v rv-V— THE EFFECTS 0? A PROGREEWE WHGHT TWMNG fiROGRAAt ON COMPETETW‘E 3MKETBALL REBOUNDING AND QN THE TIBIAL YUBEROSWY 01’ COLLEGEATE BASKETEALE. PLAYERS Thais far flu Degree of M. A. MECHIGAR STATE UN’NERSKTY Everast Paul Smith 1963 I::7@imjngmmyflmmnlnm mi; Mtgexmzy BUREAU OF ED'l-i“.1;.;.‘,L 1' . 43K CGL‘.':Z'.--‘: L E ii i.s,.- . a; Micrzuars 1: um” .uv EAJI thomu, imUHmAN ABSTRACT THE EFFECTS OF A PROGRESSIVE WEIGHT TRAINING PROGRAM ON COMPETITIVE BASKETBALL REBOUNDING AND ON THE TIBIAL TUBEROSITY OF COLLEGIATE BASKETBALL PLAYERS by Everest Paul Smith Statement of the Problem The study possessed a threefold purpose, namely: (1) to establish a workable method to correlate competitive basketball rebounding ability with the improvement of vertical Jumping ability derived from weight training; (2) to calculate said correlation for active collegiate basketball players; and (3) to deter- mine if there is any adaptive, calcification area change at the tibial tuberosity when said insertion is exposed to stresses between 1000 and 5000 poundals. Methodology In the rebounding study, four Michigan State University varsity basketball players--two centers and two forwards--were used as subjects. Two of these athletes, one from each mentioned position, were experimental candidates in a weight training program; the other two athletes were controls. This program was designed to increase vertical Jumping ability, and it Everest Paul Smith was conducted four days per week during the last two months of the basketball season. All subJects were given the Sargent Jump Test each Thursday; and their competitive rebounds were Judged on a work per unit time basis. During twenty-two basketball contests, both the number of clean rebounds secured and the amount of time played were recorded for all subJects. Individual weekly means of rebounds per minute were compared with weekly Jumping ability; and these data were analyzed by rank correl- ation. In the tibial tuberosity investigation, five Michigan State University basketball players were used as subJects. These athletes were on a sixteen week, weight training program. Instead of control subJects, the controlling factor was the progression of weight handled in the three-quarter knee bend exercise. During the training program, each subJect had four knee-lateral x-rays of both legs. To limit the tibial tuberosity area for each leg x-ray, two common reference points were located on the anterior crest of the tibia and were situated approximately a half inch above and below the tuberosity. The area between these limiting points was measured with a compensating planimeter. The variation of tuberosity area was determined by comparing the four x-rays within the same series; and because a subJect's tubercle area variation was so minute, the group mean was calculated for an Everest Paul Smith individual‘s combined right and left tuberosity areas. These data were statistically analyzed with the analysis of variance. Conclusions SubJect to the usual limitations of sample, type of training program and methodology, the following con- clusions were drawn: (1) the improvement of vertical Jumping ability and competitive rebounding ability can be statistically correlated when the weight training program is conducted during the basketball season, and when compet- itive rebounds are considered on a work per unit of time basis; (2) this study found no statistical correlation between vertical Jumping improvement and competitive re- bounding performance exhibited during the last eight weeks of a collegiate basketball season; and (3) there is no calcifiably, distinguishable area change at the tibial tuberosity when said insertion is subJected to a six- teen week, weight training program which featured a gradual progression of stresses ranging from 1000 to over 4500 poundals. THE EFFECTS OF A PROGRESSIVE WEIGHT TRAINING PROGRAM ON COMPETITIVE BASKETBALL REBOUNDING AND ON THE TIBIAL TUBEROSITY OF COLLEGIATE BASKETBALL PLAYERS By Everest Paul Smith A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTERS OF ARTS Department of Health, Physical Education, and Recreation 1963 n/-m)vv ‘j/'0U,/’2 41¢? PREFACE This researcher is indebted to many peOple for the successful completion of his study. Thanks should be extended both to Mr. Thomas Weede, M. A., for his expert supervision of the sixteen week, weight training program, and also to the athletes who worked under his charge. Much credit for the findings of this investigation should go to Coach Forrest ”Forddy" Anderson, Head Basketball Coach of Michigan State University, for, when allowing the members of his team to train with weights during the actual basket- ball season, Mr. Anderson publically rendered a vote of confidence to the system of progressive weight training. Dr. James Feurig, M. D., Director of Michigan State University Health Service, willingly gave his professional advice concerning the x-ray study, and special thanks are also in order to the members of the roentgenological department of the Health Service HOSpital. Dr. Wayne VanHuss, Ph.D., Director of the Human Energy Laboratory at Michigan State University, acted as special advisor for the bone study. Dr. Roy Niemeyer, Ph. D.,Associate Professor of Health, Physical Education and Recreation, was the official advisor for this author's graduate program; Dr. Niemeyer, a friend as well as an advisor, always made himself available when needed. 111 Many, many thanks and much credit for my Master's Degree must go to Lorraine, my beloved wife; for without her help, understanding and confidence, I surely could not have achieved this academic goal. In addition to homemaker, mother and registered nurse, she willing accepted the added responsibility of expertly typing this and all my graduate papers. TABLE OF CONTENTS Chapter Page I. INTRODUCTION. . . . . . . . . . . . . . . . . 1 Justification for the Rebound Study. . . . . 3 Justification for the Tibial Tuberosity ; Study. . . . . . . . . . . . . . . . . . . 4 Limitations of the Rebounding Analysis . . . 6 Limitations of the Tibial Tuberosity Investigation. . . . . . . . . . . . . . . 7 Statement of the Problem . Definitions. . . . . . . . . . . . . . . . . 8 II. REVIEW OF LITERATURE. . . . . . . . . . . . .12 Review of the Literature for the Rebounding Analysis. . . . . . . . . . . .12 Review of the Literature for the Tibial Tuberosity Investigation. . . . . .15 III. METHODS OF RESEARCH . . . . . . . . . . . . .21 Source of Data for Rebounding Study. . . . .21 SubJects for rebounding analysis . . . . .21 Experimental procedure for rebounding analysis . . . . . . . . . . . . . . . . .22 Chapter IV. V. Statistical technique for rebounding analysis. . . . . . . . . . . . . . . Source of Data for Tibial Tuberosity Study . . . . . . . . . . . . . . . . SubJects for tibial tuberosity investigation . . . . . . . . . . . Special equipment used in tibial tuberosity investigation. . . . . . . Experimental procedure for tibial investigation . . . . . . . . . . . . Statistical technique for tibial tuberosity analysis ANALYSIS AND RESULTS OF DATA . . . . . Analysis of Rebounding Data Results of Rebounding Data. Analysis of Tibial Tuberosity Data. Results of Tibial Tuberosity Data SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. Summary of Research . Conclusions for the Rebounding Analysis Conclusions for the Tibial Tuberosity Investigation . Research Recommendations. Page . .24 .24 .24 .26 . .26 .35 .36 .37 .41 .45 .46 .47 .47 .49 .50 Chapter Page BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . 51 APPENDIX A. A Description of Mr. Weede's Progressive Weight Training Program . . . . . . . . . . . . . . 55 APPENDIX B Determining the Amount of Stress Sustained at the Tibial Tuberosity. 58 APPENDIX C Anatomical Diagram of the Human Knee (Lateral View) . . . . . 52 APPENDIX D Supplementary Tables. . . . . . . . 64 APPENDIX E Rank Correlation of Vertical Jumping Versus Competitive Rebounding. . . . . . . . . . . . . 72 vi LIST OF TABLES Table Page I. Analysis of Variance Results: Vertical Jumping Performance. . . . . . . . . . . 40 II. Analysis of Variance Results: Rebounding ' Performance. . . . . . . . . . . . . . . 40 III. Analysis of Variance Results: Tibial Tuberosity Area Variation. . . . . . . . 46 IV. Individual and Group, Mean Vertical Jump Performances Demonstrated During an Eight Week Testing Period . . . . . . 65 V. Individual Work (Rebounds Per Minute) Performed by the Experimental Group During an Eight Week Period. . . . . . . 66 VI. Individual Work (Rebounds Per Minute) Performed by the Control Group during an Eight Week Period . . . . . . . . . . 68 VII. Individual Tibial Tuberosity Area Measurements . . . . . . . . . . . . . . 70 VIII. Mean Measurements for Both Individual and Groups, Combined Right-Left Tibial Tuberosity Areas. . . . . . . . . 71 IX. Rank Correlation for Experimental SubJect Chandler: Vertical Jumping Versus Competitive Rebounding. . . . . . 73 viii Table Page X. Rank Correlation for Experimental SubJect Thomann: Vertical Jumping Versus Competitive Rebounding. . . . . 74 XI. Rank Correlation for Control SubJect Berry: Vertical Jumping Versus Competitive Rebounding. . . . . 75 XII. Rank Correlation for Control SubJect Williams: Vertical Jumping Versus Competitive Rebounding. . . . . 76 LIST OF FIGURES Figure l. X-Ray View Box with a Visable Knee- Lateral Film. . . . . . . . . . . . . . Technique for Knee-Lateral X—Ray. . . . . Close-up of Leg Position for Knee- Lateral X—Ray . . . . . . . . . . . . . Otto Compensating Planimeter Positioned with X-Ray Film . . . . . . . . . . Working Arrangement for X—Ray Film, Planimeter and Magnifying Glass . . . . Group Mean Scores of Weekly Vertical Jumps . . . . . . . . . . . . . . . . . Group Mean Scores of Weekly Rebounds Per Minute. Relationship Between Individual Rebounding Scores and Vertical Jump Scores (Based on Data for Experimental SubJect Chandler). Relationship Between Individual Rebounding Scores and Vertical Jump Scores (Based on Data for Experimental SubJect Thomann) . . . . . . Page 39 42 , 42 Figure 10. ll. l2. l3. 