ability Rogera9 concluded that there is more than skill involved in successful perfomance in athletics. He found that skill and strength both improve through 1idem-y H. Clarke, AEElication 9g Measuranent £2 mical Educa— tion (New York: Prentice ompany, 19305, 1:55. 5 Hyman Krakower, ”Testing in Pm'sical Education," Research Quarterly, VIII (March, 1937) ,Sh. 6clerks, 22: cit., p. 155. 7Frederick R. Rogers, "The Significance of Strength in Revealing Physical Condition," Research Quarterly, V (October, 1931:), hB-hh. Braid” uh. 9Frederick R. Rogers, Fundamental Administrative Measures in msical Education (Newton, 153.: The PleIEHes Company, I957}, 13?. 8. practice and suggested that a measure of one could be called a measure of the other. Further conclusions drawn by Rogers are: 1) that strength is the most important quality in appraising athletic ability, 2) that strength can be used to equalize athletic teams and tlms pro- duce exciting and close contests, and 3) strength is a successful basis upon which to predict the outcome of league ball games .10 However, Coleman concluded that using the Rogers' strength test as a basis for classification of students for gymastics and athletics was "to classify by inference.” Nevertheless, he did state that the Rogers' test correlated .81 with his City College Athletic Index .11 In contrast Larson agreed that strength is a good predictor of motor ability. However, he postulated that I'dynamic strength is nearly three times more significant in predicting a composite index of motor ability than static, dynamometrical strength" as favored by Rogers .12 DiGiovanna'e study reinforced the claim that muscular strength is a factor associated with athletic success .13 Bovard, Cams and Wv—v—v—c—V 10mm, pp. 136-110 ‘uJames I. Coleman, "Comparison of the Rogers Test and the City College of New York Physical Proficiency Test as Bases for Classifying Stluents for Activity in Physical flotation," Research Quarterly II (lurch. 19140), pp. nut-1&9. ' ' ' - 12L. a. Ierson, u Factor and Validity Analysis of Strength Variables and Tests with a Test Combination of Chiming, Dipping, and Vertical Jump," Research Qua-nary, II (December, 191:0), 95. 13V . DiGiovanna, “The Relationship of Selected Structural and Functional Measures to Success in College Athletics," Researchguarterly XIV (lay, 191:3), 213. 9. Hagmann‘ have listed several authors who suggest strength iniices as the basis for classifying students into homogeneous groups or teams be- cause of the close relationship of strength and general motor ability. Grossls discovered that in learning a new activity - wrestling - strength has the highest correlation of all factors found in motor ed- ucability tests. llcCloy‘"6 concluded that strength stands out in nearly all analyses of the factors of motor ability variables . Furthermore, he claimed that an adequate amount of strength is needed to learn a skill at an optimum rate. Smith17 published results indicating that grip strength, added to the Carpenter Motor Ability Test, increases the prediction of motor ability in elementary school children by sixteen per cent. Strength has been found related to the choice of activities in an 18 discovered that while those en- elective program for men . Stafford rolled in less vigorous activities did not lack fundamental strength, men participating in the more strenuous sports possessed it to a greater 11‘John F. Bovard, Frederick I. Cosens and E. Patricia Hagman, Tests 313 Measurements in ¥£al Education (Philadelphia: I. B. more Company, I959) , . 15A . Gross and others, ”Relationship Between Twp Motor mucability Tests, 9. Strength Test and Urestling Ability After Eight-Weeks Instruc- tion,” Research Quarterly, mu (December, 1956), 395-h02. J’60 . H. leloy, "A Preliminary Study of Factors in Motor Educa- bility,“ Research Quarterly, II (lay, 191:0), 32. 17Jean saith, "Relation of Certain Physical Traits and Abilities to Motor learning in Elementary School Children ," Research Quarterly, XXVII (May, 1956), 220-228. ~ 1'BGeorge T. Stafford, "Guidance in Required Physical Education,“ Research Quarterly, XII (My, 19M), 278—292. 10. degree. He suggested that students with a low strength score be coun- seled to improve their weakness . Tinkle's study” gave further reason for recommerding that men with low strength be encouraged to improve it . He found that grip strength was significantly correlated with achievement in men's physical education courses at mchigan State University, as reflected in their letter grades for the courses. Carpenter20 found a definite positive relationship between strength and the general athletic performance of women. Humistonz} however, discovered that static strength, as measured by a dynamometer, showed only slight relationship to individual items in motor ability. She concluded that a good score in her tests indicated sufficient strength to meet the demands of motor situations as found in the test. In a separate study, Scott22 found that strength tests have little value in estimating the ability of college women. Anderson's23 investigation found that strength tests are not as valuable in classifying girls as they are for men. Other tests are sup— 19Wayne F. Tinkle, "An Investigation of the Relationship Between Grip Strength and Achievement in Physical Education," (Unpublished Master's thesis, Michigan State University, East Lansing, 1956), 37. 