46 KINESIOLOGIA SLOVENICA 4 (1998)1 : 46-51 TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-OFF POWER SPACE Voiko Stroinik TAXONOMSKA STRUKTURA ENTITET V v PROSTORU ODRIVNE MOCI Abstract A taxonomic analysis can provide an efficient toll to study a structure of motor abilities, as well. The aim of the present study was to employ taxonomic anal- ysis to observe the latent dimensions that describe subjects as entities in a take-off power space. A sam- ple of 11 8 proficient sportsmen from the Slovenia, participating in six different sports, was measured w ith 13 tests of take-off power and 14 anthropo- metrical measures. In the take-off power space, two taxonomic dimensions emerged: an ability to per- form vertical jumps w ith a counter movement and an ability to perform multiple jumps, where the dominant factor appeared to be one-legged hori- zontal take-off. After the partialization of the influ- ence of anthropometrical measures, the taxonomic dimension »horizontal multi-jumps« emerged clear- er, whi le at the dimension »vertical jumps« one- legged jumps were more pronounced, pointing to a demand for a greater take-off power and good take- off technique. The obtained dimensions can be in- terpreted mainly as complex abilities for performing jumps of a certain type. On the other hand, the abil- ities at the lower level that are responsible for their execution could not be identi fied reliably. Key words: motor abilities, jumping, Laxonomic ana- lysis University of Ljubljana - Faculty of Spori, Gortanova 22, 51-1000 Ljubljana, Slovenia phone: ++38661140-10-77 fax: ++38661448-148 e-mail: vstr@uni-lj.s1 I zvleček Strukturo motoričnih sposobnosti je mogoče proučevati tudi s pomočjo taksonomske analize. Namen te naloge je bil uporabiti taksonomsko anal- izo za opis latentnih dimenzij, ki opisujejo merjence v prostoru odrivne moči. Sodelovalo je 118 katego- riziranih športnikov Slovenije iz šestih športnih panog, ki so bili izmerjeni s 13 testi odrivne moči in 14 antropometrijskih mer. V prostoru odrivne moči sta bili identificiran i dve taksonomski dimenziji: sposobnost izvajanja vertikalnih skokov z nasprot- nim gibanjem ter sposobnost izvajanja mno- goskokov, kjer se je kot dominantni element pojavil enonožni horizontalni odriv. Po parcializaciji antropometrijskih mer se je taksonomska dimenzija horizontalnih mnogoskokov še dodatno utrdila, v strukturi druge taksonomske dimenzije pa so dobili večji poudarek enonožni vertikalni skoki, kar kaže na zahteve po večji odrivni moči in dobri tehniki odriva. Dimenzije je bilo mogoče interpretirati pred- vsem kot kompleksne sposobnosti izvajanja skokov določenga tipa. Sposobnosti nižjega ranga, ki so odgovorne za njihovo izvajanje, ni bi lo mogoče zaneslj ivo identificirati. Ključne besede: motorične sposobnosti, skoki, tak- sonomska analiza il e e li Vojko Strojnik TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-OFF POWER SPACE 47 1 ntrod uction As in many areas of human activity, more functional types of ju mpers in take-off power space can be ex- pected, as well. That is why the questions of how many jumpers' types and of which kind may be very actual. According to the previous research works in a field of motor abil ities (7), it was possible to conclude that taxonomic procedures may be equally applicable as factor or component analysis for a determination of a structure of motor abilities. There is an important distinction between two approaches. Factor analysis determines a structu re of observed space as defined by measured variables. Since a subject always acts asa unity, it seems reasonable to treat him in that way. This does not include only the d ifferences at a single motor test (a particular jump) but also and es- pecially the differences thatappear atall motor tests included