14. Page Relationship Between Individual Rebounding Scores and Vertical Jump Scores (Based on Data for Control SubJect Berry). . . . . . . . . . . . . 43 Relationship Between Individual Rebounding Scores and Vertical Jump Scores (Based on Data for Control SubJect Williams) . . . . . . . . . . . 43 Individual Means of Combined, Right and Left, Tibial Tuberosity Areas as Compared with Weight Extended. . . . 44 Group Means of Combined, Right and Left, Tibial Tuberosity Area Variations as Compared with weight Extended. . . . . . . . . . . . . . . . 44 Anatomical Diagram of the Human Knee (Lateral View). . . . . . . . . . . . . 63 CHAPTER I INTRODUCTION Research in the area of weight lifting is far from exhausted. Besides improving muscular power perforamnce, what are the other effects of a well planned, progressive weight training program? What is the relationship between a weight lifter‘s psychological and physiological limits? Is there any correlation between the progression of weight handled and the performance improvement rate? How do the areas of muscle insertion and origin adapt to the stress of overload? To what degree does the newly attained muscular power improve specific athletic performance? What effect does power training have on the speed of muscular contraction, on motor coordination, on body flexibility, on physical endurance? These and many other inquiries have been asked, and are still being asked and solved by investigators in the fields of physical therapy, education, and athletics. During the winter and spring of 1962, Mr. Thomas Weede, M. A.,1 conducted a highly controlled, progressive weight 1 Thomas D. Weede, "The Effect of a Controlled Weight Program on the Vertical Jump” (unpublished Master's thesis Michigan State University, East Lansing, Michigan, 1962), p. 25. training research program at Michigan State University. The purpose of his training program was to stress specific leg muscles so as to improve the vertical Jumping ability of six collegiate basketball players. The first eight weeks of the training occurred during the latter half of the 1961-62 Big Ten basketball season. Mr. Weede's research plan demanded three specific weight lifting exercises, as well as a progression of weight which was gradually added with each exercise session over a period of sixteen weeks; for a complete description of the weight training syllablus, refer to Appendix A. So as to detect the possible onset of pathology caused by the tremendous amount of weight handled (over 300 pound), the trainees were exposed to a series of four separate knee x-rays, strategically spaced throughout the training period. Such a controlled weight program afforded the oppor- tunity to investigate the following inquires: (1) What effect would such training have on a basketball player's competitive rebounding performance? (2) Would the tibial tuberosity (area of insertion for the quadriceps femoris muscles) become larger through calcification as a means of adaptation to the tremendous stress of muscular over- load? Obviously, the above two tOpical questions only have the weight training program in common; and consequently their explications shall be conducted on an individual basis throughout the greater part of this thesis. Justification for the Rebound Study Weight programs as used in basketball today are designed primarily to improve an athlete‘s vertical Jumping potential, so that in getting this athlete higher in the air, he would be afforded a better opportunity to control Jump balls, as well as offensive and defensive rebounds. Basketball coaches logically reason that if a player's ability to Jump in a vertical direction is increased by three or four inches, and if said player is conscious of his preparatory rebounding position and take-off timing: he should be able to secure more rebounds than he would had he not improved in Jumping skill. Prior to this investigation however, there had been no publication of significant research supporting or reJecting such a hypothesis, that is, there is no evidence of a statistical correlation between increased Jumping ability and competitive rebounding ability. The reason for this lack of statistical evidence might be partially related to methodology, in that the conditioning weight programs for basketball have been employed mostly before, and sometimes after, the official competitive season. When a study for such relationships had been made,2 the Jumping data and the rebounding data were not gathered during the same period of time, and con- sequently the numerous variables introduced by the element 28. Burnham, "DevelOp Your Rebounders with Weight Training," Scholastic Coach, XXX (December, 1960), pp. 16-26. of time actually rendered the opinionated findings unreliable. With these thoughts in mind, this study features the twofold purpose of both establishing a workable and reliable method of correlating vertical Jumping ability with competitive rebounding ability, and also to determine such a correlation for an eight week training program. Justification for the Tibial Tuberosity_Study Regarding the fracture of avulsion and how it is most commonly seen at the tibial tuberosity, Dr. Stein, M. D.3 asserted: "The amount of stress sustained at the tibial tubercle surpasses that of any other tendinous attachment to bone." This quotation becomes practically an understate- ment when one realizes that, as the tibia moves from a state of flexion to extension, all the contractile force of the quadriceps group is applied at the tibial tuberosity. The force sustained at this attachment point is literally phenominal. For purposes of illustration, assume than an average adult, male patient is sitting on the edge of a table so that both tibias are hanging downward toward the floor, and that evenly strapped between the patient's feet is a one hundred pound weight. In order for this subJect to raise his lower legs out and up, the tibial tuber- osities of both legs must sustain well over 1500 poundals 3I. Stein, R. 0. Stein, and M. L. Beller, Living Bone in Health and Disease (Philadelphia: J. B. Lippincott Co., 1955), p. 393. of force (for the anatomical and trigometrical explanation refer to Appendix B). The three quarter knee bend executed with weights produces exactly the same effect as mentioned above when said exercise is performed with the feet in a parallel stance and the weight load is resting evenly on the subJect'S shoulders. This exercise was executed twelve times per training session during Mr. Weede‘s weight training program. At the commencement of this training, all subJects started with the same weight load of one hundred—five pounds; their poundage was gradually increased so that during the last two weeks of the program the knee bend exercise was per— formed with over three hundred pounds of resistance. This means that toward the end of the training, all tibial tuberosity areas resisted over 4500 poundals of force each time the subJect straightened up from the modified squat position. How does the normal tibial tuberosity sustain such a tremendous stress? The exact answer is still unknown. However, it is commonly recognized by medical research authorities that human organic tissue will react to inJury and prolonged pressure by a deposition of calcium salts on and around the affected area.br Some scientists theorize 7v T—v a F. C. McLean, and M. R. Urist, Bone (Chicago: University of Chicago Press, 1955), pp. ISO-181. that continued strain at the origins and insertions of muscles causes adaptive calcification with a consequent thickening of these attachment areas.5 Since four serials of x-ray knee-laterals constituted a safety feature in Mr. Weede's program, it was felt that these films should be examined for tibial tuberosity area change caused by adaptive calcification; and that if said change were observed, then the subJects should be exposed to a later series of x—rays to determine if such change constitutes a longitudinal adaptive effect of exercise. Limitationsof the Rebounding Analysis The unavoidable limitations of this research were as follows: 1. Due to the official termination of the basketball season, this study covered only the first eight weeks of a sixteen week, weight training program. At the end of the playing season, the mean increase in vertical Jumping ability for the experimental subJects was 1.95 inChes; while at the completion of the weight training program, this same mean had progressed to 5.75 inches. 2. The vertical Jump measurement data was derived only from the Sargent Jump Test. 5Arthur H. Steinhause, "Chronic Effects of Exercise," PhysiologicalWReviews, XIII (January, 1933), pp. 146—147. 3. Previous experience in rebound testing and/or weight training was not a factor in this study. 4. The competitive playing time was not equal for each subJect, since Coach Anderson employed his team according to the dictates of the game situation. 5. There was no control over the sleep, diet, nor daily living habits of the subJects other than the basket— ball team training rules. 6. The number of subJects was four. Limitations of the Tibial Tuberosity Investigation The unavoidable limitations of this study were as follows: 1. When positioning for an x-ray knee—lateral view, the angle at which the knee is flexed is a close approximation of thirty degrees. Because of the understandable variation in length and especially width of individual bone formation, this angle might vary slightly (one or two degrees) for each subJect. 2. Even though this investigation covered a nineteen week period, none of the experimental subJects had experienced exercise with maximum weight load. 3. The individual body type was not a factor. 4. There was no control over the diet of the subJects; calcium intake was assumed equal since all these athletes ate at the same training table. 