20Aileen Carpenter, "Strength, Power and F emininity as Factors Influencing the Athletic Performance of College Women," Research Quarterly, 11 (May, 1938), 121.. 2J'Dorothy Humiston, "A Measurement of Motor Ability in College Women," Research Quarterly, VIII (May, 1937), 185. 22H. Gladys Scott, "The Assessmen of lotor Ability of College Women," Research Quarterly, 1 (October, 1939), 75. 23 Theresa Anderson, ”Studies in Strength Testing for High School Girls ," Research Quarterly, VIII (October, 1937), 73. ll. erior as aids to teachers of girls physical education. She stated that this does not prove that strength is not a valuable element in predic- ting girls' athletic ability. Hand:_ey_e Coordination 2; Accuracy For many years psychologists have included measures of accuracy in tests of motor ability. Some early tests involved tapping and trac- ing. Since 1923 more of then have consisted of rolling or throwing a ball at some form of target. Salich calls hand-eye coordination a skill element needed in popular sports and has devised several tests to assess this ability. Alden, Horton and Caldwell.25 defined accuracy as one of the fundamental body skills and likewise including throwing at a target in their motor ability battery. Yarmolenko,26 Wendler27 and senseley College28 also considered hard-eye coordination of sufficient importance to motor ability to include it as a factor in their testing . 2hElizabeth P. Salit, "The Development of Fundamental Sport Skills in Freshmen College Iomen of Low Motor Ability," Research Quarterly, IV (December, 191w.) , 330-339. 2SFlorence D. Alden, Margery Horton and Grace M. Caldwell, "A Motor Abilities Test for University Women for Classification of filtering Students into Homogeneous Groups ," Research Quarterly, III (March, 1932), 26A,Yarmolenko, "The Motor Sphere of School Age Children " Peda- gggical m 51g Journal 31; Genetic P chol ,ILVIII (1933), 2987-318. 27A. J. Vendler, "Sensori-Motor Coordination as a Factor Analysis Component," Research Quarterg, 11 (March, 1938), 7S. 28lellesley College Studies, "Tests and Analysis of General Motor Ability,” Research Quartery, I! (May, 1938), h9-Sl. McCloy29 discovered that sports involving a high degree of special skill, basketball shooting for example, correlate less highly With tests of general motor ability than do activities of a more gen- eral nature, such as field and track. Nonetheless, he included a target test of accuracy in his book. He cautioned that the reliability is low unless twenty-five trials are given. Scott30 likewise has included several types of accuracy tests in her appraisal of women's motor ability. lelich31 found no relation between measures of strength and motor ability to initial status or improvement of accuracy in learning the fencing lungs. Neither was accuracy in throwing or hitting a target related to kinesthesis as measured by an arm position test.32 Bowlig Research studies investigating the best method of aim for begin- ning bowlers are contradictory. Goellner's33 study found head pin bowl- ing superior to spot or the combination point of aim. Summers ,31‘ on the 29c . H. McCloy, Tests and Measurements in Health 313 msical _sg- ucation (New York: Appleton-Century Crafts, 1917?), IE; . 3°14. Gladys Scott, 91’.- cit., p. 71. 3:lfierald Ehrlich, "The Relationship Between the Learning of a Motor Skill and Measures of Strength, Ability, Educability and Capacity," Research QuarterliJIV (March, 191:3), 147-59. 32Olive G. 'Young, "A Study of Kinesthesis in Relation to Selected Movements ," Research Quarterly, XVI (December, 19145), 277-278. 33Iilliam A. Goellner, "Comparison of the Effectiveness of Three Methods of Teaching Beginning Bowling," Research Quarterly, XXVIII (December, 1956), 386-3914. 31“Dean Summers, "Effect of Variations of Delivery and Aim on Bowling Achievement of College Women," Research Quarterly, XXVIII (March, 1957), 77-814. 