into an analysis. According to a set of jump- ing tests, it would be possible to talk about jumper's types or dimensions that define them, respectively. A take-off power is a manifest motor ability that in the area of action's defined motor abilities fits into a speed-power (9) . According to a neuro-muscular function, the speed-power can be divided into two categories: a speed-power at concentric contrac~on and a speed-power atstretch-shortening cycle. Coh (3) analyzed the structure of a take-off power space on selected population of sportsmen of different sports. He attained three factors which preserved their structu re after a partialization of anthropomet- ric variables, as well. Sprints formed a distinctive fac- tor. More important were the other two factors: elas- tic power and explosive power. The structures of these two factors were not possible to connect with the findings of Buehrle and Schmidtbleicher (2) of two distinctive forms of the speed-power. The basic goal in motor activities described in terms of the speed-power is equal in ali occasions: explo- siveness. For that reason, it seems that a term explo- sive power may not be used to describe a special ability, since the explosiveness of the motor actions is the main characteristic of ali forms of the speed- power. A term elastic power may be even more dis- putable. Elasticity of muscles and tendons (muscle potentiation) is only one of the mechanisms to emerge at the stretch-shortening cycle. A neural po- tentiation must also be considered (1 ). For that rea- son, a term žreactive ability' has been adopted to de- scribe this phenomenon. The differences amongsubjects in the take-off pow- er tests may originate from the anthropometrical characteristics of the subjects, as well. So, the sec- ond part of the paper will try to answer on a ques- tion about the influence of the anthropometrical characteristics ona formation of jumpers' types. According to th is, the subject matter of th is paper was asa study of the take-off power and the prob- lems to so Ive: (1) establ ishing a taxonomic structure of entities in a take-off power space and (2) estab- lish ing an influence of anthropometric variables on the taxonomic structure in the take-off powerspace. M ethods Subjects. A sample of 118 proficient sportsmen from Slovenia volunteered in the study. They partic- ipated in the followingsports: athletics, ski jumping, basketball, handball, volleyball, and football. The mean age was 22.3 years, range from 16 to 37 years, and the mean training participation was 7.6 years, range from 2 to 20 years. In tirne of measurements, all the subjects were healthy and w ithout injuries. Variables. The following test were employed to as- sess the take-off power: standing broad jump (SBJ2), one-legged standing broad jump (SBJl), sargent jump (SARG2), one-legged sargent jump (SARGl ), sargent jump from dropping height of 75 cm (SARG75), abalak jump without a help of hands (ABALNO), abalak jump with a help of hands (ABAL- HA), standing broad triple jump (TRIP), broad triple jump started from dropping height of 50 cm (TRIP- DR), broad triple jump with 3 steps run (TRIP3), broad five jump with a single leg (FIVE), drop-broad jump (DRBR), and one-legged drop jump from 45 cm (DROP). A result in horizontal jumps was a dis- tance, in vertical jumps the maximal height of the jump. Each jump was repeated th ree timesv. More detailed description of tests was provided by Coh (3). The fol lowing tests were used to assess the anthro- pometrical characteristics : body height (BH), arm length (AL), leg length (LL), foot length (FL), shoulder width (SW), pelvis width (PW), ankle diameter (AD), knee diameter (KD), thigh ci rcumference (TC), thigh circumference - vastus (TCV), calf ci rcumference (CC), upper arm skinfold (AS), abdomen skinfold (BS), thigh skinfold (TS), and calf skinfold (CS). These measurements were performed in accordance with the international biological program (6). Statistics. For ali take-off variables (2nd repetition) and anth ropometrical variables the basic statistical parameters were calculated. The results of single tests (three repetitions) were transformed into the parallel projections to the first principal com ponent and used in further analysis. A taxonomic structure of the entities was established by the algorithm TAX- ON (11 ). A partialization o f take-off variables with anthropometrical variables was performed with a 48 Vojko Strojnik TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-O FF POWER SPACE mult iple regression analysis. The partialized results of entit ies in single take-off variables were presented as the students' residuals. After the partialization, the second taxonomization was performed in the take- off power space. Results Table 1 presents the basic statistical parameters of the jumping tests. Results in ali observed variables were normally distributed. The differences between Table 1. Basic statistical parameters of jumping vari- ables Variable XA so SKE ASSI OIS TEST SBJ2 265,4 17,2 ,003 ,245 ,07 ,49 SB]l 225,3 18,2 -,491 ,058 ,04 ,95 SARG2 57,4 6,3 -,323 -,044 ,05 ,80 ABALNO 54,5 7,5 ,073 ,213 ,07 ,46 TRIP 769,8 57,7 -,333 -,259 ,06 ,65 TRIPDR 802,8 66, 1 -,361 ,037 ,03 1,00 A8ALHA 66,1 8, 1 -,247 ,048 ,07 ,51 SARG75 57,8 7,5 -, 107 ,009 ,05 ,90 DRBR 283,8 27,7 , 142 -,007 ,05 ,88 SARGl 60,0 5,6 -,673 1124 ,09 ,28 TRIP3 946,4 80,1 ,293 ,114 ,06 ,73 FIVE 1308,2 98,6 -,446 -,069 ,07 ,51 DROP 57,3 5,8 , 145 -,028 ,06 ,69 XA - means, SD - standard deviation, SKE - skewness, ASSI - asymmetry, DJS- maximal distance from theoretical distribution, TEST - Kolmogorov-Smirnov test, Variables - far variable names seeMethods Table 2. Basic statistical parameters of anthropo- metric variables Variables XA so SKE ASSI OIS TEST AV 1822,9 77,3 -,613 ,278 ,06 ,61 AT 761,9 83, 1 -,097 ,486 ,10 ,17 AL 794,4 39,7 -,265 , 124 ,05 ,79 LL 1043,0 58,9 -,688 ,065 ,06 ,73 FL 268,8 14, 1 ,828 ,436 ,04 ,93 TC 563,9 27, 1 -,344 ,219 ,10 , 12 TCV 483,3 29,8 ,041 ,062 ,08 ,32 CL 384,4 18,5 -,413 -, 120 , 11 ,07 sw 399,1 19,9 -,227 -,071 ,06 ,65 PW 275,3 16,0 ,372 ,309 ,06 ,74 AD 76,0 4,3 1,303 ,688 ,09 ,25 KO 98,6 4,4 1,031 ,718 ,10 , 14 AS 55,0 16,9 1,326 ,990 ,10 ,13 BS 76,6 26,6 2,926 1,542 , 15 ,09 TS 95,7 28,8 -,401 ,257 ,08 ,35 cs 68,1 27,0 4,858 1,768 , 11 ,08 XA - means, SD - standard deviation, SKE - skewness, ASSI - asymmetry, DIS- maximal distance from theoretical distribution, TEST -Kofmogorov-Smirnov test, Variables - far variable names see Methods the lowestand the highest results were big in ali vari- ables. The basic statistical parameters of the anthro- pometric variables are shown in Table 2. Ali results' distributions, except in BS, were normal. The distri- butions in the skinfold variables, except TS, were asymmetric in direction of higher values. The analysis of correlation coefficients (Table 3) showed that the group of va riables including TRIP, TRIPDR, TRIP3, and FIVE were those w ith the high- est connections. It was possible to assume that the origin of their common variance might be found in a similar inter-muscular co-ordination. The differ- ences in a neuro-muscular function (which mecha- n isms and to w hat extent, respectively), what would have the most relevance, were not possible to de- term ine for this group of tests. The second group of connected variables, present ing the vertical jumps, displayed much lower correlation coefficients than the first group. A central posit ion in this group be- longed to SARG75, which had the highestconnec- Table 4. Uniqueness and commonalties of jumping va