5. The number of subJects was five. 6. Because of the financial burden of x-ray costs, no control subJects were utilized. Instead, the controlling factor was the amount of weight pressed during the three quarter knee bend exercise. Statement of the Problem This research was designed to study the effects of a progressive weight training program on basketball rebounding ability and on the calcification of the tibial tuberosity area. The study had A threefold purpose, namely: (1)to define a reliable research method which would permit a statistical correlation between rebounding ability and developed vertical Jumping ability; (2) to calculate the correlation between vertical Jumping performance and actual, competitive, rebounding performance exhibited during an eight week period; and (3) to determine if there is any adaptive area change from calcification of the tibial tuberosity, when said insertion point is exposed to stresses between 1000-4500 poundals of force. Definitions l. The term rebound denotes a basketball which bounces from the basket rim and/or backboard when a goal is not scored. Only "clean” rebounds——that is those FebOUHdS secured by a player before said ball touched the court floor-- were considered in the correlation investigation. 2. The expression weight training as used in these studies, denotes a routine of three specific exercises performed with heavy barbells and dumbells. Progressive weight training means that five pounds of weight is added to the barbell each scheduled day that a subJect performs said exercises. I 3. The term maximum weight load, as used in the tuberosity study, denotes the amount of weight which could be handled prOperly for a specific number of repe— titional exercises. The weight training schedule demanded two sets of the same exercise, and six repetitions per set. When, during the second set, a subJect could only perform five or less of the required six repetitions, then he was said to be experiencing a maximum weight load. All subJects started training with 105 pounds; the train- ing schedule dictated that five pounds be added each training session until maximum weight load would be a- chieved. At this time, no more weight would be added and the trainee would continue to work with that poundage until he was able to perform the required two sets of six repetitions during two successive training sessions. Then five more pounds would be added thereby establishing a higher and new maximum weight load. It is interesting to note that throughout the entire sixteen week training period, not one subJect ever reached a maximum weight load; 10 yet all subJects, on the last training day, had progressed to the point where they were exercising with 330 pounds of weight. 4. The tibia is the larger of the two leg bones, commonly called the shinbone. The upper end of the tibia, as referred to in this research, denotes the anterior Junc- tion of the epiphysis and the tibial shaft. The tibial tuberosity, or tubercle of the tibia, is a raised, roughened, oblong prominence on the anterior surface of the tibia about an inch below its upper end; this tuberosity gives attach- ment to the ligamentum patellae, see Appendix C, Figure 14. 5. The word calcification as used in the bone inves- tigation, denotes the process by which cartilagenous and osseous tissue, located on or around the tibial tuberosity, becomes hardened by the deposition of calcium salts within its substance. 6. The term target, as utilized in the discussion of roentgenological technique, denotes the positive terminal of an x-ray tube which receives the impact of electrons in the production of x-rays. 7. The target film distance is that interval be- tween the target's focal spot and the film; this distance was always forty inches when x—raying the knee-lateral for the tuberosity study. 8. The term cassette indicates the container for an x—ray film. ll 9. The expression x—rgy series, as used in the tuberosity study, denotes four separate knee lateral films taken of the same leg. The first x—ray was taken at the beginning of the study and the other three were taken at intervals of six, seven, and six weeks. The term serial refers to one of these said x-rays. CHAPTER II REVIEW OF LITERATURE Review of the Literature for the_Rebounding Analysis It is an established fact that vertical Jumping ability can be improved through the employment of a supervised weight training program, a program which stresses specific primary mover muscles by means of gradual, progressive resist- ance exercise.6 Such improvement was demonstrated by Wick— strom who utilized a six week, post season, weight training program for his basketball team. He obtained a mean increase of 1.5 inches in Jumping height over the team per- formance at the end of the season. The range of improvement was from 0 to 3.5 inches with not a single athlete decreasing in Jumping ability.7 The Sports College of Toronto, Ontario, reported the results of a similar study wherein seventeen basketball players were conditioned by progressive resist- ance exercises applied to their gastronemius and quadriceps muscles. The highest individual gain was 13 inches while 6James Murray, and Peter Karpovich, Weight Training in Athletics (Anglewood Cliffs, New Jersey: Prentice-Hall Inc., 1961), p. 38. 7R. L. Wickstrom, ”Post Season Weight Training for Basketball Players,” Athletic Journal, LIX (April, 1959), p. 38. 13 the lowest was 5.5 inches; the mean attainment was 8.5 inches.8 Edward Steitz conducted a five week, pre-season, weight conditioning program which produced a mean experi- mental vertical Jump increase of 2.9 inches, while his control group indicated an increase of only 0.6 inches. The 2.9 gain featured a "t" value of 8.7 which is signifi- cantly beyond the .01 level of confidence.9 While emphasizing the fundamentals of basketball rebounding, John Friend of Pepperdine College, California, casually mentioned: ". . . we feel that we can improve a boy's Jumping ability while he's with us. The off-season weight program is a valuable aid in improving the boy's "10 Mr. Friend seems to reflect the opinion vertical Jump. of the maJority of basketball coaches when he affirmed that an athlete's position, timing of Jump and inate Jumping ability are three basic and equally important ingredients in the rebounding technique. Many coaches reason that if position and timing are constantly equal, then the athlete who can Jump the highest will secure the most rebounds. 8"Improve Jumping Ability Eight Inches in Training," Sports College News, III (October, 1955), pp. 4-5. 9Edward S. Steitz, ”Increase the Explosive Power of Your Athletes," Athletic Journal, LIX (February, 1959), p. 18. loJohn Friend, "Rebounding ABC's," Scholastic Coach, XXXI (November, 1961), pp. 28-30. 14 In 1955, the late Frank O'Connorll of the State University of Iowa was one of the first basketball mentors to place his team on a controlled weight training schedule. The improvement mean for vertical Jump performance was 2.7 inches as measured by a standard Jump-and-reach test; coach O'Connor felt that the program made his team ". . . stronger physically for the rugged work under the basket". The first Iowa team, which used planned weight training as a group, was composed primarily of sephomores; and this young team placed second in the Big Ten Conferences As Juniors, still employing the weight exercises, this Iowa team in 1956 won their conference championship. However, since weight training for basketball players was then in its infancy, there were unfortunately no computations made to determine the statistical correlation between vertical Jump performance and game rebound performance. Three years later in 1959, Stan Burnham12 of the University of Texas conducted a six week post season training program. The final results of the Jump-and—reach test indicated that all ten of the experimental athletes improved their Jumping ability. The highest individual attainment llFrank O’Connor, and F. D. Sills, "Heavy Resistance Exercises for Basketball Players," Athletic Journal, XXXVI (June, 1956), pp. 6-8. 12Burnham, loc. cit. 15 was almost six inches while the mean gain was 3.2 inches. Perhaps the most significant aspect of this study is revealed in the season statistics for 1958—1959. The year before, the Texas team was out rebounded in twenty-three of twenty- five games. The next year, after weight training had been initiated, the statistic was reversed whereby Burnham's team out rebounded twenty—three of twenty—five opponents. The five top rebounders were among the ten players who partici— oated in the exercise program; however, becuase this training was conducted during the off—season, the increase in Jumping ability could not be statistically correlated with competi- tive rebound performance. Review of the Literature for the Tibial TuberosityfiInvestigation Dr. Baetznerl3 in 1927 reported changes in the skeleton of highly specialized athletes. His findings were primarily based on observations made during an extensive x-ray research program on the elbows of Olympic prize fighters. Dr. Baetzner observed bony processes marking the origins and insertions of primary arm muscle groups (extension: triceps and anoceneus; flexion: biceps, brochialis, brach- ioradials, and pronator teres); these physiological changes he emphasized, were not the result of a single inJury, but l3W. Baetzner, "Uber Sportschaden am Bewegungsapparat," Medizinische Klinik, XXIII (February, 1927), pp. 173-76. 16 rather due to an accumulation of minor insults or pressures caused by the incessant pounding of elbow Joint surfaces. To further substantiate this minor inJury theory, Dr. Baetzner cited surgical illustrations of torn lemniscus commonly found in the knee Joints of soccer players; he surmised that such a strain condition is also predisposed by previous pressure inJury to the cartilage. Two years later, in 1927, Dr. Heissll1L observed accessory bony structures of the sesamoid type in the olecranon region of the arms of Olympic wrestlers and on the patella ligament of Olympic runners. X-ray disclosed extraneous calcified material on the upper and lower portions of the patella. However, only one x-ray picture was taken of each knee, and therefore, without a means for comparison, Dr. Heiss could not observe any increase and/or decrease of tibial tuberosity size. Then in 1931, Professor Knoll15 reported the results of an x-ray examination on the dominant elbows of eleven tennis players; six of these athletes showed minute calcium deposits. In the discussion of his research findings, Pro— fessor Knoll challenged the Baetzner concept (1. e. minor 14F. Heiss, "Rontgenologische Gelenkunterschugen an Olympiakampferny Klinische Wochenschrift, VIII (April, 1929), pp. 648-51. 