Differences of body dimensions in female volleyball players (cadets) in relation to volleyball playing position

Submitted by Aleksandra Vujmilović and Tamara Karalić

ABSTRACT
This research presents a test of the hypothesis that there are differences in morphological characteristics, which affect effective realization of the elements of the game, which are influenced by many factors from the area of anthropological status of the volleyball players. The study examines the relations of body-dimensions of cadet female volleyball players and provides the answers to a question of how different are they

in that segment, depending on which position in the team they play. The research was conducted on a sample of 55 female volleyball players. The sample was grouped as follows: opposites, middle blockers, outside hitters, setters and liberos. To determine the physical size differences between groups, the authors used the univariate analysis of variance (ANOVA), while for the precise determination of the sources of variability between groups the authors used a Post Hoc analysis, Tukey HSD test as a method of multiple comparisons. A model of physical dimensions was used, that contains the five (5) variables: body height (ATV), range of hands (RAR), body weight (ATT), maximum reach with one hand from a place (MDOH1RM) and maximum reach with two hands from a place (MDOH2RM). With this model the differences have been found in body height (ATV) p=0.001, range of hands (RAR) p=0.003, maximum reach with one hand from a place (MDOH1RM) p=0.000, and maximum reach with two hands from a place (MDOH2RM) p=0.000. Based on the results of a post hoc analysis, statistically significant differences have appeared between the group Liberos and other groups of specialists. In scientific research practice there is a lack of research of this kind. In this sense, this research is conceived as a small contribution to the advancement of the profession especially in the domain of training technologies and optimal functioning of female volleyball players in training process, and manner of its planning and programming.

INTRODUCTION
Volleyball is a popular recreational or competitive sport enjoyed by many people of all ages and skill levels. However, for the future growth and success of volleyball, it is of primary importance that a large number of young people are attracted to it. The interest in volleyball should be encouraged for several reasons. One of them is the nature of volleyball movements, which bring together a great number of children and young people. Previous researches (Ivanić, 1988; Skender, 2004; Tabaković, Skender & Turković, 2006; Hodžić & Mekić, 2008; Ćeleš, 2009; Bajrić, O., Šmigalović, Bašinac & Bajrić, S., 2012; Šmigalović, Bajrić, O. & Lolić 2012; Nešić, Ilić, Majstorović, Grbić & Osmankač, 2013) have shown that this sport can solve problems of physical development, of certain forms of behavior, and problems of spiritual and moral values. The next step is selection itself as optimal way of selecting health, constitutional and other characteristics of the young people adapted to the needs of volleyball. Formation of one volleyball player is a long and complex process that implies quantitative and qualitative learning. One of the processes of becoming a volleyball player involves volleyball camps, where a review and training are done of all that a player has learned and mastered by then. In the camp the young volleyball players about finesses of a sport they have up to that point practiced through individual work with coaches (volleyball specialization), they also practice specific volleyball skills and get directions to improve the performance of the general elements of volleyball. Previous practice (Đurković, 2009; Karalić, 2010; Karalić, Marelić & Vujmilović, 2012; Vujmilović, 2013) has shown that there are some differences in morphological characteristics and that effective realization of the elements of the game are directly and indirectly affected by many factors from the area of anthropological status of the volleyball players. The subject of this research is the differences in body dimensions of female volleyball players-cadets in relation to the playing position. The task of this research is to explore and determine how much are female volleyball players different in body dimensions, depending on their position in the team, and whether these potential differences are statistically significant. In practice (Viera & Ferguson, 1996; Jovičević, 2008; Janković, Đurković & Rešetar, 2009; Dávila-Romero, García-Hermoso, & Saavedra, 2012) it is known that the category[1] of volleyball cadets in particular stands out. The sample is interesting because it is about the age and the period in which the universal model of playing passes to specialized model. It then strives to find appropriate functions in relation to the qualities, characteristics and skills especially in female volleyball players, which are undoubtedly closely associated with successful realization of technical and tactical elements of the game of volleyball. In this regard statistically significant differences are expected in body dimensions of female volleyball players compared to the play’s position. Unfortunately, the body of research addressing issues of anthropological status of male and female volleyball players is not deep. Any scientific research always strives to every ”why” getting its ”because”, and starting this research we are determined to find our ”because”.

