Proceedings 2011. (2012), Vol 3, ISSN 1986-8146
www.sportkon.com
CANONICAL RELATIONS BETWEEN
THE SYSTEM OF MOTOR AND CONATIVE
VARIABLES OF FEMALE ADOLESCENTS
Veroljub Stankovi}1 and Dragan Popovi}2
Fakultet za sport i fizičko vaspitanje u Leposaviću, Univerzitet u Pri{tini, Srbija
Faculty of Sport and Physical Education at Leposavić, University of Pri{tina, Serbia
1
ORIGINAL SCIENTIFIC PAPER
ORGINALNI NAUČNI ČLANAK
doi​: 10.5550/SP.3.2011.04
UDK: 196.012.1-053.6 Summary
Sažetak
The sample of 400 female participants, aged 15-18 years,
was applied to the system of 21 motor variables and 10
conative variables. The aim was to determine statistically
significant relations between the systems of variables of motor abilities, cognitive variables and variables of conative
characteristics. The data were processed by canonic correlation analysis. Between the system of motor variables and the
system of conative variables three canonic correlations were
got (R1=.56, R2=.36, R3=.35) which are statistically significant.
The results of the research showed that adolescent females
achieve better results concerning motor variables of the
motion structure, tonus regulation and synergy regulation,
intensity and duration of excitation if they have increased
values concerning conative variables of the efficiency of the
system of regulation and control of defence reaction (ALPHA),
efficiency of the system of regulation and control of offence
reaction (SIGMA) and efficiency of the system of coordination of regulative functions (DELTA).
Na uzorku 400 ispitanika ženskog pola, uzrasta 15-18 godina, primenjen je sistem od 21 varijable motoričkih sposobnosti i 10 varijabli za procenu konativnih karakteristika,
sa ciljem da se utvrde statistički značajne relacije između
dva sistema koji pripadaju različitim antropolo{kim prostorima. Podaci su obrađeni pomoću kanoničke korelacione
analize. Između sistema motoričkih varijabli i sistema
konativnih varijabli adolescentkinja dobijena su tri značajnih
kanoničkih korelacija (R1=0,56, R2=0,36, R3=0,35). Rezultati istraživanja su pokazali da adolescentkinje bolje rezultate
postižu u motoričkim varijablama strukturiranja kretanja,
regulaciji tonusa i sinergijskoj regulaciji, intenzitetu i trajanju ekscitacije ukoliko imaju povećane vrednosti u konativnim
varijablama efikasnosti sistema za regulaciju i kontrolu organskih funkcija (HI), efikasnosti sistema za regulaciju i
kontrolu reakcija odbrane (ALPHA), efikasnosti sistema za
regulaciju i kontrolu reakcije napada (SIGMA) i efikasnosti
sistema za koordinaciju regulativnih funkcija (DELTA).
Key Words: female adolescents, motor abilities, conative
characteristics, relations.
Introduction
The development of motor skills represents a basic component of the overall development of one’s personality. Their
development depends on the development of conditioned-reflex connections in the central nervous system. Due to
the fact that motor skills are one of the basic factors responsible for all types of movement, that is, represent the ability
which is the basis for movement, the monitoring of the
development of the motor skills of children and young adults,
and is of special interest for coaches, teachers, instructors
and psychologists.
The determination of the relations between motor skills and
other segments of the anthropological status of female adolescents at present represents a very current practical and
theoretical problem, which is of great significance, primarily
due to the effective monitoring of the development of
Ključne riječi: adolescentkinje, motoričke sposobnosti,
konativne karakteristike, relacije.
Uvod
Razvoj motoričkih sposobnosti predstavlja sastavni deo
sveukupnog razvoja ličnosti. Njihov razvoj zavisi od stvaranja
uslovno-refleksnih veza u centralnom nervnom sistemu. Iz
razloga {to je motorna sposobnost jedan od osnovnih činilaca za sva kretanja, tj sposobnost koja formira osnovu za
kretanja praćenje razvoja motoričkih sposobnosti dece i
omladine od posebnog je interesa za trenere, nastavnike,
pedagoge i psihologe.
Utvrđivanje relacija motoričkih sposobnosti sa drugim segmentima antropolo{kog statusa adolescentkinja predstavlja
u sada{njem trenutku veoma aktuelan praktičan i teorijski
problem, koji je od velikog značaja, pre svega, zbog efikasnog
praćenja razvoja relevantnih antropolo{kih karakteristika ali
i mogućnosti formiranja {to racionalnijih procedura u teh-
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ORIGINAL SCIENTIFIC PAPER
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KANONIČKE RELACIJE IZMEÐU SISTEMA MOTORIČKIH I
KONATIVNIH VARIJABLI KOD ADOLESCENTKINJA
ORIGINAL SCIENTIFIC PAPER
ORGINALNI NAUČNI ČLANAK
Stankovi}, V. i Popovi}, D.: CANONICAL RELATIONS BETWEEN THE SYSTEM ...