13. other hand, stated that his investigation showed superior results had been obtained from the spot point of aim . Webster,35 likewise, found that bowlers aiming at a spot on the alley over ten feet from the foul line or rolling for both a spot and the pins were superior to those using other techniques. He also re- ported that a bowler whose average is in the 120-129 range may be ex- pected to receive 1.6 strikes, 2.9 spares, 1.10 splits and Id; misses per game, whereas a bowler of 180-189 class will get 3 .5 strikes, h.2 spares, 0.9 splits and 1.3 misses .36 Roloi‘f37 reported no signifith correlation betwen either kinesthesis or motor ability and final women's bowling scores. Horwood38 found that grip and wrist strength are significantly related to the be- ginning bowling performance of college men. In another study comparing the traditional and Perceptual methods of teaching bowling, Walters” used grip, arm and shoulder girdle strength plus underhand throwing ability to equate her groups of women 3SRandolph I. Webster, “Psychological and Pedagogical Factors in Motor Skill Performance as Exemplified in Bowling," Research Quarterly, II (December, 1910) , 50. 361bid., p. 51. 37Louise Roloff, "Kinesthesis in Relation to the Isarning of Selected Motor Skills," Research Quarterly, XXIV (May, 1953), 210-217. 38William A. Horwood, "The Relationship of Selected Wrist and Grip Strength Measures to Beginning Bowling Performance," (Unpublished Master's thesis, Michigan State University, East Lansing, 1957), 19. 39E‘tta C. Walters, "A Perceptual Approach to the Teaching of Bowling," Perceptual 33; Motor Skills Research Exchange, IV (March, 1952), 75- e 11:. college students . She found that bowlers whose first five lines aver- aged between lOO-llO had higher means in all four of these tests. However, the differences were not statistically significant. Similarly, the women who showed superior, good and average improvement over the course had higher means on the strength and throwing tests, but again the results were not significant. CHAP’I‘m III METHODOLCXEY A total of seventy-seven women students participated in this study . Ten students were chosen at random from each of eight women's beginning bowling classes during the winter term. Three of the classes were taught by the author. The other five bowling classes were taught by four different instructors. “bro subjects were dropped when absence or illness made complete scores impossible. All subjects were measured for grip strength and accuracy. Bowling achievement was determined by the average of the last six games bowled in the course, by the total term average, and by the letter grade received for the course. Grip strength of the bowling hand was measured by the Narrogansett Hand Dynamometer as described by Hunsicker and Montoye.1 Tm trials were given separated by a short interval of thirty seconds to one minute. The reading was recorded to the nearest pound and the best of the two trials was used for computation. Accuracy was measured with a test devised by the author. The instrument used for this measurement is depicted in Figure 1. It con- sisted of three tin markers suspended over the alley. Each marker was 1Paul A. Hunsicker and Henry J. Montoya, A lied Tests and Measurements in Mical Education (New York: Prent ce Ham-Inc ., I933), 55. .- 50.34. wdfiaom one. do pdoomwswm maaasnsez >92:on .H oaauna 17. 5/16 inch wide. The distance befieen the inner edges of the markers was one and l/h inches. The three markers hung from an iron rod which was supported by wooden frames sitting in the gutters. The apparatus was placed so that the bottom edge of each marker was between 8-1/1; and 8-5/16 inches from the alley surface. The middle marker was directly over the near edge of the second range finder arrow from the bowling side. For right-haulers this was the second from the right. For left-headers the apparatus was placed over the second arrow from the left. I The apparatus was checked before beginning each series of tests, when reversing the instrument for left-handers, and at selected times throughout the tests . The checking procedure was done with a ruler to measure distance from the alley to the marker and by plumb line for position over the arrow. The accuracy tests consisted of ten trials. The subject attempted to roll the bowling ball exactly over the designated range finder arrow. No pins were set on the alley. Subjects were instructed to aim for the marking on the floor rather than the tin markers, although the latter were visible. A ball rolling directly over the second arrow either spun or moved the middle marker and a three point value was recorded for the trial. Balls rolling a little to either side moved the outer markers and the trial received a score of one. In some cases where the ball was only slightly off the target both the middle and an outer marker moved. If one marker moved and the other spun completely around, the score of the spinning marker was given. here both either spun or 18. moved,a score of two was tallied. No score was given for a ball that did not move a marker. With ten trials composing each test, a total of thirty points for each