15W. Knoll, ”Ellenbogenbefunde Bei Hervorragenden Tennissipielern," Deutsche Medizinische Wochenschrift, LVIII (January, 1932), pp. 8H4861 l7 inJuries cause calcification at origins and insertions) by contending that in most cases the Joint and bone changes may be traced to some actual accident to that Joint, and when such an explanation is not to be found, then said change is better interpreted as an adaptation rather than an inJury. Professor Knoll16 also made x—ray observations on the feet and ankles of fifty-four nonathletic subJects and he disclosed that 43% of the people had bony growths similar to those described by Baetzner. Again it was im- possible to determine the amount of area increase due to calcification, since serial x-rays were not taken. Also in 1931, Dr. Heiss 17 reported that he had observed, through a three year series of x—rays, the feet, ankles, knees, and elbows of forty-nine physical education students. He discovered that certain already existing bony processes increased, and that new ones, attributed to the student activity program, made their appearance during this thirty-six month observational period. However, nothing pertinent was offered in the Heiss report concerning the tibial tuberosity, and a progressive weight training program was not part of the physical education curriculum. l6W. Knoll, "Sportschadenlind sportverletzungen," ft, LXI (September, 1931), pp. 905-912. 17F. Heiss, "Ueber einige Veranderungen im Sprunggelenk bei Sportsleuten," Deutsche Medizine Wochenschrift, LVII (December, 1931), pp. 2138—39. 18 Referring Specifically to the calcification of tendon, McLean and Urist18 maintain that bone formation normally occurs in the substance of modified tendinous tissue at the point of bony insertion; and of course, this contention is directly related to the possible increase of tibial tuberosity area. In 1940, McLean and Bloom19 conducted an extensive histological research on the ligementum patellae to the tib- ial tuberosity of three hundred alline rats. Exercise of these animals was not a factor in the study. These researchers found that at the age of seven weeks, the tubercle of the tibial had not formed as a distinguishable protuberence, but rather that it lay dormant as a center of ossification consisting of calcified cartilage matrix, lying within the patella tendon. McLean and Bloom further observed that as the tendon passed into this cartilage from above, it exhibited direct transformation of tendon cells into cart— ilage cells. In the animals examined at ages six to seven months, the anterior tuberosity was fused with the epiphysis, but it was still calcified cartilage which had not undergone replacement by bone. It was also discovered that the patella tendon passed out of and below the tibial tuberosity l8 19 F. C. McLean, and W. Bloom, "Calcification and Ossification. Calcification in Normal Growing Bone," Anatomical Record, LXXVIII (March, 1940), pp. 333-60. McLean, op. cit., p. 198. 19 in much the same fashion that it had passed into it from above, exhibiting the reverse transition from cartilage cells back to tendon cells. Furthermore, and of most importance to this study, the patella tendon (again trans- formed into cartilaginous tissue) became continuous with the anterior portion of the tibia shaft, not at the tuberosity, but rather below the tuberosity. Lewis20 in 1958, while making observations on human dry bones and human surgery cases, substantiated the above animal observation when he reported that the ligamen— tum patellae of human beings, would often, but not always, pass into and through the tibial tuberosity making its permanent attachment on the anterior shaft of the tibia some three or four centimeters below the tubercle. Supplemental to the above actual case studies, McLean and Budy21 in 1959 stated that the remodeling of adult bone was formerly believed to be caused by the pressures from weight bearing; whereas now scientists theorize that such a remodeling of bone is determined by a metabolic function. They claim that this function maintains a continuous supply of reactive bone by the transfer of calcium and phOSphate between bone and blood. 20O. J. Lewis, "The Tubercle of the Tibia," Journal cf_AnaI2mx. XCII. no. 4 (October. 1958). pp. 587-92. 21F. c. McLean, and A. M. Budy, "Connective and Supportin Tissues: Bone, " Annual Review of Physiology, XXI (1959 . pp. 69-90. 2O McLean and Urist22 theorize that the general property of calcification cannot be attributed to any single factor It is felt that one must postulate a local mechanism for calcification; and they therefore, contend that any calcified condition is caused by both chemical and physical components acting and reacting together within the living organism. They further postulate that the chemical component is chiefly that of an enzyme system, while the physical component might easily be surface forces in and/or on the colloidal matrix (1. e. the forming mold containing the subdivision of matter in which individual particles are of submicroscopic size). Steinhaus2 agrees with this theory stating that in the remodeling of adult bone there are constitutional factors which determine whether the changes shall lead to mere thickening of the bone or to more defi- nitely pathological changes. 22 McLean and Urist, op. cit., pp 66—67. 23Steinhaus, loc. cit. CHAPTER III METHODS OF RESEARCH This research was designed to study the effects of a weight training program on basketball rebounding ability and on the calcification of the tibial tuberosity area. The study featured a threefold purpose, namely: to define a reliable research method so as to statistically correlate basketball rebounding ability with increased vertical Jumping ability; to calculate said correlation for members of a collegiate basketball team; and to discover if there is any adaptive calcification of the tibial tuberosity when said insertion is stressed by 1000 to 4500 poundals of force. Source of Data for Rebounding Study SubJects for rebounding analysis. The subJects used in this research phase were varsity members of the 1961— 1962, Michigan State University, basketball team. Origin- ally six athletes were planned for the investigation—— three experimentals and three controls. However, an early inJury to one of the experimental subJects necessitated a substitution, which was effected by Coach Anderson. Said substitute proved to be an excellent candidate for Mr. 22 lkede's weight training program; but the athlete did not participate in any basketball games, and therefore, he and his control counterpart could not be utilized in the rebound study. The four remaining subJects were paired by Jumping ability and playing position. Both the experi- mental and control groups consisted of one athlete who played the center position and another who participated at the forward position. The experimentals were placed on a supervised weight training program which was designed specifically to improve basketball vertical Jumping ability. This program was conducted during the last half of the basketball season. These active players, in addition to their normal practice and competitive schedule, trained with weights four days a week and approximately four minutes a day. For a description of the weight training syllabus, refer to Appendix A. The control subJects did not lift weights; their train- ing consisted of regular basketball practice and scheduled games. Experimental procedure for the rebounding analysis. Mr. Weede's weight training program commenced on January 11, 1962 which was the first school day after the Christ- mas vacation; consequently the basketball season was nearly half completed with only eight weeks remaining. Because the weight program was designed for sixteen weeks, this 23 rebounding analysis was affected by only the first half of the over-all weight training program. Vertical Jumping ability was determined on a weekly basis Just prior to every Thursday practice. Each of the experimental and control athletes would execute the Sar- gent Jump Test three successive times, and the mean Jumping performance was recorded as the measure of the player's vertical Jumping ability for that week. Refer to Appendix D, Table IV for the individual and group Jumping perform— ances. Rebounding ability was considered only from the standpoint of game competition. During the eight week period allotted to the study, this researcher analyzed twenty-two contests of which twelve were scheduled games and ten were officiated gamescrimmages conducted during a scheduled practice. Rebounding ability was determined on the basis of work per unit of time. This was achieved by observing the number of minutes an athlete competed in a game and the number of clean rebounds he secured during that game. Rebounds per minute--or work per unit of time-~was deter- mined'uydividing the individual's rebounds (work) by the number of minutes (time) he played. Both the experimental and control subJects were Judged in this manner. During the ten practice scrimmages, this researcher, by using a stOp watch, was able to record to the nearest second, the l l 24 time each subJect entered and left the contest; also recorded was the number of clean rebounds made by each subJect. In reference to scheduled games, the individual rebounds and the individual competitive times were obtained from the Michigan State University, 1961-1962, varsity basketball, statistic book. Such information was gathered at the scouting desk by a member of the university basket- ball staff. Refer to Appendix D, Tables v and VI for the individual rebounds per minute master charts. Statistical technique for the rebounding analysis. The analysis of varianceel4 was applied to rebounds per minute versus time, and also to vertical Jump performance versus time; this was done with the purpose of determining the degree of variation between individuals as well as between groups. Rank correlation25 was applied to individ- ual rebounds per minute versus individual vertical Jump performance with the purpose of determining statistical significance for each athlete. Source Of Data for Tibial Tuberosity Study SubJects for tibial tuberosity investigation. The subJects for this research phase consisted of five, Michigan 24Helen M. Walker, and Joseph Lev, Statistical Inference (New York: Henry Holt and Company, 1953), pp. 54—60. 