Proceedings 2011, 29–37
anthropological characteristics, but also the possibility of
forming the most rational procedures in the technology of
physical education, sport and sports training, in the planning,
programming and control of the training process (Stanković,
2001, 2008). Several previous studies (Boli, Popović, &
Popović, 2012; Ismail, 1976; Ismail & Gruber, 1971; Horga,
1979; Mraković, Gredelj, Metiko{, & Ore{ković, 1974;
Bala, Ho{ek, & Momirović, 2002; Valant Valant Velepec,
Pori, Tu{ak, & Pori, 2009) have determined significant, and
on occasion vital correlations between personality traits,
which determine the modality of behavior, evaluated within
various models of conative functioning, and the motor skills
of participants who found themselves in a relatively stationary phase of their conative and motor development. Even
though an insufficient number of studies have been carried
out over the past few years regarding the relations between
personality traits and motor dimensions, on the basis of the
results of previous research, strong correlations between
motor skills and conative characteristics were expected (Ismail,
1976; Mraković et al., 1974). In addition, over the past 30
years, much has been done to construct reliable measuring
instruments and to systematically analyze anthropological
space (Malacko & Popović, 2001; Momirović et al., 1999;
Stanković, Popović, & Popović, 2011)).
nologiji fizičkog vaspitanja, sporta i sportskog treninga,
planiranju, programiranju i kontroli treninga u toku trenažnog
procesa (Stanković, 2001, 2008). U vi{e prethodnih istraživanja (Boli, Popović i Popović, 2012; Ismail, 1976; Ismail i
Gruber, 1971; Horga, 1979; Mraković, Gredelj, Metiko{ i
Ore{ković, 1974; Bala, Ho{ek i Momirović, 2002; Valant
Valant Velepec, Pori, Tu{ak i Pori, 2009) nađeno je da postoje značajne, a ponekad i supstancijalne korelacije između
osobina ličnosti, koje određuju modalitete pona{anja, procenjenih pod raznim modelima konativnog funkcionisanja,
i motoričkih sposobnosti kod ispitanika koji su se nalazili u
relativno stacionarnoj fazi konativnog i motoričkog razvoja.
Iako se u poslednjih godina nije mogao naći veći broj istraživanja o relacijama osobina ličnosti i motoričkih dimenzija
na osnovu rezultata prethodnih istraživanja, očekivalo se
dobijanje jakih korelativnih veza između motoričkih sposobnosti i konativnih karakteristika (Ismail, 1976; Mraković
i saradnici, 1974). Takođe, u poslednjih 30 godina mnogo
je učinjeno da se konstrui{u pouzdani merni instrumenti i
da se sistematski analizira antropolo{ki prostor (Malacko i
Popović, 2001; Momirović i saradnici, 1999; Stanković,
Popović i Popović, 2011).
Methods
Metode
Sample of participants
Uzorak entiteta
A sample of 400 female participants, age 15-18, was included in a study which was based on the application of 21
variables of motor skills and 10 variables for the evaluation
of conative characteristics.
Na uzorku 400 ispitanika ženskog pola, uzrasta 15-18 godina, primenjen je sistem od 21 varijable motoričkih sposobnosti i 10 varijabli za procenu konativnih karakteristika.
Variables
Varijable
In order to evaluate motor skills, the following motor variables were used (Gredelj, Ho{ek, Metiko{, & Momirović,
1975; Metiko{, Prot, Horvat, Kule{, & Hofman, 1982): the
structuring of movement: 1. the three-ball slalom (S3L), 2.
hand tapping (TAR), 3. foot tapping (TAN), 4. foot tapping
against a wall (TAZ), 5. the forward-backward bend (PZK);
the regulation of tonus and synergy regulation: 6. standing
on one foot (RZO), 7. maintaining balance on a reversible
floor balance beam (ROK), 8. maintaining balance on a sideways balance beam (RPK), 9. hyperextensions (DPR), 10.
darts (PIK); the regulation of excitation intensity: 11. the
standing depth jump (SDM), 12. the 20m run with a high
start (20V), 13. the high jump (VIS), 14. the triple jump (TRS),
15. throwing a medicine ball from a prone position (BML);
the regulation of excitation duration: 16. hanging pull-ups
(VUZ), 17. push-ups on a bench (SKL), 18. torso lifts for 30s
(PTR3), 19. the maximum number of torso lifts (PTR), 20.
straightening of the torso (IST), 21. torso lifts on a vaulting
box (ISTS).
To evaluate the pathological conative characteristics from
the C.I.-N4 battery, the author of the Cornell Index version
standardization (C.I.-N4) is K. Momirović (1964), we used
the following variables which belong to the factors of the
first order (manifest variables), factors of the second order
factors (syndromes) and the cybernetic model of the effectiveness of regulatory systems: to evaluate the effectiveness
of the system for the regulation and control of defensive
reactions (ALFA): 1. anxiety (ANXT), 2. phobias (FOBT), 3.
hypersensitivity (HIPS); to evaluate the effectiveness of the
system for the regulation and control of organic functions
(HI): 4. cardiovascular conversion (KVKO), 5. inhibitory
conversion (INKO), 6. hypochondria (HIPO); to evaluate
the effectiveness of the system for the regulation and control
of a reaction to an attack (SIGMA): 7. impulsivity (IMPL), 8.
Za procenu motoričkih sposobnosti primenjene su sledeće
motoričke varijable (Gredelj, Ho{ek, Metiko{ i Momirović,
1975; Metiko{, Prot, Horvat, Kule{ i Hofman, 1982): strukturiranje kretanja: 1. slalom sa tri lopte (S3L), 2. taping rukom
(TAR), 3. taping nogom (TAN), 4. taping nogama o zid (TAZ),
5. pretklon-zaklon (PZK); regulacija tonusa i sinergijska regulacija: 6. stajanje na jednoj nozi (RZO), 7. ravnoteža na
obrnutoj klupici (ROK), 8. ravnoteža na poporečnoj klupici
(RPK), 9. duboki pretklon na klupi(DPR), 10. pikado (PIK);
regulacija intenziteta ekscitacije: 11. skok u dalj s mesta
(SDM), 12. trčanje 20m. iz visokog starta (20V), 13. skok u
vis (VIS), 14. troskok (TRS), 15. bacanje medicinke iz ležanja
(BML); regulacija trajanja ekscitacije: 16. vis u zgibu (VUZ),
17. sklekovi na klupici (SKL), 18. podizanje trupa za 30s
(PTR3), 19. podizanje trupa do otkaza (PTR), 20. ispravljanje
trupa (IST), 21. uspravljanje trupa na sanduku (ISTS).