trial was possible. Three tests were given to ' each subject. Scores on the three trials were averaged for use in the calculations. Heights of participating students were collected from them within a month of the term end. All testing was done by the author. Accuracy was measured during the eighth and ninth weeks of the term. Grip strength was taken during the ninth week with “0 exceptions as necessitated by absence. These two exceptions were obtained by the tenth week. Reliability coefficients ,2 comparing the different trials, were determined for grip strength, accuracy, and the two halves of the six game average. They were then stepped up by the Spearman-Brown Prophecy formula .3 Pearson product moment correlation coefficients’4 were calculated for grip strength and accuracy with both last six game and total term bowling average, for grip strength and accuracy, and for grip strength and weight. Correlation coefficients were corrected for attenuation.5 ZQuinn McNemar, {whological Statistics (New York: John Wiley am 30115, 1955), 1190 3'Victor H. Noll, Introduction to Educational Measurement (Boston: Houghton wflln Company, I937). o. themar, 92.: Cite, p. 1190 S J. P. Guilford, Fundamental Statistics in Pa cholo and Education (New York: McGraw Hill Book Company, E o , - o. 149. A multiple regression analysis was calculated to determine the percentage of contribution of accuracy and grip strength to bowling criteria .6 An analysis of variance7 was calculated for grip strength, accuracy and strength residuals with letter grade for the course. 60yril H. Goulden, Methodsof Statistical Analysis (New York: John Wiley and Sons, 1952 )TI‘SBZEI? CHAPTER IV ANALYSIS AND WWTATIQJ CF DATA The purpose of this study was to determine the relationship be- tween grip strength and accuracy and begiming bowling achievement. Seventy-five women from Michigan State University beginning bowling classes participated in this experiment. Data gathered on the subjects consisted of term bowling average, last six game average, grip strength, accuracy, weight, and letter grade for the course. Analysis of the 23.3.3 The data was analyzed as follows: 1) the ranges and means were determined for all variables, 2) reliability coefficients were deter- mined and stepped up by the Spearman-Brown formula, 3) intercorrelations of strength, accuracy and weight and their correlations with bowling achievement were calculated, 1;) correlation coefficients were corrected for attenuation 5) multiple regression equations and percentages of contribution for grip strength and accuracy with both six game and total term bowling average were figured, 6) strength was predicted from a re- gression equation, and 7) an analysis of variance was determined between grip strength, accuracy and strength. residuals and letter grade. 21. _Brgsentation of Findings Eggggg‘ggg‘ygggg. The data, in regard to the range and means for strength, accuracy, weight and bowling average are presented in Table I. Grip strength ranged from 314-th and had a mean of 651:8 pounds. The range of accuracy was from 6.0 to 18.7 with a mean of 11.70. The spread of the last six games ran from 82.7 to 133.0 while the range of the total term average was 67.8 to 129.2. The mean of the last six games was 101; .37, while that for the term average was 99 .51. Both the range and mean of the last six games were higher than the total term scores, indicating that improvement has taken place during the latter part of the term. The range for weight was 100.0-150.0 and the mean was 123 .91 . TABLE I RANGE AND MEANS (F GRIP STRENGTH, ACCURACY, WEIGHT AND BOILING AVMGE ‘—:—_ 1 F _‘A— A‘ Experimental Number Variable of Cases Range Mean Best Grip Strength 75 3h .0 - 10h.0 65 J48 Accuracy Average 75 6.0 - 18.7 11.70 Six Game Average 75 82 .7 - 133.0 101: .37 Total Term Average . 75 67.8 - 129.2 99.51 Weight 59 100.0 - 150.0 123 .91 22. Reliability _o_f_ Measures _o_f_ Variability. Table II shows the actual and corrected reliability of experimental variables . Comparison of the two trials on grip strength showed a reliability of .71414. Re- liability of the'three accuracy trials gave very low individual figures (.309, .119 and .195) and a low average of .208. Scores between bowling games likewise revealed great fluctuation, and comparison of the two halves of the final six games resulted in an r of .1493. By using the Spearman-Brown prophecy formula1 to extend the length of the tests three times all reliability coefficients were stepped up to yield higher figures. Thus, the average accuracy reliability rose from .208 to .h27. Grip strength reliability increased from .7141; to .897. These corrections show that the reliability of the measures of variability would have been higher had the number of cases been greater. TABLE II ACTUAL AND C(RREETFD RELIABILITY COEFFICIBVTS (1" EXPERIMENTAL VARIABLES ' Actual Corrected Variable Reliability Reliability Grip Strength .7141; .897 Accuracy Tests First and Second .309 .573 Second and Third .119 .288 First and Third .195 .1121 Average Accuracy .208 .h27 Bowling Games (split halves .1493 of six game average 1Victor H. Noll, Introduction to Educational Measurement (Boston: Houghton, Mifflin C6mpanyfl957), . 