25c. w. Odell, Introduction to Educational Statistics (New York: Prentice—Hall Inc., 1946), pp. 35-38. State University basketball players, two from the varsity squad and three from the freshmen team. These players were active candidates in a supervised, sixteen week, weight training program which was designed to improve vertical Jumping ability. During the last eight weeks of the basketball season, these athletes trained with weights four days a week, Monday through Thursday; and at the completion of their competitive season, they continued for an additional eight weeks of training by exercising three days a week (Monday, Tuesday and Wednesday). One of the safety features in the training program consisted of four distinct knee x-rays taken over a nine- teen week period. Originally six subJects were scheduled for this bone investigation; however, an unfortunate yet unavoidable situation arose in that one athlete was inJured, and his substitute had missed two of the required four serial x—rays; consequently, said substitute could obviously not be included in this investigation. All subJects were right handed, and were therefore considered right leg dominant. The controlling factor was the amount of weight extended during the three-quarter knee bend exercise. Each experimental basketball player started with the same amount of weight (105 pounds) and all progressed at the identical rate of 5 pounds per lifting session. Instead of comparing 26 the tibial tuberosity areas of weight-lifters with those of nonlifters, this investigator compared each subJect's tibial tuberosity size with the amount of weight he had handled Just prior to the day his knee was x-rayed; and in this way the added financial burden of x-ray costs for control subJects was eliminated. Special equipment used in the tibial tuberosity investigation. A homemade, x-ray, view box was constructed so as to observe the knee-lateral films. This box was a hallow wooden structure measuring fourteen inches by nineteen inches by eight inches high; a frosted thirteen by nine inch glass plate was inserted in a cutout on tOp; while within and on the base were mounted two, forty-five watt, electric light bulbs which would direct light rays through the glass plate. Several quarter inch diameter ventilation holes were drilled into the sides of the box, and a small electric blower was placed within so as to counter any excessive heat which might damage the x-ray films. An x-ray picture was made distinguishable by placing it on the frosted glass when the bulbs were lighted; Figure I, page 27, shows a knee—lateral film made observable by the View box method. Experimental procedure for the tibial tuberosity investigation. The methodological procedure for this bone analysis should be considered in four subsequent steps, namely: (1) the taking of x-rays;(2) the selection of constant 27 e 1 b a S .1 V a h t 1m W1 .1 XnI O bl a WP ee .lt V8 1.. e m Figure l. 28 reference points on the anterior tibia; (3) the outlining of x-rayed tibial tuberosity areas; and(4) measuring the tibial tuberosity areas. For ease of explanation, this phase sequence will be adhered to. Concerning the taking of x-rays, it was advised by Dr. James S. Feurig, M. D., Director of Michigan State University Health Service, that an x-ray lateral view of the knee would best distinguish the tubercle area of the tibia. The routine technique for photographing knee-laterals was employed whereby the x-ray tube is centered to the cassette allowing the principal ray to be perpendicular to the film; the patient reclines on the x-ray table in such a manner that the outside of the leg being photographed is pressing against the table; the knee being x-rayed is shifted into position on the film so that the principal ray is centered over the midpoint of that Joint; this knee is also flexed at an.approximate 30 degree angle and its outer side is in contact with the cassette; the Opposite leg is acutely flexed and drawned upward and forward out the way.26 Figures 2 and 3 on page 29 diaplay this roentgeno- logical position. Both knees were separately x-rayed in this manner. 26L. R. Sante, Manual of Roentgenological Technique (Ann Arbor, Michigan:"‘Edwards‘BFDEHEPS'Inc. ,‘19448I,'p. '123. 29 Technique for knee lateral Figure 2. x-ray Close-up of leg position for knee lateral x-ray Figure 3. 30 The target film distance was maintained at a constant forty inches, and the same x—ray technician took all the photos. During a nineteen week period, each subJect had both his knees x-rayed four times; this happened within the time intervals of six, seven, and six weeks respectively. The first serial of two pictures (right and left knees) was taken Just prior to the 1961 university Christmas vacation, which was twenty days before the commencement of the weight training program. These photographs established the size of the tibial tuberosity before said insertion was exposed to the strain of a knee bend exercise executed with weights. The second serial of x-rays was taken four weeks after the program had begun; the athletes were then extending one hundred and fifty pounds, for a weight increase of forty- five pounds over the initial training session. The third set of x—rays was photographed seven weeks later; at that time the athletes were extending two hundred and forty-five pounds, or one hundred and thirty—five pounds above their initial exercise load. The fourth and final serial of knee- laterals was taken six weeks later, i. e. immediately fol- lowing the completion of the training program; at that time, the trainees had progressed to a tibia extention of three hundred and thirty-five pounds which indicated the tremen- dous over-all weight increase of two hundred and twenty- five pounds. 31 In order to determine the tibial tuberosity area for an individual leg, it was necessary to select two reference points which were constant in each series of four x-rays. Both these points were located on the anterior crest of the tibial shaft; one point was located on the upper end of the tibia about one-half inch above an estimated upper tubercle extreme, while the second point was placed approx- imately one-half inch below a lower tubercle extreme. Since these points were above and below the tibial tuberos- ity, it was believed that any variation in tuberosity area would be due to an addition or deduction of extraneous calcium salts between said points. Concerning the actual selection of constant reference points, one film was chosen from either the second or third x—ray serial for a given leg. Selection criteria was photographic clarity. It was to this selected x-ray that the other three serial films were individually super— imposed, and from which the identical reference points were established. An example of the selection process follows. When we desired to select constant reference points for the right leg of subJect Chandler, we first placed the second and third x—rays of his right leg side by side on the box viewer. We determined that the third photograph was the better x-ray by trial superimposition of films one, two, and four; and therefore the third film was fastened to the glass plate of 32 the view box. We then selected and marked the two above mentioned reference points. These markings were in the form of an arrow point sketched in black ink on the clear bone section of the x-ray; and it was these arrow marks that pointed to the constant reference points which would be utilized for the other three right leg x-rays. Leaving film three on the viewer, film one was superimposed over it, and the identical reference arrow points of film three were drawn by tracing them onto film one. Removing film one, film two was then superimposed and the same reference points were traced onto it. Finally, this same process was repeated for film four. The point selection technique was then re-employed for subJect Chandler's left leg. Because the left and right tibias of each athlete were studied, the distance between reference points often varied for each subJect. These reference distances always differed between the five subJects. Such variations did not hinder the study since this researcher was interested only in detecting area variation for individual bones, and therefore, each tibia established its own constant factor. After marking the reference points for the right and left knee series, the tibial tuberosity area was outlined on each x-ray. Again the View box was utilized. With the aid of a raised ruler, the reference points were connected by a straight line. Then the curved portion (including the 33 tuberosity) of the anterior tibia crest located between the two points was slowly sketched so that the edge of the ink barely touched the outer edge of the bone shadow. A fine pen point and white ink were employed. White ink was chosen in order that the outlined tibial tuberosity could then be readily distinguished without the use of a view box, The measuring of each tuberosity area was accomplished with an Otto Compensating Planimeter (see Figure 4 page 34). By slowly tracing the inner edge of the inked outline with the tracer of the planimeter, the area for each figure was determined to the nearest ten thousandths of a square inch. A table magnifying glass was employed to facilitate both the tracing of the outline and the reading of the venier divisions. Figure 5 page 34 diSplays the working arrange- ment for x-ray film, planimeter and magnifying glass. The outlined area of each x-ray was measured ten separate times; the measurement deviation never exceeded, and rarely reached, three thousands of a square inch. The arithmetic mean of each serial's ten readings was considered the tibial tuberosity area measurement for that particular x-ray. This measuring process was repeated for each of the four x-rays in both the right and left leg series; refer to Appendix D, Table VII forthese individual tibial tuberosity area measurements. 