riables UNI COM SBJ2 1184 ,816 SBJl ,388 ,611 SARG2 ,243 ,757 ABALNO ,288 ,712 TRIP , 126 ,874 TRIPDR , 168 ,832 ABALHA ,293 ,707 SARG75 ,209 ,791 DRBR ,251 ,749 SARGl ,394 ,606 TRIP3 1190 ,810 FIVE ,182 ,818 DROP ,467 ,533 UNJ - uniqueness, COM - communality Table SA. Principal components of correlation ma- trix of jumping variables PCOM LAM % 1 7,99 61 ,5 2 1,62 12,5 3 ,71 5,5 4 ,52 4,2 5 ,46 3,6 6 ,35 2,7 7 ,30 2,4 8 ,29 2,3 9 ,21 1,7 10 ,17 1,4 11 ,15 1,2 12 , 11 ,9 13 ,06 ,5 PCOM - principal component, LAM- lambda value, %-relative share o( variance o( the system Vojko Strojnik TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-O FF POWER SPACE 49 Table 3. Correlation coefficient matrix of jumping variables 1 2 3 4 5 6 7 8 9 10 11 12 13 1 SBJ2 1,00 2 SBJ1 ,64 1,00 3 SARG2 ,75 ,so 1,00 4 ABALNO ,52 ,28 ,58 1,00 5 TRIP ,85 ,63 ,69 ,49 1,00 6 TRIPDR ,77 ,60 ,56 ,43 ,90 1,00 7 ABALHA ,61 ,38 ,59 ,66 ,49 ,40 1,00 8 SARG75 ,75 ,45 ,80 ,63 ,71 ,63 ,62 1,00 9 DRBR ,58 ,63 ,36 ,20 ,68 ,71 ,25 ,43 1,00 10 SARG1 ,62 ,60 ,59 ,33 ,64 ,64 ,43 ,60 ,53 1,00 11 TRIP3 ,62 ,58 ,43 , 19 ,78 ,80 ,25 ,4 7 ,72 ,57 1,00 12 FIVE ,68 ,69 ,50 ,36 ,83 ,81 ,38 ,55 ,72 ,58 ,79 1,00 13 DROP ,61 ,54 ,51 ,38 ,59 ,57 ,39 ,57 ,49 ,69 ,49 ,57 1,00 Numbers in matrix presents a pearson correlation coeff,oent far pa,rs of vanables. Far vanable names see Methods. Table 5B. Correlation coefficients between jumping variables and principal components PC1 PC2 SBJ2 ,89 , 11 SBJ1 ,74 -,23 SARG2 ,77 ,39 ABALNO ,57 ,61 TRIP ,93 -,09 TRIPDR ,88 -,20 ABALHA ,61 ,57 SARG75 ,80 ,37 DRBR ,73 -,45 SARG1 ,77 -,04 TRIP3 ,78 -,43 FIVE ,85 -,30 DROP ,73 -,00 PC1 - first principal component, PC2 - second principal com- ponent tions with other variables from this group. The com- monalties (Table 4) of motor variables were high to middle high. A high common variance of the take- off power space was very likely influenced by the fact that the subjects ach ieved more or less similar results in single tests (referring to the position in a distri bu- tion) or that the groups of better or worse subjects were relative stable, respectively. Two principal components were extracted from the correlation matrix according to the lambda criterion (Table 5). The first princ ipal component explained much as 61 .5% of the whole common variance of included motor variables. According to the amount of the explained variance, it was possible to assume the first principal component asa general factor. The second principal component discriminated the vari- ables. 1 n general, the highest and positive projections to the second principal component displayed the variables presenting jumps with a counter move- ment. The variables presentingjumps with a very in- tensive stretch-shorteningcycle had mainly negative projections. Table 6 shows the parallel and orthogonal projec- tions of the jumping variables to both taxonomic di- mensions. The same projections, but after the par- tia lization of the athropometrical variables, can be seen in the Table 7. Discussion The most important finding of the presentstudy was thatthe set of analyzed jumpingtests led to two well- defined taxonomic d imensions. The firsttaxonomic dimension was mostly determined by variables pre- senting the jumps w ith a counter movement. The variables (ABALNO, FIVE, TRIP3), in which the neu- ro-muscular mechanisms differed the most in any di- rection, had low and statistically non-significant pro- jections. For that reason, it would be difficu lt to de- fend a thesis that the main characteristics to dis- criminate the subjects was the speed-power at con- centric muscular contraction or jumpingwith a con- centric muscle action, respectively (4). For this taxo- nomic dimension, the fol lowing mechanisms from the speed-power can be important: a capability