Za procenu patolo{kih konativnih karakteristika iz baterije
C.I.-N4, Autor standardizacije Kornel indeks verzija (C.I.-N4)
je K. Momirović, 1964. primenjene su sledeće varijable
koje pripadaju faktorima prvog reda (manifestne varijable),
faktorima drugog reda (sindromima) i kibernetičkom modelu efikasnosti regulacionih sistema: za procenu efikasnosti
sistema za regulaciju i kontrolu odbrambenih reakcija (ALFA):
1. anksioznost (ANXT), 2. fobičnot (FOBT), 3. hipersenzitivnost (HIPS); za procenu efikasnosti sistema za regulaciju i
kontrolu organskih funkcija (HI): 4. kardiovaskularna konverzija (KVKO), 5. inhibitorna konverzija (INKO), 6. hipohondrija (HIPO); za procenu efikasnosti sistema za regulaciju i kontrolu reakcije napada (SIGMA): 7. impulsivnost
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Zbornik radova 2011, 29–37
aggression (AGRE); to evaluate the effectiveness of the system
for the coordination of regulatory functions (DELTA): 9.
depression (DEPS), 10. paranoia (PRND).
(IMPL), 8. agresivnost (AGRE); za procenu efikasnosti sistema
za koordinaciju regulativnih funkcija (DELTA): 9. depresivnost
(DEPS), 10. paranoidnost (PRND).
Statistical analysis
Statistička analiza
All of the data used in this study were processed at the
Center for Multidisciplinary Research at the Faculty of Sport
and Physical Education at the University of Pri{tina, using a
system of programs for data processing developed by Momirović, & Popović (2003), Popović (1980, 1993). The
method for the asymmetric analysis of redundancy proposed
in this paper is based on an earlier publication by Momirović, [talec and Zakraj{ek (1973) regarding generalized
image transformations and the method for the decomposition of latent structures proposed by Dobrić, Karaman and
Momirović (1983). The essence of the proposed method is
a canonical analysis of covariance (Momirović, Dobrić and
Karaman, 1983) of one set of variables and an image transformation of that group of variables derived from the projection of that group in the space being stretched by the
vectors of some other group of variables. Even though the
aim of the proposed method is to a certain extent similar to
the aim of the classical method for the analysis of redundancy (Van Den Wollenberg, 1977) and the methods for the
canonical factor analysis of redundancy (DeSarbo, 1981),
the criterion function of the canonical analysis of covariance in the generalized image space is different than the criterion function in the Van Den Wollenberg and DeSarb
method, so that the interpretation of the obtained associative measures depends on completely different assumptions.
The canonical correlation analysis, which is usually defined
as the maximization of the correlation between stochastically independent linear composites derived from two
groups of variables, can be defined as the maximization of
the scalar products between two groups of orthogonalized,
centered and normalized vectors, thus, as the solution to
what is essentially a geometric problem (Malacko & Popović,
2001; Popović, Stanković, Popović, Petković, & Stanković,
1987). Naturally, it is trivially easy to show that all, or almost
all the elementary statistical methods are reduced to an
ultimately simplified model of a canonical correlation analysis,
for the simple reason that these methods are merely special cases of a general linear model, and thus special cases of
a regression analysis. Nevertheless, the canonical correlation
analysis on its own is not a statistical method (Popović, 1993).
It could only be one if certain conditions were met, of which the most decisive factor is that the variables from groups
B1 and B2 have a multivariate normal distribution in the
population P with non-singular matrices of covariance. In
this case variables
Svi podaci u ovom istraživanju, obrađeni su u Centru za
multidisciplinarna istraživanja Fakulteta za sport i fizičko
vaspitanje Univerziteta u Pri{tini pomoću sistema programa
za obradu podataka koji je razvio Momirović i Popović
(2003), Popović (1980, 1993). Metoda za asimetričnu analizu prepokrivanja predložena u ovom radu zasnovana je na
jednom davno publikovanom radu Momirovića, [taleca i
Zakraj{eka (1973) o generalizovanim image transformacijama i na metodi za dekompoziciju latentnih struktura koju
su predložili Dobrić, Karaman i Momirović (1983). Su{tina
predložene metode je kanonička analiza kovarijansi (Momirović, Dobrić i Karaman, 1983) jednog skupa varijabli i
image transformacije tog skupa varijabli izvedenoj projekcijom tog skupa u prostor koga razapinju vektori nekog drugog
skupa varijabli. Iako je cilj predložene metode u izvesnom
smislu sličan cilju klasične metode za analizu prepokrivanja
(Van Den Wollenberg, 1977) i metode za kanoničku faktorsku analizu prepokrivanja (DeSarbo, 1981), kriterijska
funkcija kanoničke analize kovarijansi u generaliziranom
image prostoru različita je od kriterijske funkcije Van Den
Wollenbergove i DeSarbove metode, tako da se interpretacija dobijenih mera asocijacije zasniva na sasvim različitim
pretpostavkama. Kanonička korelacijska analiza, koja se
obično defini{e kao maksimiziranje korelacija između stohastički nezavisnih linearnih kompozita izvedenih iz dva
skupa varijabli, može se definisati i kao maksimiziranje
skalarnih produkata između dva skupa ortogonaliziranih
centriranih i normalizovanih vektora, dakle kao re{enje jednog
u su{tini geometrijskog problema (Malacko i Popović, 2001;
Popović, Stanković, Popović, Petković i Stanković, 1987).