METHODS
The sample (N= 55) was grouped in the following way: opposites, middle blockers, side hitters, setters and liberos. To determine the body size difference between the groups univariate analysis of variance was used (ANOVA), while for the precise determination of the sources of variability between groups, a Post hoc analysis was used, respectively, and Tukey HSD test as a method for multiple comparisons. A model of body dimension was used which has five (5) variables: body height (ATV), range of hands (RAR), body weight (ATT), the maximum reach with one hand from a place (MDOH1RM) and maximum reach with two hands from a place (MDOH2RM). Each test was interpreted in detail, and the subjects were familiar with the method, technique and conditions under which each is performed. It was pointed out what needs to be done, which movements are important, and those that are unnecessary. Method of demonstration was used to help participants gain a general, visual idea of the actions that they need to do. The tests were done by qualified persons and six licensed volleyball coaches at different levels. The selected tests were used in research by the following authors: Marelić & Janković, 1997; Stojanović & Kostić, 2002; Janković, V., Janković, G. & Đurković, 2003; Jurko, Grgantov & Čular, 2008; Marelić, Đurković & Rešetar, 2008; Rešetar, 2011. A research technique of observing with registration was used for variable of morphological dimension of female volleyball players was. To process the obtained data methods of descriptive statistics and discriminate analysis were used.

RESULTS AND DISCUSSION
With the application of the above statistical methods for data processing, the obtained results should provide information about the acceptance or rejection of the assumptions of this study. In this part of the study the basic statistical parameters of five dimensions are interpreted to assess morphological status of cadet female volleyball players. From this a longitudinal dimension of the skeleton and the volume and weight of the body were assessed. Tests that have been applied are defined as follows: a test to assess body height (ATV), a test to assess body weight (ATT), a test to assess range of hands (RAR), the maximum reach with one hand from a place (MDOH1RM) and maximum reach with 2 hands from a place (MDOH2RM). In Table 1 the arithmetic mean value (Mean) and standard deviation (St. Dev.) were interpreted, then the value of symmetry (Skew.) and flatness (Kurt.) dissemination of results, and the coefficient of variation (Var.) to verify homogeneity of results of cadet female volleyball players (n=55) in the morphological space. Accordingly, the arithmetic mean (Mean) for variable body height (ATV) was 176.0 ± 4.90, for a variable range of hands (RAR) it was 176.3 ± 5.88, while for a variable of body weight (ATT) the mean value was 61.2 ± 7.76. The arithmetic mean (Mean) for a variable of maximum reach with one hand from a place (MDOH1RM) was 227.8 ± 6.59, and for a variable of maximum reach with two hands from a place (MDOH2RM) it was 225.7 ± 6.68. Table 1. The basic statistical parameters body size of cadet female volleyball players

Variable

N

Mean

Min.

Max.

Var.

Std.

Dev.

St.

Error

Skew.

Kurt.

Body height (ATV)

55

176.0 165.0 187.0 .027 4.90 0.69 0.28 -0.02
Range of hand (RAR)

55

176.3 165.0 192.0 .033 5.88 0.83 0.18 0.13
Body weight (ATT)

55

61.2 49.0 86.0 .127 7.76 1.10 1.11 1.17
Maximum reach with one hand from a place (MDOH1RM)

55

227.8 217.0 246.0 .028 6.59 0.93 0.71 0.38
Maximum reach with two hands from a place (MDOH2RM)