to recruit as much as possible motor un its in the short- esttime, a capabi li tyto develop the highest possible fi ring rate of motor neurones, a good synchroniza- tion of motor units and muscles, bigger muscle transversal area, more fast motor units, etc., which are typical for a concentric contraction, but also the capability to include a myotatic reflex (neural po- tentiation), as well as elasticity of muscles and ten- dons (muscle potentiation), which aretypical forthe stretch-shortening cycle (8). So it seemed, that it would be possible to talk about a complex capabili- ty of jumping performance, wh ich was close to per- formingjumps with counter movement. 50 Vojko Strojnik TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-O FF POWER SPACE Table 6. Complex and structure of taxonomic di- mensions Complex Structure TAXl TAX2 TAX1 TAX2 SBJ2 ,69 ,02 ,70 ,47 SBJl ,71 ,26 ,88 ,72 SARG2 ,67 -, 16 ,57 ,28 ABALNO ,35 -,07 ,3 1 , 16 TRIP ,64 ,23 ,79 ,65 TRIPDR ,45 ,47 ,75 , 76 ABALHA ,65 -,36 ,41 ,07 SARG75 ,69 -, 16 ,59 ,29 DRBR ,46 ,40 ,73 ,71 SARG1 ,78 ,02 ,79 ,53 TRIP3 , 13 ,73 ,61 ,81 FIVE ,31 ,65 ,73 ,85 DROP ,89 -,24 ,73 ,34 TAX1 -first taxonomic dimension, TAX2 -second taxonomic di- mension The second taxonomic d imension was mostly de- fined with the horizontal multijumps with a preced- ing run (substantial horizontal speed atthe beginning of jumping). The first common feature that discrim- inated the subjects could be a jumping technique. The second ones could be the differences in per- forming the stretch-shortening cycle. Next to the in- tra-muscular co-ordination, it should be mentioned that the horizontal jumps differ from vertical ones in an involvement of the muscle groups, as well. This means, that a topologic factors must also be en- countered. The second taxonomic dimension can be defined asa complex capability responsible for a variability in the horizonta l jumps. The first taxonomic dimension after the partializa- t ion of the anthropometrical variables (Table 7) was defined clearer as before. lts comparison w ith the factor of elastic strength (3) showed that the first tax- onomic dimension differentiated the variables of take-off power more than the factor of elastic pow- er. However, there were also much similarities be- tween both. From a contents, itwould be possible to characterize the fi rst taxonomic d i mension asa con- sol idation of a motor model to perform the horizon- tal multijumps. In anycase, it was a factthatthe mul- t ijumps, asa quite uniform motor structure, dis- criminated the subjects the most. It was possible to assume that th is was a result of a specific tra in ing where in certain sports the multijumps presented one of the basic tools of preparation while in others were rarely presen t. After the partialization of the an- thropometric va riables this became even more ob- vious. The second taxonomic dimension after the partial- ization did not correspond well to the first one be- fore the partialization. However, even if the parallel projections were much different it was possible to Table 7. Complex and structu re of taxonomic di- mensions after partialization Complex Structure TAXl TAX2 TAX1 TAX2 SBJ2 , 17 -,51 ,57 -,64 SBJl -, 1 2 -1 ,02 ,68 -,92 SARG2 -, 18 -,65 ,33 -,51 ABALNO , 1 7 -,01 ,18 -, 15 TRIP ,68 -,22 ,85 -,75 TRIPDR ,81 -,04 ,84 -,68 ABALHA -,43 -,70 , 12 -,36 SARG75 , 1 O -,39 ,40 -,47 DRBR ,70 -, 14 ,81 -,69 SARG1 -, 13 -,82 ,52 -, 72 TRIP3 ,79 -, 1 2 ,88 -,74 FIVE ,80 -, 11 ,88 -, 74 DROP ,07 -,59 ,53 -,64 TAX1 :-- first taxonomic dimension, TAX2 -second taxonomic di- mens1on conclude on similar mechanisms. A contents of the second taxonomic dimension could be defined asa capability to perform vertical jumps w ith an empha- sis ona one-legged take-off. Although at the