Naravno, trivijalno je lako pokazati da se sve, ili gotovo sve
elementarne statističke metode svode na neki krajnje upro{ćeni
model kanoničke korelacijske analize, iz prostog razloga {to
su te metode samo posebni slučajevi generalnog linearnog
modela, dakle posebni slučajevi regresione analize. Međutim, kanonička korelacijska analiza nije, sama po sebi, statistička metoda (Popović, 1993). Ona to može postati samo
ako su ispunjeni neki uslovi, od kojih je presudan uslov da
su varijable iz skupova B1 i B2 multivarijatno normalno
distribuirane u populaciji P sa nesingularnim matricama
kovarijansi. U tom slučaju varijable
χ p2 = (n − 1 2 (m1 + m2 + 3) log e ∏ np (1 − ρ p2 )
have, if, the population value of some canonical correlation
has a value of zero, an asymptotic distribution with (m1-p)
(m2-p) degrees of freedom. The identification of the canonical variables on the basis of the coefficients in the vectors
x1p and x2p is as a rule very difficult, as it is clear that
these coefficients are actually parallel projections of the
vectors used to represent the canonical variables in the
coordinate systems defined by vectors which are used to
represent variables from B1 or B2. For this reason, for the
identification of the significant canonical variables, structural vectors of canonical factors are often used, defined
through the following operations:
t
1 1p
s1 p = Z k = R1 x1 p
s2 p = Z 2t k2 p = R2 x2 p
χ p2 = (n − 1 2 (m1 + m2 + 3) log e ∏ np (1 − ρ p2 )
imaju, ako je, populacijska vrednost neke kanoničke korelacije jednaka nuli, asimptotski distribuciju sa (m1-p)(m2-p)
stepeni slobode. Identifikacija kanoničkih varijabli na osnovu koeficijenata u vektorima x1p i x2p je po pravilu vrlo
teška, jer je očigledno da su ti koeficijenti, u stvari, paralelne projekcije vektora kojima su reprezentovane kanoničke
varijable na koordinatne sisteme defisane vektorima kojima
su reprezentovane varijable iz B1 odnosno B2. Zbog toga
se za identifikaciju značajnih kanoničkih varijabli obično
upotrebljavaju strukturalni vektori kanoničkih faktora, definisani operacijama:
s1 p = Z1t k1 p = R1 x1 p
s2 p = Z 2t k2 p = R2 x2 p
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ORIGINAL SCIENTIFIC PAPER
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Stankovi}, V. i Popovi}, D.: KANONI^KE KORELACIJE IZME\U SISTEMA...
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and sometimes cross-structural vectors, defined by the following operations
c1 p = Z1t k2 p = R12 x2 p
ORIGINAL SCIENTIFIC PAPER
ORGINALNI NAUČNI ČLANAK
c2 p = Z 2t k1 p = R21 x1 p
Naturally, the coefficients in these vectors are standard,
non-extremized correlations, and so the variances of these
elements, within the framework of the hypothesis that their
population value is zero, are of the n-1 order. Even though,
by definition, the variances of the canonical variables have
a value of 1, their actual variances can be determined based
on the squares of the forms of the matrices of range 1 defined through the following operations:
a ponekad i kros strukturalni vektori, definisani operacijama
c1 p = Z1t k2 p = R12 x2 p
c2 p = Z 2t k1 p = R21 x1 p
Naravno, koeficijenti u tim vektorima su obične, neekstremiziovane korelacije, pa su varijanse tih elemenata, pod
hipotezom da je njihova populacijska vrednost jednaka
nuli, reda n-1. Iako su, po definiciji, varijanse kanoničkih
varijabli jednake 1, njihove se stvarne varijanse mogu odrediti na osnovu kvadratnih formi matrica ranga 1 definisanih
operacijama:
R11 p = s1 p s1t p
R11 p = s1 p s1t p
R22 p = s2 p s2t p
R22 p = s2 p s2t p
and thus the variances, are, actually, the squares of the norms
of the structural vectors, and thus:
očigledno, te su varijanse, u stvari, kvadrati normi strukturalnih vektora, dakle:
σ 1 p = s1t p s1 p
σ1p = s s
t
1p 1p
σ 2 p = s2t p s2 p
σ2p = s s
t
2p 2p
For the evaluation of the importance of the canonical factors
we will more frequently than not, for no apparent reason,
take into consideration the relative variances, that is, variances and divided by m1, or m2. Nevertheless, through
the application of the elementary postulates of the classical
theory of measuring, we can easily show that the lower level
of the generalizability of the canonical variables is:
Za ocenu važnosti kanoničkih faktora če{će se, zbog ne
sasvim jasnih razloga, uzimaju relativne varijanse, dakle
varijanse i podeljene sa m1, odnosno m2. Međutim, primenom elementarnih postulata klasične teorije merenja
lako se može pokazati da je donja granica generalizabilnosti kanoničkih varijabli:
α1 p = 1 − σ 2−2p
α1 p = 1 − σ 2−2p
α 2 p = 1 − σ 1−p2
α 2 p = 1 − σ 1−p2
and that these measurements are a more appropriate basis
for the evaluation of the importance of canonical factors
(Bosnar et al., 1984; Popović, 1993).