55

225.7 214.0 243.0 .029 6.68 0.94 0.58 0.24

The sample of cadet female volleyball players (N = 55) was selected according to age groups, and is limited to the mean, so that there is no distinctly below average, or above-average values. This finding is confirmed by the coefficient of variation (Var.) that ranged from 0 – 0.2, and it can be claimed that this is a very homogeneous results selected for this study. The values of skewness[2] (Skew.) and kurtosis[3] (Kurt.) distribution of the results for the entire sample female volleyball players (N = 55) were mostly within the normal distribution and ranges from -1 to +1. Figure 1. Graphical representation of the results for the variable distribution of body weight (ATT) Capture However the variable body weight (ATT) deviates from the claims of normality of distribution coefficients, as skewness is beyond the scope of normal distribution and shows a small positive asymmetry (1.11). So the curve (Graph 1.) is shifted to lower values and the frequency of better results was higher in female volleyball players with lower (normal) values of body weight. This phenomenon can be explained as follows: the majority of selected sample consists of girl cadet volleyball players with normal body weight, and there are no major discrepancies, but given that small positive asymmetry was found, it is assumed that there were players in the sample with a slightly higher or a slightly lower body weight than the average. This is a very small variation which does not affect further statistical analysis. According to the degree of flatness, namely kurtosis values that can range from 0 to ± 2.75, it is estimated that there is essential homogeneity of results in the area of selected body dimensions, so it can further data processing can be done in discriminative, as well as in comparative analysis.

THE DIFFERENCES BETWEEN BODY SIZE OF CADETS FEMALE VOLLEYBALL PLAYERS IN RELATION TO PLAYING POSITION
With statistic methods that analyzes interdependence all the variables in the model are assessed in the same way, with the aim is to determine a behavior pattern of variables, so to determine which variables are similar to each other, and which are not. In this sub-chapter body dimensions are assessed, and these have five (5) variables: body height (ATV), range of hands (RAR), body weight (ATT), maximum reach with one hand from a place (MDOH1RM) and maximum reach with two hands from a place (MDOH2RM). Also, exploring the physical dimensions of the cadet female volleyball players, values of body mass index (BMI) were calculated for the observed sample and it was determined if any differences exist in this domain. The differences in the univariate level between the groups in terms of the playing position The results were obtained based on the value of degrees of freedom df1= 4 and df2= 50 and the limit value of F-test. Those where (limit) value of F-test is greater or equal to 2.56[4] at the significance level of p= 0.05 were confirmed as s significant. Table 2. Univariate analysis of variance (ANOVA) morphological space: Body height (ATV)

Source of variability

SS

df

MS

F

P-value

Between groups

553.78

4

138.44

5.587

0.001

Within the groups

1239.06

50

24.78

Total

1792.84

54

df1= 4; df2=50; f=2.56; p= 0.05

Legend: SS – Sum of Squares; MS – Means Squares; df – Degree of Freedom; F – F test;

P-value – the significance level;

Table 2, in which body height variable (ATV) was analyzed shows that the value of F-test is 5.587, which is higher than the calculated limit. On this basis, it can be concluded that the differences between the groups for body height variable (ATV) exist and are statistically significant. This confirms the value of the P-value that equals to 0.001. Table 3. Univariate analysis of variance (ANOVA) morphological space: Range of hands (RAR)

Source of variability

SS

df

MS

F

P-value

Between groups

586.57

4

146.64

4.503

0.003

Within the groups

1628.41

50

32.57

Total

2214.98

54

Table 3, in which the range of hands variable (RAR) was analyzed shows that the value of F-test is 4.503, and it is higher than the calculated limit. On this basis, it can be concluded that the differences between the groups for variable range of hands (RAR) exist and are statistically significant. This confirms the value of the P-value that equals to 0.003. Table 4. Univariate analysis of variance (ANOVA) morphological space: Body weight (ATT)

Source of variability

SS

df

MS

F

P-value

Between groups

432.37

4

108.09

1.942

0.118

Within the groups

2783.37

50

55.67

Total

3215.75

54

Table 4, in which body weight variable (ATT) was analyzed shows that the value of F-test is 1.942, which is lower than the calculated limit. On this basis, it can be concluded that the differences between the groups for variable body weight (ATT) do not exist and are not statistically significant. This confirms the value of the P-value that equals to 0.118. Table 5. Univariate analysis of variance (ANOVA) morphological space: Maximum reach with one hand from a place (MDOH1RM)