jumps, which resu lts had the highest projections on that di- mension, the concentric speed-power was consid- ered as the main component, it had to be recog- nized, especially in a line with our experiences of measuring jumps with a force plate, that a basic movement pattern at that jumps included the stretch-shortening cycle. It was also possible to recognize a significant ho- mogenization of the variables which defined the first taxonomic d imension after the partialization. That was not observed to the same extent at the second taxonomic dimension. Nevertheless, it was possible to observe that both taxonomic dimensions dis- criminated employed variables much more after the partialization. The results of the taxonomic analysis showed obvi- ously that the existence of two taxonomic dimen- sions in a take-off power space was rea l. The paral- Jel projections of the variables on both taxonomic di- mensions formed a simple sol uti on. Even so, it was difficult to define what was a un ique variance of each dimension and what was a substance that con- nected or discriminated them, respectively. The obtained taxonomic dimensions proved thatthe subjects, when observed for their jumping perfor- mance, should be analyzed in the terms of one- legged mult ijumps and vertical jumps separately. A take-off action in each of the observed jumps could be performed concentrically as well as a stretch- shortening cycle. Although there was not possible to assign directly any of the jumps to any of both neuro- muscu lar actions, our experiences with measure- Vojko Strojnik TAXONOMIC STRUCTURE OF ENTITIES IN THE TAKE-O FF POWER SPACE 51 ments w ith farce plate strongly suggested that no jump was perfarmed purely concentrically. A sportsmen special ization should also be taken in- to account. The specialization showed itself through the results obtained in the jumps which were close to those at competit io n. For that reason, the relations among obta ined results in single jumps were under this influence. A group of the track and field athletes dominated in the horizontal mult ijumps while the volleyball players dominated in the vertical jumps. The obtained results could also be observed through the optics of one- or two-legged jumps (5, 1 O). A bi- lateral deficit can be influenced by t raining. In the sportsmen experiencing more two-legged jumps (as in vol leyball) this deficit is lower. That the uni-later- ali ty had an important role (at least in th is sample of subjects) showed the variables with the highest pro- ject ions on both taxonomic dimensions simultane- ously, which presented one-legged jumps. lnside the observed sample o f t he subjects, these variables could have a dominant ro le in a d iscrimination of the subjects. A high correlation between both dimen- sions could testify this. W hat about the applicatio n of these results? In the take-off power space, the subjects could be differ- entiated according to two criteria. The fi rst one was an abil ity to perfarm the horizontal multij umps and the second o ne an ability to perfarm the vertical jumps. A good results in one criteria d id notexclude automatically a good result in another criteria. It can be said: nothing espec ially new, we already knew this w ithoutany arithmetic. And there is a lot of truth in this. So it seems that some other conclusions, which fallow from the above, need to gain mo re at- tention far its consequences: how to tackle an ex- periment of such kind and a problem of relationship between the employed methods and obtained re- su lts or/and conclusions. As much as we approach to the elementary motor abilities, lesser is possibility far further explanation of a human function w ith complex results obtained w ith motor tests. 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