23. Relationship 2f_ Accurac , Grip Strength 199. Weight and; their Relationship with Bowling Criteria. The relationship between grip strength and bowling achievement, using both the last game and the total term average is shown in Table III. The highest correlation found was .2146, betwaen grip strength and total term average. This coefficient was significant at the five per cent level. The correlation coeffic- ient of strength and six game average was not significant (.186). This may be due to the fact that total term bowling average is a better ap- praisal of one's ability than the last six game scores. The correlation coefficients were too low to have much predictive value. However, the tendency of the correlation coefficients seems to indicate that strength may be of some value in the beginning bowling performance of college women as determined in this study. Accuracy and bowling achievement showed a relationship that was higher. The correlation coefficient of accuracy and six game average was .356 (significant at the one per cent level).2 Accuracy arxl total term average were correlated at .509 (significant at the .1 per cent level). The difference between the r's was .153. This difference was not great enough to be significant. The intercorrelation of accuracy and grip strength variables was found to be quite low (.005). This low correlation coefficient seems to indicate no relationship between strength and accuracy as measured in this study. ‘— 2Quinn MzNemar, Psychological Statistics (New York: John Wiley am 30118, Inc.’ 1955), 3 - 0 2140 Weight and grip strength in this study showed a correlation of .280 (significant at the five per cent level). TABLE III C(RREIATIONS a“ EXPERIMBVTAL VARIABLES WITH BOWLING CRITERIA AND THEIR INTFRCORREIATIQVS — ____ ._ ._ —_ .v_. - -,__,-..-., ,__.._...___.- -v .— Experimental Six Game Total Term Strength Variables Average Average Strength .186 2146* --- Accuracy .356” 509*“ .005 Weight 280* *significant at the .05 level “significant at the .01 level “significant at the .001 level The low reliability of the variability measures could have been responsible for the low correlations between the variables and bowling achievement. To see what these relationships would be if the strength and accuracy measures were perfectly reliable, the correlation coeffic- ients were corrected for attenuation .3 The attenuated scores showed a relationship of .285 for grip strength and total average and .306 with the six game scores. Accuracy and total term average gave an attenuated coefficient of 1.111, while accuracy and six game average also resulted in an attenuated r of 1.111. The fact that these last two corrections are greater than 1.00 is probably due to the fact that the original 3.1. P. Guilford, Fundamental Statisti_c§ in Pa chol 3199. Education (New York: McGraw-EEII Book Company, 1950, - . 25. reliability of the accuracy test was so 10W. It also indicates, as might be expected, that there is a high theoretical correlation between accuracy and bowling. The differences between actual and attenuated correlation coefficients appear in Table IV. TABLE IV ACTUAL AND ATTENUATED CORRELATION COEFFICIENTS BETWEEN GRIP STRHVGTH AND ACCURACY AND BG’ILING ACHIEVEMENT Variables Actual Attenuated Correlation Correlation Grip Strength and Six Game Average .186 .306 Grip Strength and Total Average .2146 .285 Accuracy and Six Game Average .356 1.111 Accuracy and Total Average .509 1.111 Multiple Reggession Analysis . The multiple correlationh of strength and accuracy with the criteria of bowling achievement as well as their percent of contribution appear in Table V and Table VI. A multiple R of .14008 was calculated between final six game average and the two variables, grip strength and accuracy. This correlation is statistically significant at the .1 per cent level. Strength contrib- uted 21.2 per cent and accuracy 78.8 to the predictive variance. Ac- curacy would seem to be nearly four times as valuable in predicting bowling achievement of women. In comparing the variables with total term 1‘Charles C. Peters and Walter R. Van Voorhis, Statistical Procedures and their Mathematical Bases (New York: McGraw-HiII Book Company, 1910) {7263231. 