Results
The effectiveness in the performance of any kind of human
activity is not independent of any of the features which regulate the modalities of human behavior. Namely, it is known
that some features of conative space directly limit effectiveness in various activities, indirectly in others, for example,
due to their contaminating effect on certain other anthropological features, abilities or characteristics (Popović &
Simonović, 2008; Popović & Stanković, 2005). We have
also not ruled out the possibility that in some of the activities, the same conative features represent the restrictor, and
in some the stimulator of effectiveness, especially in situations where they play a part in the success of certain activities. In this respect, there is the rule that there are no two
subjects whose structure would be completely identical,
either in terms of their conative abilities or any other ones
at that, irrespective of their final number. For these reasons,
being familiar with the complexities of some activity, which
also includes the space of conative characteristics, is an
important assumption of the operationalization of the goal
of each activity. In the process of determining statistically
significant relations, that is, obtaining the maximal connection between the multivariate system of motor variables and
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Proceedings 2011, 29–37
i da su ove mere sigurniji osnov za procenu važnosti kanoničkih faktora (Bosnar i saradnici, 1984; Popović, 1993).
Rezultati
Efikasnost u obavljanju bilo koje ljudske aktivnosti nije nezavisna od osobina koje reguli{u modalitete čovekovog
pona{anja. Naime, poznato je da neke osobine iz konativnog
prostora ograničavaju efikasnost u različitim aktivnostima
direktno, a u nekim drugim idirektno, na primer, zbog kontaminirajućeg delovanja na neke druge antropolo{ke osobine, sposobnosti ili karakteristike (Popović i Simonović, 2008;
Popović i Stanković, 2005). Nije isključena ni mogućnost da
u nekim aktivnostima iste konativne osobine predstavljaju
restriktor, a u nekim stimulator efikasnosti, posebno u situacijama ako učestvuju u uspehu određene aktivnosti. U
vezi s tim, vredi i pravilo da ne postoje ni dva subjekta kod
kojih bi bila potpuno istovetna struktura bilo kojih, pa i
konativnih osobina, bez obzira na njihov konačni broj. Iz tih
razloga je poznavanje kompleksiteta neke aktivnosti, u koji
spada i prostor konativnih karakteristika, važna pretpostavka operacionalizacije cilja svake aktivnosti. U proceduri
utvrđivanja statistički značajnih relacija, odnosno dobijanja
maksimalne povezanosti između multivarijantnog sistema
motoričkih varijabli i sistema konativnih varijabli primenjena
the system of conative variables, we used a canonical correlation analysis of covariance with the parameters of the
canonical correlation (Rc) and the determinant of the coefficient (R2) and its statistical significance. By testing the statistical significance of the canonical correlation coefficient
(R=.57;), we explained the linear combinations between
groups of variables, that is, the connection between two
different systems of variables (Table 1). By solving the characteristic equations of the cross-correlation matrix, we also
obtained, as the root of these equations, the square (the
determinant coefficient) of the canonical correlation (R2=.32),
which explained the common variance of the variables from
the two groups from the overall variability of the analyzed
variables. Using the canonical correlation analysis, we carried out 4 statistical tests (Wilks' Lambda, Pillai's Trace,
Hotelling-Lawley Trace, Roy's Greatest Root). All 4 tests are
based on characteristic roots. The null hypothesis for each
of these tests is the same: the independent variable does not
affect any of the dependent variables.
Zbornik radova 2011, 29–37
je kanonička korelaciona analiza kovarijansi sa parametrima
kanoničke korelacije (R) i koeficijenta determinacije (R2) i
njegove statističke značajnosti. Testiranjem statističke značajnosti koeficijenta kanoničke korelacije (R=0,57), koji
obja{njava linearne kombinacije između skupova varijabli,
tj. povezanost dva različita sistema varijabli (Tabela 1).
Re{avanjem karakteristične jednačine kroskorelacione matrice dobijen je, kao koren tih jednačina, i kvadrat (koeficijent determinacije) kanoničke korelacije (R2=0,32), koji
obja{njava zajedničku varijansu varijabli iz dva skupa od
ukupnog varijabiliteta analiziranih varijabli. Pomoću kanoničke korelacione analize su izračuna i 4 statistička testa
(Wilks' Lambda, Pillai's Trace, Hotelling-Lawley Trace, Roy's
Greatest Root). Sva 4 testa su zasnovana na karakterističnim
korenovima. Nulta hipoteza za svaki od ovih testova je ista:
nezavisna varijabla nema uticaja na bilo koju od zavisnih
promenljivih
Tabela 1: Kanonička korelaciona analiza kovarijansi
Table 1: The canonical correlation analysis of covariance
Adjusted R
Approximate R
b
R2
.57
.52
.03
.32
Eig. val.
Differ.
Cumula
Ratio
F
df
p
.47
.32
.42
.36
1.91
400
.0001
Statstcs
Wilks' Lambda
Pillai's Trace
Value
F
df
p
.36
1.91
400
.0001
.92
1.83
400
.0001
Hotelling-L.T.
1.14
1.99
400
.0001
Roy's Grea test
.47
8.60
400
.0001
Legend/Legenda: R - Canonical correlation (Kanoni~ka koreacija), R2 - Square of the canonical
correlation (Kavadrat kanoni;ke korelacije): p - Probibility (Vjerovatno}a), df - Degrees of
freedom (Stepeni slobode).
The applied canonical correlation analysis of covariance
offered a pair of canonical factors in the space of the group
of motor skills and the group of conative regulatory functions
(Table 1). The first canonical factor in the motor space was
bipolar. The positive pole included the tests of force (straightening of the torso), repetitive strength (push-ups) and
flexibility (hyperextensions) while the negative pole included
the tests of coordination (foot tapping, tapping one's foot
against a wall, hand tapping), balance (standing on one leg,
eyes closed) and explosive strength (the triple jump, the
standing depth jump and the high jump).