34 Otto compensating planimeter positioned with x-ray film Figure 4. Working arrangement for x-ray film, planimeter and magnifying glass Figure 5. 35 The tibial tuberosity area variation for each tibia was calculated as the largest, area measurement difference existing within an x-ray series. Because this area vari- ation was so minute (0.1 to 0.3 square inches), the mean of a combined right and left tubercle area was determined for each individual subJect, and for the entire experi- mental group; refer to Appendix D. Table VIII for these calculations. Statistical technique for tibial tuberosity investi- gation. An analysis of varience27 was employed to determine if there was any significant difference between x-ray pictures, as well as between individual subJects. 27Walker, loc. cit. CHAPTER IV ANALYSIS AND RESULTS OF DATA This research presented a two phase proJect, namely: (1)a basketball rebounding analysis; and Uz)a tibial tuberosity area investigation. The purpose of the first proJect was to define a reliable research method that could statistically correlate a player's rebounding per- formance with his increased vertical Jumping ability which was derived through weight training. The subJects used in the correlation were four varsity members of the 1961-1962 Michigan State University, basketball team; and the study was conducted during the last two months of their competitive season. Individual rebounds were placed on a work per unit of time basis, and both the experimental and control groups were tested on vertical Jumping ability once per week by means of the Sargent Jump Test. The purpose of the second research proJect was to determine if any adaptive calcification occurred on the tibial tuberosity because of tendon stresses of 1000 to 4500 poundals. A weight program featured the knee bend . exercise with a load graduation of 105 to 330 pounds pro- gressively applied over a sixteen week training period. 37 Five collegiate basketball players participated in the program, and their knees were exposed to a series of four x-rays spaced throughout nineteen weeks. Individual x-ray serials were compared for calcium deposits. Analysis of Rebounding Data The statistics employed in this study were twofold; namely: the analysis of variance and the rank correlation. The application of these statistical methods will be dis- cussed separately. The analysis of variance was applied to both vertical Jumping ability and rebounding performance. The data used for these computations were all of the individual, weekly vertical Jump performances and all of the weekly means for individual rebounds per minute. In addition to the group comparison, the variances which were attributable both to the differences in individuals and to the changes in per- formance throughout the eight week testing period, were computed. Figure 6 displays the group mean score of vertical Jump performance for each week of this eight week study, and Figure 7, page 39, graphs the group mean scores for rebounds per minute. Table I, page 40, shows conclusive evidence that the experimental group advanced a great deal more in vertical Jumping ability than did the control group; while Table II page 40, displays that the same experimental subJects as a group did not advance in rebounding ability during the first eight weeks of their weight training. 38 25.5 .. 25.0 J cxfiggf'g’ofi/n I A 24.5 - ’ A ,I 4‘ . 24-0 -i I, \V’JI \ \éf‘figv/ My; 255 I w m //76‘/7¢~S‘ 25.0 .. 225- 220- 2/.5., 2/.o§ / 2 3 133' 2 i a weeks F/G‘Meé'é 6900/9 MEA N \S‘C 01(9fo 0247' WEEKLY V5977C‘Aé MOWG‘ 39 J9 - exp em. eh/«/- -— - 60): 790/ ‘ Rebounds ‘ per m/hm‘c ,24_ zaszeai? weeks £760.05" 7 620 VA M54 xv 360 pg"? 01" We?! K17 PfgoaA/py P59 M/A/V 72" 40 TABLE I ANALYSIS OF VARIANCE RESULTS: ----- VERTICAL JUMPING PERFORMANCE SS DF M. S. . F. Total 248.29 31 8.01 ' Groups 8.40 1 8.4 13.0** Individuals 202.95 3 67.65 10,5** Tests 24.07 7 3.44 5,3*. Error 12.87 20 .644 - **p = .01 *p = .05 TABLE II ANALYSIS OF VARIANCE RESULTS: REBOUNDING PERFORMANCE m SS DF M. S. F Total 0.357 31 0.012 Groups .003 l .003 1.214 Individuals .015 3 ..005 .357 Tests .061 7 .008 .571 Error .278 20 .014 **p = .01 *p = .05 Note: None of the F values in Table II are significant at the .05 level of confidence. 41 The other statistic of rank correlation was applied to Jumping and rebounding performances. Again the data used were weekly Jump scores and mean weekly rebounding performances. The relationship between vertical Jump performance and rebounding ability was computed for each in- dividual and for the group. Figures 8, 9, 10, and 11 pages 42-43 graph for each subJect, the relationship between his individual rebounding scores and his vertical Jump scores attained throughout the eight week period of this study. Tables IX, X, XI, and KUIin Appendix E, exhibit conclusive evidence that there was no significant correlation between a subJect's Jumping ability and his competitive rebounding performance. Results of Rebounding Data The results of the analysis of variance may be seen in Tables I and II. The following material is an explanatory synthesis of the various parts of said Tables: 1. Groups. The over—all differences between groups in Jumping performances was significant at the .01 level, but there was no significant difference between these same groups in rebounding ability. 2. Individuals. The response of individuals to the eight week training program diSplayed a significant differ- ence at the .01 level, however, the rebounding performance for these same subJects was nonsignificant. 42 .60. 54- x ' I46 .. .42 . n .3 6 .. " r95 0 (I)? 08‘ .50 .7 x a: per .24.. mi») (If: ./a _ x x x ,. ' x 0’2 - .06 1 22.5 23.5 28.0 27-3 :40 261/ “.6 25." won”; ve rf/c a//2/m/O (07643.?) £760.05 6 Piano/WM» fiffoE/V //l/fl/V/0 (x44 2:23 amm- //V6 $60.05? A/Vo V6? 77644 l/Z/A/fi J6 can? (6AM?) O/V 0.4 7.4 for [XPIAQ/Mf/VI'AA Sad/[67' 639444401159) .70 _ . 65 a x " .5 6 .. x .49 - .42 .. rob 00/708: .55.. " x P .26 .. x mfife .2/ - ./4 I x .07 s . x x XX x XXX 8! X 8 22: 2} 22': as 23.6 22:: 25.6 215' week/f ver x‘c car/Jaime (Mcfieey £760.95 .9 .6524 770mm» 6[7W£Z'/V Wfl/ way.“ .055 OVA/fl - /A/6‘ 360.259 Ali/D V5? 77044 JUMP x01?! 6‘ (BASED ON 04734 [0.0 [X1950 (”7:44 6‘05 t/A’cr rA/OMAA/A/ 43 .89 a so- " .77 .60: .J7. rcAat/ha’d‘ .42- " ,eer .35.. " min (”’0 .24.. " x : x ‘ «M71 x I 5 .06: x x " 24's 25 do :24 ab 121 ai- “'3 we My var fie cr/J'wn/o (faded) XX F/éY/Ré‘ 10 éfldf/mJH/fl MIA/50V WWI/mm; 4230mm- M \S‘C‘Oflfd‘ AND 1453077621 A c/aA/fi \S‘COIAJ‘ (54.9!» av rye—9.47:4 £0.42 con/7x904 Jae uzcr .5592 r) .68- .6/ - .54.. .47- .401 3: Nbaaha/J‘ .33.. x eh .26.. " mfiaz‘c ./9 - x g g i: x x ./2 .05 " " x X /a.'.5' 4;: as la} 20.: 2a): M m wacky var/f: 04/va (Mafia!) Heme; 11 PEMWWMfl fiffWEE/V //W/V/flV/4 assay/va- //v&‘ 6095? mm Vii/76:44 wax/.0 mew‘ was? 03/ @4721 for GOA/7'42 oz {/43 (4527' wax/440) 44 3. Egggp, The test results showed that there were significant differences between testing periods at the .05 level indicating significant improvement in all subJects; weekly rebounding displayed no significant differences. As evidenced by Tables IX, X, XI, and XII, the cor- relation of rebounds per minute and vertical Jump increase showed no statistical significance for individuals. The experimental subJects had individual correlation coeffici- ents of zero and minus .05, while the control subJects had coefficients of minus .23 and plus .25; all these figures are extremely low. The geometric mean of average individual correlation was .017 which again was not statistically significant. Analysis of Tibial Tuberosity Data The statistic employed in this x-ray study was the analysis of variance. The data used were the mean area variations for the combined right and left tuberosities of each individual subJect. The items computed were the area changes effected during the nineteen week investigation and also the variance attributable to differences in individuals. Figure 12 page 45, graphs the individual means of the combined right and left tuberosity areas for each x-ray serial and the amount of weight extended by that individual one day prior to his x-ray. Figure 13 page 45 shows the group mean area variations for the combined right and left tuberosities. Table III page 46, renders conclusive evidence that the 45 .44 4 .40 .. .36 1 " Ii " $5 .32 1 x X . . . , .28 _ x x /Do//V/b’00'/,‘C‘omb/hcofi .24. .. x x ,, fade/"0677‘; dream? .20 _ x (Sq. #7675) ./6 .. x x " ./2 .. x .08 _. x x .04 /05 A50 220 330 Vie/907‘ 0x74”: 04: 0’ ([669 flé‘aéf 12 Ava/mm; M54 M9 0; cow/Mr, £6.97 Aw [SE/7; 773/41. 70.650097? 40546“ Ad? 60/1/- PAflEfl W/7'// WE/6/7’7' [X7f/Vflffl .04/40 _ .03 726 J .033/2 _ .02698 _ .02484 _ gro ”(b, COM/é/beo; /0.6:r- .020 70 l OJ‘I/ Var/'a'f/bb 6‘ , 0/6 56 . (6‘62. Arc/f) . 0/242 _. .00628 _, .0/03 .004/4 .4 .0045 .000” /05 ISO 230 .330 wc/gvé/ axis): 00 0’(/.6~$‘) F760;?! 