26,. average the nnlltiple R was found to be 56111. This was also significant at the .1 per cent level. For this comparison strength contributes 18.8 per cent to bowling achievement and accuracy 82.2 per cent. From the results of this analysis it again appears that accuracy is four times as valuable as strength in predicting women's bowling scores . TABLE V MULTIPLE RMRFSSICN ANALYSIS RESULTS WITH FINAL SIX GAME AVDIAGE AS BOWLING CRITERIA kperimental B 32 Per Cent of Variables Contribution Strength .18h3 .03h0 21 .2 Accuracy .3551 .1261 78 .8 .1601 100 .0 R - .1008 (significant at the .001 level) TABLE VI MULTIPLE REGRESICN ANAHSIS REULTS WITH TOTAL TERM AVERAGE AS THE BONLING CRITEUA Experimental 2 Per Cent of Variables B B Contribution Strength .21135 .0593 18 .7 Accuracy .5078 .2579 81.3 .3172 100 .0 R - .56141 (significant at the .001 level) 27. Angysis o_f_ Grip Stre th, Accuracy _a_r£i_ Strength Residuals and Letter Grade. The ranges and means of experimental variables according to each letter grade group appear in Table VII. The means of each letter grade group reveal that the mean strength of the A students was considerably higher than that of both the B and C groups. The differ- ence between the means of the B and C groups was less marked. Again, the lower the mark the lower the strength score. 01‘ the three groups the 0 students had the greatest range. Thus, the results of this study show that the higher the course grade the higher the grip strength. The accuracy scores likewise increased with letter grade. A students had the highest mean accuracy score with the B students next. In this comparison the greatest difference was found between the means of the B and C groups. The ranges are not considerably different in the three grade levels. The greatest range is found among the group of students receiving an A. An additional strength measure was obtained on sixty of the sub- jects by predicting grip strength from weight. The following line of regression was derived from the correlation data: X' - .3h2y + 23 .14114, where X' =- predicted grip strength in pounds and y - weight in pounds. Then the predicted strength was compared with the actual grip strength for each subject. If the actual strength was above the predicted strength a plus residual was recorded. If the predicted strength was higher than the actual, a negative residual was tallied. The grip strength residuals showed an increase with the letter grade. Those students receiving a C had a mean residual of -l.140, meaning that their strength was 1.140 pounds less than their predicted 28. strength. The mean of B Students was -1 .01. That of the A group was 8.146, imiicating that they had developed their strength 8.146 pounds more than was predicted . Study of the ranges showed that the C students showed the greatest divergence, and the spread of the range decreased as the letter grade increased . TABLE VII RANGE AND MEANS OF STRDIGTH AND ACCURACY MEASURES (F LETTHi GRADE GROUPS I ! Number Variable of Cases Range Mean Strength of A Students 11 51.0 - 914 .0 73.36 Strength of B Students 32 311.0 - 89.0 65.36 Strength of C Students 32 26.0 - 1d; .0 63.72 Accuracy of A Students 11 8.0 - 18.7 12.79 Accuracy of B Students 32 7.0 - 15 .3 12.dl Accuracy of 0 Students 32 6.0 - 16.3 10.99 Residual of A Students 11 41.7 - 33 .3 8.1.16 Residual of B Stlxienta 23 -28 .7 - 21A .5 -l .01 Residual of 0 Students 26 -31.9 - .32 .7 -1.h0 An analysis of variance was calculated for over-all comparison of these variables. Table VIII sumarizes the f ratios of letter grade and grip strength, accuracy and grip strength residuals . Grip strength gave an f ratio of 2.33 and accuracy one of 2.69. The f ratio of grip strength residuals was 2.1:3 . Since none of these was significant at the five per cent level5 no further analysis was made. While these figures were not significant, it is interesting to note the trend of gMcNamar, 92, cit., PP. 389-391. 29. higher scores in all three variables as the letter grade increased. Thus, although there is almost as much variance within each letter grade group as there is between grade levels, it appears that students with greater strength, regardless of weight, and those who are more accurate will attain higher grades. TABLE VIII F RATIOS (1" LETTER GRADE AND GRIP STRENGTH, ACCURACY AND GRIP STRENGTH REIDUAIS - ‘J Variables f Ratio 1 Grip Strength and Letter Grade 2.33 Accuracy and Letter Grade 2.69 Grip Strength Residuals and Letter Grade 2.b3 sum, mum's, RECOMlm'NDATIGVS AND CONCLUSIONS Summagy Seventyqfive'beginning'women'bowlers'were selected from eight instructional classes at Michigan State University to participate in a study comparing grip strength and accuracy measures with beginning bowling performance. The measures obtained were grip strength of the bowling hand, accuracy score in ability to roll a bowling ball over a selected spot on the alley, and weight. The bowling criteria were the final six game scores, the bowling average.for the total term and the letter grade for the course. Statistical analyses done were intercor- relations of grip strength, accuracy and'weight, and correlations of these variables with the bowling criteria. Analyses of variance were calculated for the variables and letter grade. A multiple regression 'was done to determine the percent of contribution of strength and ac- curacy to bowling criteria. Results The results are as follows: 1. Grip strength is significantly related (at the five per cent level) to total term bowling average of beginning college ‘women. It was not significantly related to the last six game average. 