The corresponding factor in conative space without a doubt
acts as a general factor of neuroticism. All of the evaluated
variables have the same statistically significant high projections on this canonical function. The greatest projections
could be found for the test vectors of variables of anxiety
(.79), hypersensitivity (.71) and phobias (.55) which were
used to evaluate the effectiveness of the of the system for
the regulation and control of defensive reactions, aggression
(.71) and impulsivity (.60) which were used to evaluate the
effectiveness of the system for the regulation and control of
reactions to attack, and paranoia (.66) and depression (.50)
as instruments for the evaluation of the effectiveness of the
system for homeostatic regulation. The smallest projections
were determined for the variables of cardiovascular and
inhibitory conversions and hypochondria, which were used
to evaluate the effectiveness of the system for the regulation
and control of organic functions (Popović, 2004).
Primenjena kanonička korelaciona analiza kovarijansi dala
je jedan par kanoničkih faktora u prostoru skupa motorike
i skupa konativnih regulatornih funkcija (Tabela 1). Prvi
kanonički faktor u prostoru motorike je bipolaran. Na pozitivnom se nalaze testovi sile (ispravljanje trupa na sanduku),
repetitivne snage (sklekovi) i fleksibilnosti (duboki pretklon
na klupici) a na negativnom polu testovi koordinacije (taping
nogom, taping nogama o zid, taping rukom), ravnoteže
(stajanje na jednoj nozi zatvorenim očima) i eksplozivne
snage (troskok, skok u dalj s mesta i skok u vis).
Korespodentni faktor u konativnom prostoru se bez ikakve
sumnje pona{a kao generalni faktor neurotizma. Na ovu
kanoničku funkciju sve procenjivane varijable imaju statistički značajne visoke projekcije. Najveće projekcije imaju
test vektori varijabli anksioznost (0,79), hipersenzitivnost
(0,71) i fobičnost (0,55) kojima je procenjivana efikasnost
sistema za regulaciju i kontrolu odbrambenih reakcija, agresivnost (0,71) i impulsivnost (0,60) kojima je procenjivana
efikasnost sistema za regulaciju i kontrolu reakcija napada,
paranoidnost (0,66) i depresivnost (0,50) instrumenti za
procenu efikasnosti sistema za homeostatičku regulaciju dok
su sa najmanjim projekcijama varijable kardiovaskularne i
inhibitorne konverzije i hipohondrije kojima je procenjivana efikasnost sitema za regulaciju i kontrolu organskih
funkcija (Popović, 2004).
33
ORIGINAL SCIENTIFIC PAPER
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Stankovi}, V. i Popovi}, D.: KANONI^KE KORELACIJE IZME\U SISTEMA...
Stankovi}, V. i Popovi}, D.: CANONICAL RELATIONS BETWEEN THE SYSTEM ...
Proceedings 2011, 29–37
Tabela 2: Kanonička struktura motoričkih i konativnih varijabli
Table 2: The canonical structure of motor and conative variables
Varibales
Motor
varibales
Varibales
ORIGINAL SCIENTIFIC PAPER
ORGINALNI NAUČNI ČLANAK
Kan - 1
Konative
variable
Kan - 1
S3L
.05
ANXT
.79
TAR
-.11
FOBT
.55
TAN
-.20
HIPS
.71
TAZ
-.20
KVKO
.42
PZK
.05
INKO
.30
RZO
-.17
HIPO
.15
ROK
-.09
IMPL
.60
RPK
-.03
AGRE
.71
DPR
.12
DEPS
.50
PIK
.09
PRND
.66
SDM
-.16
20V
.14
VIS
-.12
TRS
-.17
BML
-.02
VUZ
-.12
SKL
.24
PTR3
.04
PTR
-.02
IST
.05
ISTS
.91
Legend/Legenda: S3L - The three-ball slalom (Slalom sa tri lopte); TAR - Hand tapping (Taping
rukom); TAN - Foot tapping (Taping nogom); TAZ - Foot tapping against a wall (Taping
nogama o zid); PZK - The forward-backward bend (Pretklon-zaklon); RZO - Standing on
one leg (Stajanje na jednoj nozi); ROK - Maintaining balance on a reversible floor balance
beam (Ravnoteža na obrnutoj klupici); RPK - Maintaining balance on a sideways balance
beam (Ravnoteža na poporečnoj klupici); DPR - Hyperextensions (Duboki pretklon na
klupi); PIK - Darts (Pikado); SDM - The standing depth jump (Skok u dalj s mesta); 20V
- The 20m run from a high start (Trčanje 20m iz visokog starta); VIS - The high jump
(Skok u vis); TRS - The triple jump (Troskok); BML - Throwing a medicine ball from a prone positions (Bacanje medicinke iz ležanja); VUZ - Hanging pull-ups (Vis u zgibu); SKL
- Push-ups on a bench (Sklekovi na klupici); PTR3 - 30s toros lifts (Podizanje trupa za
30s); PTR - The maximum number of torso lifts (Podizanje trupa do otkaza); IST - Straightening of the torso (Ispravljanje trupa); ISTS - Torso lifts on a vaulting box (Uspravljanje
trupa na sanduku); ANXT - Anxiety (Anksioznost); FOBT - Phobias (Fobičnost); HIPS Hypersensitivity (Hipersenzitivnost); KVKO - Cardiovascular conversion (Kardiovaskularna
konverzija); INKO - Inhibitory conversion (Inhibitorna konverzija); HIPO - Hypochondria
(Hipohondrija); IMPL - Impulsivity (Impulsivnost); AGRE - Aggression (Agresivnost); DEPS
- Depression (Depresivnost); PRND - Paranoia (Paranoidnost).