13 6900.0 MiA/VJ‘ 0F COMzB/A/[fl wax/7410 [£72- 7743441 705590.9/ 77/ .4954 War/A 770/14)“ AJ‘ cat/Amaze W/zw WflGA/f [Xff/VDED 46 tuberosities had not undergone permanent change in area size during the period of weight training. Results of Tibial Tuberosity Data The results of this analysis of variance may be seen in Table III. The following material is an explanation of the various parts: 1. Tgppp, There were no significant differences of tibial tuberosity areas found within the four individual serials of x-rays. 2. Individuals. The tibial tuberosity areas sig- nificantly differed between individual subJects throughout the entire nineteen week period. This was expected since the individuals were different- TABLE III ANALYSIS OF VARIANCE RESULTS: TIBIAL TUBEROSITY AREA VARIATION SS DF M. S. F Total 0.2047 19 0.0108 Individuals 0.1612 4 0.0403 ll.l944** Tests 0.0000 3 0.0000 0.0000. Error 0.0435 12 0.0036 **p = .01 CHAPTER V SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summarygof Research This research possessed a threefold purpose, namely (1) to establish a reliable and workable method to correlate competitive basketball rebounding ability with the improvement of vertical Jumping ability derived from progressive weight training; (2) to determine the correlation between vertical Jumping improvement and com- petitive, basketball rebounding performance exhibited during the last eight weeks of a collegiate Big Ten, basketball season; and (3) to determine if there is any adaptive area change due to calcification at the tibial tuberosity when said point of insertion is exposed to the stresses of progressive weight training. In the rebounding study, four Michingan State University, varsity basketball players--two centers and two forwards--were used as subJects. Two of these athletes, one from each mentioned position, were experi- mental candidates in a weight training program; the othe two athletes were controls . The training program was designed to increase vertical Jumping ability, and it 48 was conducted four days per week during the latter half of the basketball season. On Thursday of each week, both the experimental and control subJects were given the Sargent Jump Test. Their competitive rebounds were Judged on a work per unit of time basis. During twenty—two basketball contests—-twelve scheduled games and ten officiated scrimmages-—both the number of clean rebounds secured and the amount of time played were recorded for all subJects. Each subJect's weekly mean of rebounds per minute was compared with his weekly Jumping ability; and these data were analyzed by rank correlation. The analysis of variance was applied both to the group means of weekly Jumping ability and weekly rebounding performance. In the tibial tuberosity investigation, five Michigan State University basketball players--two from the variety and three from the freshmen team-—were used as experimental subJects. These athletes were on a progressive weight training program which was conducted four days per week during the basketball season, and three days per week thereafter for a total of sixteen training weeks. Instead of control subJects, the controlling factor was the progression of weight handled in the three-quarter knee bend exercise. During the training program, each subJect had both knees x-rayed at four different times; the knee lateral view was utilized. To limit the tibial tuberosity area for each 49 leg, two constant limiting points were used for a subJect's series of four knee x-rays. These common reference points were located on the anterior crest of the tibia and were situated approximately a half inch above and below the tuberosity. The area between these limiting points was measured with a compensating planimeter, which featured a venier unit range of ten thousandths of a square inch. The variation of tuberosity area was determined by comparing the four x-rays within the same series, and because a sub— Ject's ubercle area variation was so minute, the group mean was determined for an individual‘s combined right and left tuberosity areas. These data were statistically analyzed with the analysis of variance. Conclusions for the Reboundinngnalysis SubJect to the usual limitations of sample and type of training program, the following conclusions may be drawn: (1) the improvement of vertical Jumping ability and com- petitive rebounding ability can be statistically correlated when the weight training program is conducted during the basketball season, and when the competitive rebounds are considered on a work per unit of time basis; (2) in this study there was no statistical correlation between vertical Jumping improvement and competitive rebounding performance exhibited during the last eight weeks of a collegiate basket— ball season. However, it should be noted that when this study was conducted, the subJects were active players on the 50 second highest rebounding team in.the Big Ten Conference during the 1961-1962 basketball season. Conclusion for the Tibial Tuberosity Investigation SubJect to the usual limitations of sample and type of methodology, the following conclusion seems Justifible: there was no calcifiably, distinguishable area change at the tibial tuberosity when said insertion was subJect to a six- teen week, weight training program which featured a gradual progression of stresses ranging from 1000 to over 4500 poundals. Research Recommendations Upon conclusion of this study, it is recommended that some thought be given to the following problems: 1. An extensive statistical correlation should be made between improved vertical Jumping ability and competitive re- bounding performance. Six to eight subJects should be used and the supervised, progressive weight training program should commence four weeks preseason and continue throughout the entire competitive season. Weight progression should be in the amount of five pounds and a four or more series of knee x—rays is mandatory. 2. It is strongly suggested that further study--roent— genography, surgery, and clinical observation-—be conducted to determine the effect of stressful leg exercise to the tibial tuberosity. Because this insertion is capable of withstanding a phenominal degree of stress, a longitudinal adaptive effect of exercise may be discovered. BIBLIOGRAPHY BIBLIOGRAPHY BOOKS Jung, Frederic T. Anatomy and Physiology. Philadelphia: F. A. Davis Company, 1955. McLean, F. C., and M. R. Urist. Bone. Chicago: University of Chicago Press, 1955. Millard, Nellie D. Human Anatomy and Physiolo . Philadelphia: W. B. Sanders Company, 19 . Murray, James and Peter Karpovich. Weight Training in Athletics. Englewood Cliffs, New Jersey: Prentice- Hall Company, Inc., 1961. Odell, C. W. An Introduction to Educational Statistics. New York: Prentice-Hall Company, Inc., 1946. Sante, L. R. Manual of Roentgenologgcal Technique. Ann Arfigr, Michigan: Edwards Brothers Company, Inc., 19 . Stein, 1., R. O. Stein, and M. L. Beller. LivingBone in Health and Disease. Philadelphia: J. B. Lippincott Company, 1955. Walker, Helen M., and Joseph Lev. Statistical Inference. New York: Henry Holt and Company, 1953. PERIODICAL ARTICLES Baetzner, W. "Uber Sportschaden am Bewegunsapparat," Medizinische Klinik (Berlin), XXIII (February, 1927). pp. 173-76. Burnham, S. "DevelOp Your Rebounders with Weight Training," Scholastic Coach, XXX (December, 1960), pp. 16-26. Fell, H. B., and R. Robinson. "The Development of the Calcifying Mechanism in Avian Cartila e and Osteoid Tissue "Biochemical Journal, XXVIII %April, 1934) pp. 22A3-2253. 53 Francis, 0. C. "The appearance of Centers of Ossification from Six to Fifteen Years," American Journal of Physical Anthr0pology, XXVII (January, 1940), pp;_l27-138}‘I Friend, John. "Rebounding ABC's," Scholastic Coach, XXXT (November, 1961), pp. 28-30. Haines, R. W. "Note on the Independence of Sesamoid and Epiphysial Centers of Ossification," Journal of Anatomy (London), LXXV. ' Heiss, F. "Rontgenologische Gelenkuntersuchugen an Olympiakampfern," Klinische Wochenschrift, VIII (April, 1929), pp. 648-5I. '— . "Ueber Einige Veranderungen im Sprunggelenk bei Sportslenten, Deutsche Medizine Wochenschift (Stuttgart), LVII (December, 1931), pp. 2138-2139. "Improve Jumping Ability Eight Inches in Training," Sports College News, III (October, 1955), pp. 4-5. Knoll, W. "Ellenbogenbefunde Bei Hevorragenden Tennissielern," Deutsche Medizinische Wochenschrift (Stuttgart), LVIIIP(January, 1932), pp. 84-86. . "Sportschaden und Sportverletzungen," Schweizerische Medizinische Wochenschrift, LXI (September, 1931), PP- 905-912. Lewis, 0. J. "The Tubercle of the Tibia," Journal of Anatomy (London), XCII, No. 4 (October, 1958), Pp. 587-92. McLean, F. C., and W. Bloom "Calcification and Ossification. Calcification in Normal Growing Bone,” Anatomical Record, LXXXVIII (March, 1940), pp. 333-360. , and A. M. Budy. "Connective and Supporting Tissues: ““"Bone," Annual Review of Physiology, XXI (1959), pp. 69-90. O'Connor, R., and F. D. Sills. "Heavy Resistance Exercise for Basketball Players," Athletic Journal, XXXVI (June, 1956), pp. 6-8. Steinhaus, Arthur H. "Chronic Effects of Exercise," Physiological Reviews, (January, 1933), pp. 103-47. 54 Steitz, Edward S. "Increase the Explosive Power of Your ' Athletes," Athletic Journal, LIX (February, 1959), p. 18. Weidmann, S. M. "Review of Modern Concepts on Ca1cification,’ Archives of Oral Biology (London), I (January, 1960), pp. 259‘640 Wickstrom, R. L. "Post Season Weight Training for Basket- ball Players," Athletic Journal, LIX (April, 1959), p. 38. UNPUBLISHED MATERIAL Weede, Thomas D. "The Effect of a Controlled Weight Program on the Vertical Jump." Unpublished Master's Thesis, Michigan State University, East Lansing, Michigan, 1962. APPENDIX A A DESCRIPTION OF MR. WEEDE'S PROGRESSIVE WEIGHT TRAINING PROGRAM The weight lifting exercises in this program were those which stressed, through the overload principle, the primary mover muscles used in basketball Jumping. There were three exercises employed, namely: (1) the three-quarter knee bend stressing the quadriceps femoris; (2) the heel raise emphasizing the gastronemius; and (3) the arm thrust stressing the deltoid and pectoral muscles. The three-quarter squat and heel raise exercises were initiated with a load of one hundred five pounds for every subJect. This was approximately one-half of each individual's body weight. The weight was increased by five pounds each training period, and the final mean load was three hundred and thirty pounds. The arm thrust exercise was started with ten pound dumbells held in each hand, and the weight progressed six times by two and one-half pounds for a final arm thrust load of twenty- five pounds. The over-all length of the program was sixteen weeks. The subJects trained four days a week, Monday through Thursday, during the last two months of their collegiate basketball season, and three days thereafter (Monday, 57 Tuesday, and Wednesday). A training session consisted of two sets of six repetitions for each exercise. A subJect's average "workout" time was four minutes, and this training COuld be done in street clothes. On the last training day of each week, the athletes were tested in vertical Jumping ability. Each subJect executed the Sargent Jump three successive times, and a mean score was recorded as his week's Jumping performance. At the termination of the program, all experimental athletes increased their vertical Jumping ability by over five inches with the range of tabulation being between five and one-quarter to seven inches gained; this was statistically significant at the .05 level of confidence. APPENDIX B DETERMINING THE AMOUNT OF STRESS SUSTAINED AT THE TIBIAL TUBEROSITY Textbook anatomy states that the quadriceps femoris, which form insertion to the tibia by way of the liga- mentum patellae at the tibial tuberosity, constitute the maJor extensor muscles Of the leg,28 and that for the average male adult, the angle Of attachment formed by the patella ligament and the tibial tuberosity varies between ten and fifteen degrees.2 Because the femur, knee Joint and tibia establish a third class lever system, the amount of force sustained at the tibial tuberosity varies with individuals according to tibia length and the size of attachment angle. Nevertheless, one can Obtain an understanding of the stress intensity experienced at the tibial tuberosity by using the set of mean figures which were acquired from experimental subJects during the 1961-1962 Michigan State University, varsity basketball season. With this in mind 28Frederic T. Jung, Anatomy and Physiology (Philadelphia: F. A. Davis 00., 1955l, p. 183. 