2. Accuracy is significantly related (at the one per cent level) to the bowling achievement of beginning women'bowlers as 31. measured by both total term and last six game average. 3 . Accuracy and total term average show the greatest relation- ship. A. Grip strength and accuracy show no relationship. 5. Weight and grip strength are significantly related. 6. Accuracy contributes three to four times as much as grip strength to the beginning bowling achievement of college women. 7. The relationship of grip strength, grip strength residuals and accuracy to letter grade in the beginning bowling achievement of college women is not statistically significant. However, comparison of the mean scores indicated that those students receiving a higher grade had a higher score in strength and accuracy. . 8. The mean scores in grip strength and strength residuals showed a greater divergence between the B and C levels. The accuracy means revealed a greater difference between the B and 0 student. 9. Bowling averages increase during a ten week term. The last six game average is higher than the total term average. Conclusions Within the limits of this study it was found that: 1. Grip strength and accuracy are important factors in begin- ning bowling performance of college women, as determined by bowling scores . 2. 3. 32. Accuracy shows a consistently higher relationship to bowling performance than strength. Strength and accuracy are not statistically related to beginning bowling performance as determined by letter grade for the course. The trend is for students receiving a higher grade to rate higher in both strength ard accuracy. Recomendations The following recommendations are made for additional study of grip strength, accuracy and beginning bowling performance: 1. An investigation of the relationship of grip strength to achievement in other women's physical education classes might show whether each student should be counseled to meet a strength minimum before enrolling in elective activities. 2. A similar study of the relationship of accuracy to bowling achievement could be conducted in men's classes to see if accuracy, like strength, shows a higher relationship with men than with women. An investigation to determine the relationship of balance, hand-eye coordination and power might prove valuable. Further investigation of the accuracy test involving a greater number of trials might improve its reliability and increase its validity as a testing or teaching device. Comparison of the bowling scores throughout a term might reveal a relationship like or unlike that of consecutive accuracy tests . 33. 6 . Measuring accuracy and grip strength throughout the term would show if they increased with bowling experience, and might show how their relationship to bowling score changes with practice. 7. The results of this study seem to indicate that student performance in beginning bowling might be improved by having students analyze and improve their accuracy through practice sessions of rolling the ball over a selected spot on the alley . BIBLICGRAHH BOOKS Bovard, John F., Frederick W. Cozens and E. Patricia Hagman. Tests and Measurements _ig ical Education. Philadelphia: T713. SaundErsTompany, . Clarke, Henry H. Amlication 21; Measurement _tfi Health and flysical Eiucation. New or : entice Hall, Inc., I955. Cureton, Thomas K. tifflysical Fitness A raisal and Guidance. St. Louis: The . . osby Compamr, I957. _— Espenchade, Anna. "Organic and Neuronmscular Development ," Children in Focus. Washington: American Association for Hummm Question and Recreation, 1951:. Goulden, Cyril H. Methods 21; Statistical M. New York: John liley ani Sons, I935. Guilford, J. P. Fundamental Statistics in Psychoggz and Education. New York: l9§0. Hunsicker, Paul A. and Henry J. Montoye. A lied Tests and Measure- ments _in_ Mical Education. New York: Prentice Hall: Inc. McCloy, Charles H. Tests and Measurements in Health and Elysical Education. New York-lfipletonZentury-Crofts, Inc., 9 . McNemar, Quinn. Psgchological Statistics. New York: John Wiley and $0118, Inc 0’ 9 Noll, Victor H. Introduction to qucational Measurement. Boston: Houghton MiffIin Tompany ,1??? Peters, Charles C. and Walter R. Van Voorhis. Statistical Procedures and their Mathematical Bases. New York: McGrawleII Book Wm, 191:0. Rogers, Frederick R. Fundamental Administrative Measures 3 msical Education. Newton, Mass.: The PleiadEs Company, I537. PERIODICALS Alden, Florence D. , Margery Horton and Grace M. Caldwell. “A Motor Ability Test for University Women for Classification of filtering Students into Homogeneous Groups ," Research Quarterly, III Anderson, Theresa I . "Student Strength Testing for High School Girls," Research Quarterly, VIII (October, 1937). 