Discussion
Diskusija
During the discussion of the relations between canonical
factors from two different anthropological spaces, obtained
by using the canonical correlation analysis of covariance, we
rely on the well-known rule that the linear increase in the
values of the resulting vector of the canonical factor variables
from the first space is proportional to the increase in the
growth of the values of the resulting factor of the canonical
factor variables from the second space, naturally, under the
condition that the correlation between the two studied sy-
Prilikom rasprave o relacijama između kanoničkih faktora
iz dva različita antropolo{ka prostora, dobijenih primenom
kanoničke korelacione analize kovarijqansi, koristi se uobičajeno pravilo koje se sastoji u tome, da linearnom porastu
vrednosti rezultirajućeg vektora varijabli kanoničkog faktora
iz prvog prostora, odgovara proporcionalno linearan rast
vrednosti rezultirajućeg vektora varijabli kanoničkog faktora
iz drugog prostora, naravno, pod uslovom ako je korelacija
34
Zbornik radova 2011, 29–37
stems of variables in the different spaces is statistically significant. In addition, the same rule also applies for the inverse
direction of the relations, that the linear decrease in the
values of the results in the canonical factor of the first space
is directly proportional to the linear decrease in the values
of the results in the first canonical factor of the second space (Stanković & Malacko, 2008).
A constant reciprocal relationship exists, in which certain
dimensions of the personality determine the successful realization of motor tasks, while on the other hand, they in
turn have an effect on the formation and development of
certain patterns of behavior and personality traits (Kornspan,
2009; Powell & Royce, 1981).
The first domain of personality makes a distinction between
adaptability or emotional stability and maladjustment and
neuroticism. Men and women with high N values are more
prone to irrational ideas, have a weaker control of their
impulses and have weaker capacities for overcoming stressful situations. Individuals with low N values are emotionally
stable, composed, relaxed and able to deal with stressful
situations without excess panic and disturbance.
From the correlation of the only pair of canonical factors we
can determine that anxiety appears as the dominant feature of adolescent females and probably has a negative influence on their motor effectiveness. This is primarily manifested through weaker coordination, slower movements,
especially of the alternative type, but also weaker results in
the tests of synergy regulation and tonus regulation. This is
probably the consequence of the negative influence of
subcortical inhibitions on the alternative inclusion and
exclusion of agonists and antagonists.
Thus, though anxiety is the dominant factor in neuroticism,
its content is determined more broadly in the sense of a
general conative dysfunction, a dysfunction which includes
more serious dissociative disorders and activity disorders.
The activity regulator is indirectly responsible for activities
and the energy level at which the other systems function,
including the motor system. This could be used to explain
the projection of tests, primarily of coordination and explosive strength on the negative end of the canonical function.
In addition, the regulator of defense reactions is also partially responsible for the determination of this factor, and is
responsible for the greatest part of the variance of the general factor of neuroticism.
između dva ispitivana sistema varijabli u različitim prostorima statistički značajna. Takođe, isto pravilo važi i prilikom
inverznog smera relacija, da linearnom opadanju vrednosti
rezultata u kanoničkom faktoru prvog prostora, odgovara
srazmerno linearno opadanje vrednosti rezultata u prvom
kanoničkom faktoru drugog prostora (Stanković i Malacko,
2008).
Konstantna povratna veza postoji, u kojoj pojedine dimenzije ličnosti određuju uspe{nu realizaciju motornih zadataka,
dok sa druge strane, one imaju povratni uticaj na formiranje
i razvoj određenih obrazaca pona{anja i osobina ličnosti
(Kornspan, 2009: Powell i Royce, 1981).
Prvi domen ličnosti razlikuje prilagođenost ili emocionalnu
stabilnost od neprilagođenosti i neuroticizma. Mu{karci i
žene visoki na N skloni su iracionalnim idejama, slabije
kontroli{u svoje impulse i imaju slabije kapacitete za preovladavanje stresnih situacija. Individue koje imaju nisko N
su emocionalno stabilne, staložene, relaksirane, u stanju su
da se suoče sa stresnim situacijama bez ekscesne panične
uznemirenosti.
Iz korelacije jedinog para kanoničkih faktora vidi se da anksioznost javlja kao dominantno obeležje adolescentkinja i
ona verovatno ima negativan uticaj na njihovu motoričku
efikasnost. To se manifestuje pre svega slabijom koordinacijom, sporijim pokretima, naročito alternativnog tipa, ali i
slabijom rezultatima u testovima sinergijske regulacije i regulacije tonusa. To je, verovatno, posledica negativnog
uticaja subkortikalne inhibicije na alternativno uključivanje
i isključivanje agonista i antagonista.
Dakle, mada je anksioznost dominirajuća odrednica neurotizma njegov sadržaj je {ire određen u smislu generalne
konativne disfunkcije, disfunkcije koja uključuje i teže disocijativne poremećaje i poremećaje aktiviteta. Regulator
aktiviteta je neposredno odgovoran za aktivitet i energetski
nivo na kom funkcioni{u i ostali sistemi između kojih i motorički. Time se i može objasniti projekcija testova pre svega
koordinacije i eksplozivne snage na negativnom polu kanoničke funkcije. Takođe, jednim delom za dobijanje ovog
faktora je odgovoran i regulator reakcija odbrane koji je
odgovoran za najveći deo varijanse generalnog faktora neuroticizma.