29Nellie D. Millard, Human Anatomy and Physiology (Philadelphia: W. B. Saunders Co., 1951), pp. 105 and 173. 60 I imagine the "average' collegiate basketball player sitting on the edge of a table and completely extending a one hundred pound weight which is fastened to his right foot; assume further that the angle of insertion for his patella ligament into the tibial tuberosity is three inches, and that the length of the tibia is twenty inches- The problem to be resolved is: how much force is exerted at the athlete's right tibial tuberosity during the act of extension. By using the formula FORCE times FORCE ARM equals LOAD times LOAD ARM (Fa=Lb), one first determines the amount of force required to extend one hundred pounds at the Optimal level angel of ninety degrees (90°): LOAD (L). . . . . . . . 100 pounds LOAD ARM Eb). . . . . . 20 inches LOAD ARM a . . . . . . 3 inches FORCE . . . . . . . . . unknown Fa = Lb F3 = 100 x 20 F = 2000 f 3 F = 666 + poundals required to extend 100 lbs. at a 90° attachment angle. By employing the Pythagorean theorem, the force sustained at the player's fifteen degree (15°) angle attachment can now be calculated: sin 0 = a E c sin 15°= 666 r c .2588 = 666 + c c = 2575 poundals required to extend 100 lbs. at a 150 attachment angle. 61 This 2575 poundals is the amount Of force sustained by the above "average" collegiate basketball player when the quadriceps femoris of one Of his legs perform all the work of extending a one hundred pound resistance. If the one hundred weight were fastened evenly between both feet, thereby requiring the two tibias to extend simultaneously, then both quadriceps femoris would share approximately half the work of extension, and therefore each tibial tuberosity would sustain half of 2575 poundals or about 1787 poundals of force. When both legs equally extend three hundred pounds of weight, then it follows that the amount of stress supported at both tibial tuber- osities would be 1787 poundals threefold, or approximately 5360 poundals of force. Since the athletes in Mr. Weede's weight training program performed knee bends with three hundred and thirty pounds resting evenly on their shoulders, then each tibial tuberosity area was sustaining a stress well over five thousand poundals. APPENDIX C 63 APPEND/X C‘ L ocro’Nccs 9’ Mar/3? 3/ erma» ' 713%)? cr/ :0» . /¢ Jan‘s/kt //9'0*men/a 7‘0»; ‘ ‘V ex fer/0r e / 6 3‘13“ CXfiWM/cm dy/e A .42 #w ’22:)! (7 saw /06e)-o.s~/z‘y \ ‘ fififa {7160/01 £760.05 14 A/VA 70/12/044 raced/v 0; 72/: A/Z/xI/A/l/ AWE @7224 waw) APPENDIX D 55 .monocfi m.:oH mm: .mEMHHHH3 mafia: mocozfi mm.wm mos psoEOADmmoE zooms one Osman m.hhhom** .monoca moa mm: m.::mEo:B OHHB3 mesons m.ooH no: pcoEomsmmoE comma one ocean m.hoaccwno* .za wm.mm .sa mm.mH .ca mm.mH .ca mm.mm gee m:.mm .sa we.:m coo: .se Hm.oma .cfi ms.mma .sH :.som .ca em.mma .oa w.msa .ca mo.me Hoeoe mm.mm mm.m: m.mH ma.mm mm.mm m.ss m.mm :.mm m mm.mm mm.ss m.ma mm.sm H.mm m.om m.mw p.0m s mz.mm mm.mz w.om mo.om 0.3m o.me m.mm H.mm o mm.mw mw.m: H.om ms.mm ms.mm mm.ss m.mm ms.sm m mz.mm mm.:: m.ma mm.pm ms.:m m:.m: mm.mm m.sm e mm.Hm m.m: ms.sa me.em ms.mm m.m: m.mm o.mm m mH.mm mm.ez m.mH ms.mm mm.mm mm.m: ms.Hm m.mm m .sa mm.am .ce mm.ms .sa m.mH .sa ms.:m .ca o.mm .se 0.3: .:a m.Hm .ca m.mm H coo: Hence senEsafifiaz saasnom coo: Hobos scscsone *soHocsno Q5096 ozonu weennsm weennsm ozonw asonw poofinsw pecansm zooz mbomw Qomfizoo All mDQmU A¢BszHmmmxm All] QOHM mm UZHEWMB |H|I|l lJl xmmz Bmch Z¢ GZHmDD QmB zHQZH >H mqm¢6 l 66 o m . H . com: com. mm m m N. am m owoeeason am: : sow. om m mam. NH a cabana .n> one : mmm. SH 8 mad. SH m ownesason pm: : Hmm. mma. soc: em. 0: HA oH. as m ommEEAAom mm: m own. mm m mmm. m m csoonosnosoz .n> em: m mmm. mmm. coo: 0mm. Hm m com. m H showcases .n> mm: m mme. mm :H Hem. s : sameness .n> mm: m mma. me 8 mac. mm m omossason em: m Hem. ems. one: “so. 0: m cod. 0: s embassson on: A see. me w wad. SH m cabana .m> em: a 000. .ofie o o mmm. .cae am e naooaaaH .m> on: H ##03 CEHB TENS mUCSOQmmwfi XLOB OEHB mEmU mUCSOQ mfik p m mp COD x m 03 zzHQZH > magi. 67 dam. Hem. cows .33 m 0mm ow mmm Hm Hence .x: w m N. m. coo: mmo. mH H wmw. mH s soonoocHz .n> m H@#. mm mH :mH. Hm w omeEHaOm m wow. mma. coo: cos. 0H a com. m H csoomosnosoz .n> s m30. :H m 000. m 0 MCMHUCH .w> N. mSH. mm m mam. mm HH omsesHson s mwm. coo: mza. :H m owMEEHnom m 00m. mm :H OBOH .m> w mHH. mm m oano .m> m mmm. mom. coo: m m. Hm m :z:. wH w omeEHAom m mmm. m: N. 00m... OH m CHmCOomHB .m> m HHH. cHe m H msH. .cHs SH m owmssHson m xhoz TEHB meow monsonomfi xnoz oEHB meow mocsonomfi. swepcoo zoo: 73.2205 mamgmo HoossHocoov > mHmae 68 NNH. NEH. CNOS me. HH m on. 0H 3 ommEEHHom : #NH. mm 3 me. mm m Gianna .m> : ©NH. SH m mmo. NH H owmeaHnom : mmm. Gmmz Hmm. mm m ommeanom m @33. mm MH Choumoznunoz .m> m 5mm. NN. Emmi www. m m mam. 0 mm m spomOCCHS .m> m 000. m m m3m. mm OH GmmHQOHZ .m> N m30. 0: N #wo. mm m mmeEHhom N .MHH. mmH. com: 50. o: m me. o: m ommEEHaom H Hmm. mH m owm. mm a tsetse .n> H meo. .sHe mm H 000. .cHs m o nHosHHHH .n> H xnoz DEHB meow mcczonom%_ xnoz oEHB meow meadonomfi. pompnoo Boo; mE¢HHHH3 H1.Hmmmm IA All QOHmmm MMMZ Bmem z< wZHmDQ mbomc Homazoo Mme Hm omzmoammm Ameezez med nnzpommmv ago: HapoH>HozH H> mHmdB 69 Hom. mom. new: .33 w Ham MOH Sdm mm HMDOB .33 w mSH. mHH. cams com. ON 3 m m. mH m mpommccHz .m> m mmm. mm HH SSO. om m omMEEHmom m mam. omH. new: N3N. mm mw CON. mH m cchummznuhoz .m> S. mew. mm S mSH. SH m oschcH .n> S Swm. om HH 3mH. mm S omeEHnom S 00H. m m. new: on. mH m m. om S owMEEHAom w 3HN. mm m 00m. ON 3 OHQO .m> w 0mm. NH m wSH. 3m m OHno .m> o mmm. .mmmw new: w m. wH m 333. mH w owmafiHHom m Swm. mH 3 mm3. mm mH CHmcoomHz .m> m 0mm. .oHe 0H 3 com. .sHs om w omoseHson m 3903 oEHB meow mpcsonomfi xnoz oEHB meow monsonom%. pmouzoo xooz. gHHHH3 Mmmmm lb HoossHesoov H> mnmae 70 TABLE VII INDIVIDUAL TIBIAL TUBEROSITY AREA MEASUREMENTS RIGHT TUBEROSITY AREAS Subject X-ray #1 X-ray‘#2 X-ray #3 X-ray #4 Vanderjagt .519 sq. in. 370 sq.in. 527 sq. in 595 sq.in. Floberg .464 .432 44 5 .501 Lytle .269 .321.297 .342 Thomann .112 .103 .061 .081 Chandler .154 .139 .105 .133 Mean .3036 sq.1n..2730 sq.1n..2870 sq.1n..3304 sq.in. LEFT TUBEROSITY AREAS Subject X-ray #1 X—ray #2 x—ray #3 X-ray #4 Vanderjagt.113 sq.in .124 sq.1n .137 sq.1n. .152 sq.in. Floberg .295 .305 .341 .278 Lytle .201 .254 .201 .200 Thomann .136 .215 .144 .065 Chandler .203 .260 .272 .222 Mean .1896 sq.in..2316 sq.in..2190 sq.in..1836 sq.in. TABLE VIII 71 MEAN MEASUREMENTS FOR BOTH INDIVIDUAL AND GROUP COMBINED RIGHT-LEFT TIBIAL TUBEROSITY AREAS Subject X-ray #1 X-ray #2 X-ray‘#3 X-ray #4 VanderJagt .3160 sq.1n..2470 sq.in..3320 sq.1n..3735 sq.1n. Floberg .3795 .3685 .3930 .3895 Lytle .2350 .2875 .2395 .2710 Thomann .1240 .1590 .1025 .0730 Chandler .1785 .3780 .1885 .1775 Group Mean .2466 sq.in..2880 sq.in..2511 sq. in..2569 sq.in. APPENDIX E 73 TABLE IX RANK CORRELATION FOR EXPERIMENTAL SUBJECT CHANDLER: VERTICAL JUMPING VERSUS COMPETITIVE REBOUNDING W Rebounds Rank‘ Rank Per Vertical 0f 0f 2 Minute Jumps Rebounds Jumps Differences Difference 0.18 22.5 inches 5 7 -2 4 .26 23.5 3 5 -2 4 .16 23.0 6 6 0 0 .15, 27.2 7 1 6 36 .31 24.8 2 4 -2 4 L20 26.2 4 2 2 fi .37 25. l 3 -2 2'8 56(2. D2) + p = l - 6fiED2 N(N2—1) p = 1 — 6X56 7(49-1) = l - 336 = 1—1 336 0 therefore r = 0 ’0 ll 74 TABLE X RANK 0F CORREALTION FOR EXPERIMENTAL SUBJECT THOMANN: VERTICAL JUMPING VERSUS COMPETITIVE REBOUNDING Rebounds Rank Rank Per Vertical 0f 0f 2 Minute Jumps Rebounds Jumps Difference Difference 0.37 21.5 inches 2 8 -6 36 .30 21.8 3 7 -4 16 .28 22.5 4.5 4.5 0 0 .24 22.3 8 6 2 4 .25 22.8 7 3 4 16 .27 22.9 6 2 4 16 .4g 23.6 4 4 0 0 .2 22.5 .5 .5 0 O 55' 88 (5.132) +10 p==1--6£D2 N(N2-1) p = 1 — 6X88 8 (54-1) = l - 528 = 1-1.0476 p - —.048 therefore r = -.05 75 TABLE XI RANK CORRELATION FOR CONTROL SUBJECT BERRY: VERTICAL JUMPING VERSUS COMPETITIVE REBOUNDING Rebounds Vertical Rank Rank Per Jumps of of 2 Minute (inches) Rebounds Jumps Difference Difference 0.14 24.8 7 7.5 -0.5 0.25 .23 25.8 4 5.5 -1.5 2.25 .39 24.8 2.5 7.5 -5 25 .18 26.4 6 2 4 16 .39 25.8 2.5 5.5 -3 9 .41 26.1 1 4 -3 9 .19 27.9 5 1 4 16 .12 26.2 8 3 5 25 -13 102.5(£D2) +13 2 p = 1 _ 6.2 D N (N2 - 1) p = 1 - 6 X 102°5 = 1 -.§12 e. 1-1.22 8 (64-1) 504 p = -.22 therefore r = -.23 76 TABLE XII RANK CORRELATION FOR CONTROL SUBJECT WILLIAMS: VERTICAL JUMPING VERSUS COMPETITIVE REBOUNDING Rebounds Vertical Rank Rank Per Jumps 0f 0f Minute (inches) Rebounds Jumps Difference Difference2 0.12 18.5 7 6 1 1 .44 18.5 1 6 -5 25 .18 18.5 5.5 6 -0 5 0.25 .27 20.1 3 2 1 1 .19 20.8 4 l 3 .23 19.3 2 3.5 -1.5 $.25 .1 19. 5.5 3.5 2 ‘ -7 7l"“"2.5 (£132) +7 p=1-6£D2 N(N2-1) p = 1 — 6X42.5 = 1 - 255 = 1-,7589 7(49—1) 336 +.24l therefore r = +.252 '0 ll HICHIGRN STRTE UNIV. 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