69-73. Carpenter, Aileen. ”Strength, Power, and Femininity as Factors In- fluencing the Athletic Performance of College Women," Research Quarterly, I! (May, 1938), 120-127. Coleman, James I. “Comparison of the Rogers' Test and the City College of New York Pkwsical Proficiency Test as Bases for Classifying Students for Activity in Pmical Education," Research Quarterly, XI (March, 191:0), -1h9. DiGiovanna, V. "The Relation of Selected Structural and Functional Measures to Success in College Athletics," Research Quarterly, XIV (May, 191:3), 199-216. "'""""" Ehrlich, Gerald. "The Relationship Between the Learning of a Motor Skill and Measures of Strength, Ability, Educability, and Cap- acity,“ Research Quarterl , XIV (March, 19143), h7-59. Goellner, William A . "Comparison of the Effectiveness of Three Methods of Teaching Beginning Bowling " Research Quarterly XXVI (Decanber, 1956), 383-391;. ’ ’ Gross, E. A . and others . "Relationship Between Two Motor Educability Tests, a Strength Test, and Wrestling Ability after Eight-weeks Instruction," Research Quarterly, XXVII (December, 1956) , 395- 1:02. Housman, W. G. ”The Big Bowling Boom," Coronet, XLIII (December, 1957)) 76-790 Humiston, Dorothy. "A Measurement of Motor Ability in College Women," Research Quarterly, VIII (May, 1937), 181-185. Krakower, Hyman. "Testing in nysical Education," Research Quarterl , VIII (March, 1937), 514-67. """"‘"“ Larson, L. A. "Strength and Motor Ability," Research Quarterly, XI (December, 191:0), 82-95. 37. McCloy, Charles H. "A Preliminary Study of Factors in lbtor Educa- bility," Research Quarterly, II (May, 191:0), 28—39. "Prosperous and Proper," Time, III! (April 22, 195?), 87. Rogers, Frederick R. ”The Significance of Strength in Revealing mcal Condition," Research Quarterly, V (October, 19314), 3 . Roloff, Louise. "Kinesthesis in Relation to the Learning of Selected Motor Skills," Research Quarterly, XXIV (May, 1953), 210-217. Salit, Elizabeth P. "The Development of Fundamental Sport Skills in Freshmsn College Women of Low Motor Ability ," Research Quarterly, XV (December, 191414), 330-339. Scott, M. Gladys. "The Assessment of Motor Ability of College Women," Research Quarterly, I (October, 1939), 63-83. Smith, Jean A. "Relation of Certain Physical Traits and Abilities to Motor Learning in Elementary School Children," Research Quarterly, XXVII (May, 1956), 220-228. Stafford, George T. "Guidance in Required Physical Education," Research Quarterly, XII (May, 191.1), 278-292. Summers, Dean. ”Effect of Variations of Delivery and Aim on Bowling Achievement of College Women," Research Quarterli, XXVIII (March, 1957), 77-8140 uWinkle," Anerican Eazine, CXXXIII (June, 191:2), 78. "Twinkle's Gold," Time, XLIX (January 19, 191:2), 55. Walters, Etta C . "A Perceptual Approach to the Teaching of Bowling," Perceptual 3d Motor Skills Research mohaggg, IV (March, 1952) - 9 . Webster, Randolph W. "Psychological and Pedagogical Factors Involved in Motor Skill Performance as manplified in Bowling," Research Quarterly, XI (December, 19140), 1:2-52. Wellesley College Studies. "Tests and Analysis of General Motor Ability," Research Quarterly, IX (lay, 1938), 139-51. lendler, A. J. "Sensori-Motor Coordination as a Factor Analysis Component," Research Quarterly, IX (March, 1938), 611-76. Yarmolenko, A. "The Motor Sphere of School Age Children," Pad 0 ical Swim and Journal _o_f_ Genetic Psychology, XLII (19331, 3985313. 38. Young, Olive G. HA Study of Kinesthesis in Relation to Selected M0vements," Research Quarterl , XVI (December, 19h5), 277-287. UNPUBLISHED MATERIALS Herwood,'William A. "The Relationship of Selected Wrist and Grip Strength measures to Beginning Bowling Performance." Un- published Master's thesis, Michigan State University, East Lansing, 1957 . Tinkle, Wayne F. HAn Investigation of the Relationship Between Grip Strength and Achievement in Physical Education." Unpublished master's thesis, Michigan State University, East Lansing, 1956. APPDVDIX 1:0. N. NS N m. NS N. NH N N . N N. N. N. NN .3 m. cm N 0. m2 N. .n am N . :N N. d H. N Na N. :2 N N. N: N. N NN N . N N. NN N. NN mNN m. NS 4 N. NH N. N a N . NN N47 N. NN mi N. NN N N. N: m. NH R N .HN N. d? N. N NE N. N2 N m. .3 N. S Nm N .8 N. N: N. N NS m. NN N N. NN N. NH an N . S N. N N. N N." m. NS N N. Na N. S NN N . 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