Conclusion
Zaklju~ak
The research was carried out with the aim of determining
the relations between motor skills and regulatory conative
mechanisms among adolescent females. With the aim of
determining the relations between motor skills and regulatory conative mechanisms, a total of 400 female adolescents
were included in the study, all aged 15-18. In order to
evaluate their motor skills, a total of 21 motor tests were
used. The tests were selected based on the structural model
of Gredelj et al. (1975) and Popović (1990, 2004), defined
as the mechanism for the structuring of movement, the
mechanism for synergy regulation and tonus regulation, the
mechanism for the regulation of excitation intensity, and the
mechanism for the regulation of excitation duration. To
evaluate the pathological conative characteristics, from the
C.I.-N4 battery, the author of the Cornel Index version
standardization (C.I.-N4) is Momirović (1964), we used the
following variables which belong to the factors of the first
order (manifest variables), factors of the second order (syndromes) and the cybernetic model of the effectiveness of
the regulatory systems: for the evaluation of the effectiveness
of the system for the regulation and control of defensive
reactions (ALFA): 1. anxiety (ANXT), 2. phobias (FOBT), 3.
Istraživanje je sprovedeno sa ciljem da se utvrde relacije
između motoričkih sposobnosti i regulativnih konativnih
mehanizama kod adolescentkinja. U svrhu utvrđivanja relacija između motoričkih sposobnosti i regulativnih konativnih mehanizama, ispitano je 400 adolescentkinja starih
15-18 godina. Za procenu motoričkih sposobnosti upotrebljen
je 21 motorički test. Testovi su odabrani prema strukturalnom
modelu Gredelja i saradnika (1975) i Popović (1990, 2004).
godine definisanim kao mehanizam za strukturiranje kretanja, mehanizam za sinergijsku regulaciju i regulacije tonusa,
mehanizam za regulaciju intenziteta eksitacije, i mehanizam
za regulaciju trajanja ekscitacije. Za procenu patolo{kih
konativnih karakteristika iz baterije C.I.-N4, Autor standardizacije Kornel indeks verzija (C.I.-N4) je Momirović (1964)
primenjene su sledeće varijable koje pripadaju faktorima
prvog reda (manifestne varijable), faktorima drugog reda
(sindromima) i kibernetičkom modelu efikasnosti regulacionih sistema: za procenu efikasnosti sistema za regulaciju i
kontrolu odbrambenih reakcija (ALFA): 1. anksioznost (ANXT),
2. fobičnot (FOBT), 3. hipersenzitivnost (HIPS); za procenu
35
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Stankovi}, V. i Popovi}, D.: CANONICAL RELATIONS BETWEEN THE SYSTEM ...
Proceedings 2011, 29–37
hypersensitivity (HIPS); for the evaluation of the effectiveness
of the system for the regulation and control of organic functions (HI): 4. cardiovascular conversion (KVKO), 5. inhibitory conversion (INKO), 6. hypochondria (HIPO); for the
evaluation of the effectiveness of the system for the regulation and control of reactions to an attack (SIGMA): 7. impulsivity (IMPL), 8. aggression (AGRE); for the evaluation of
the effectiveness of the system for the coordination of regulatory functions (DELTA): 9. depression (DEPS), 10. paranoia (PRND). All of the data in this research were processed at
the Center for Multidisciplinary Research of the Faculty of
Sport and Physical Education at the University of Pri{tina
using the system for data processing developed by Popović
(1980, 1993) and Momirović and Popović (2003). The applied canonical correlation analysis of covariance resulted
in a pair of canonical factors in the space of the group of
motor skills and the group of conative regulatory functions.
The first canonical factor in the space of motor skills was
bipolar. At the positive end of the scale we found the tests
of force, repetitive strength and flexibility, and at the negative end, tests of coordination, balance and explosive strength.
The corresponding factor in this conative space without a
doubt acts as a general factor of neuroticism. All of the
studied variables have statistically significant high projections
on this canonical function. By using a parallel analysis of the
canonical factors, in both groups, it could be determined
that the effective performance of motor tasks depends on
the effectiveness of motor regulatory mechanisms and the
effectiveness of conative regulatory mechanisms both at the
cortical and subcortical level and even at the energy level.
efikasnosti sistema za regulaciju i kontrolu organskih funkcija (HI): 4. kardiovaskularna konverzija (KVKO), 5. inhibitorna konverzija (INKO), 6. hipohondrija (HIPO); za procenu efikasnosti sistema za regulaciju i kontrolu reakcije
napada (SIGMA): 7. impulsivnost (IMPL), 8. agresivnost
(AGRE); za procenu efikasnosti sistema za koordinaciju regulativnih funkcija (DELTA): 9. depresivnost (DEPS), 10.
paranoidnost (PRND). Svi podaci u ovom istraživanju,
obrađeni su u Centru za multidisciplinarna istraživanja Fakulteta za sport i fizičko vaspitanje Univerziteta u Pri{tini
pomoću sistema programa za obradu podataka koji je razvio
Popović (1980, 1993) i Momirović i Popović (2003). Primenjena kanonička korelaciona analiza kovarijansi dala je jedan
par kanoničkih faktora u prostoru skupa motorike i skupa
konativnih regulatornih funkcija. Prvi kanonički faktor u
prostoru motorike je bipolaran. Na pozitivnom se nalaze
testovi sile, repetitivne snage i fleksibilnosti a na negativnom
polu testovi koordinacije, ravnoteže i eksplozivne snage.
Korespodentni faktor u konativnom prostoru se bez ikakve
sumnje ponaša kao generalni faktor neurotizma. Na ovu
kanoničku funkciju sve procenjivane varijable imaju statistički značajne visoke projekcije. Paralelnom analizom kanoničkih faktora, u oba skupa, moglo bi se zaključiti da
efikasno izvođenje motoričkih zadataka zavisi od efikasnosti
motoričkih regulativnih mehanizama i efikasnosti konativnih
regulacionih mehanizama kako na kortikalnom tako i na
subkortikalnom nivou pa čak i na nivou energetike.
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Korespodencija/Correspodence to:
Dr Veroljub Stankovi}
Phone: 00381648904600
E-mail: veroljub.stankovicªpr.ac.rs
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