Source of variability

SS

df

MS

F

P-value
Between groups

1433.77

4

358.44

7.743

0.000
Within the groups

2314.66

50

46.29

Total

3748.44

54

Table 5, in which maximum reach with one hand from a place variable (MDOH1RM) was analyzed, shows that the value of F-test is 7.743, so higher than the calculated limit. On this basis it can be concluded that the differences between the groups in term of maximum reach with one hand from a place variable (MDOH1RM) exist, and that these are statistically significant. This confirms the value of the P-value that equals to 0.000. Table 6. Univariate analysis of variance (ANOVA) morphological space: Maximum reach with two hands from a place (MDOH2RM)

Source of variability

SS

df

MS

F

P -value
Between groups

1471.81

4

367.95

7.601

0.000

Within the groups

2420.37

50

48.41

Total

3892.18

54

Table 6, in which maximum reach with two hands from a place variable (MDOH2RM) was analyzed, shows that the value of F-test is 7.601, and therefore that it is higher than the calculated limit. On this basis it can be concluded that the differences between the groups for maximum reach with 2 hands from a place variable (MDOH2RM) exist and that they are statistically significant. This confirms the value of the P-value that equals to 0.000. Table 7. Univariate analysis of variance (ANOVA), body mass index for cadets female volleyball players: BMI

Source of variability SS df MS F P-value
Between groups

14.61648

4

3.654

0.773

0.548

Within the groups

236.4879

50

4.730

Total

251.1044

54

Table 7, in which body mass index variable (BMI) was analyzed, shows that the value of F-test is 0.773 and that it is lower than the calculated limit. On this basis it can be concluded that the differences between the groups in terms of body mass index variable (BMI) do not exist and that these are not statistically significant. This confirms the value of the P-value that equals to 0.548. In the analysis of body size difference between the groups it is necessary, first of all, to talk about specific positions on the court. It has already been mentioned that modern volleyball requires extremely tall players in all positions. This is particularly desirable in the game at the net, and differences found in relation to body height of cadet female volleyball players can partly be explained by taking into account the height of the net as a limiting factor, crucial for success in volleyball. The net height is set, according to the rules of the game, at 224 cm for women. In order to better understand the relation of body height requirements and playing positions, this study can be compared with some earlier research, in terms of the parts that look at analysis of body dimensions. Vuković, Krneta, Đurđić & Simić (2007) have found statistically significant differences in body height between female students who practice volleyball and female students who do not practice volleyball. Jurko, Grgantov & Čular (2008) have conducted research on a sample of junior volleyball players by the criteria of different situational success among other things they examined the differences in body height. The results illustrated that the female volleyball players with different situational efficiency also significantly differ in body height. Marelić, Đurković & Rešetar (2008) with research done on 39 volleyball players, members of Croatian senior and youth teams, found statistically significant differences in the body height variables, in favor of seniors. Figure 2. Relation of mean values of body height (ATV) and range of hand (RAR) in groups (cm) figure 2 From the point of modern volleyball very tall females have objectively more prospective for successful engagement in volleyball, which every year becomes more of a ”privilege” of tall male and female players. Today, the average height of male players (Cadet age) is approaching 200cm (Vuković & Milošević, 1996). In this study, the average value of body height for female cadets is below 180cm. Of course, body height is not the only factor of success in volleyball. In addition to that, a number of different factors should be noted, which contribute to this success. In addition to the longitudinal dimension of the skeleton and body height as its biggest representation in the anthropometric characteristics, it is important to also emphasize body weight, girth measurements and body fat (Vuković et al. 2007). The best example to prove this is a comparison of liberos, middle blockers and opposites. Liberos usually do not participate in the game on the net, so body height is not crucial for this player position. Middle blockers are important in defense and then efficiency depends mostly on their anticipation, ability to react quickly and their maximum reach. Because of this, they are most often tallest players in the team. On the other hand, the middle blockers are not primarily involved in the process of serve receiving because liberos replaces them in back of the court. Finally, in order to complete their specific tasks successfully, opposite must have the ability of generating high power at the moment of attack, which often depends (except body height) on the different morphological characteristics – body weight, girth of different body parts, body fat … etc. By analyzing the basic data obtained testing of the sample, (Figure 2) the relation of body height (ATV) and range of hands (RAR) in groups is generally proportional and there are no major discrepancies. However first to be noticed is the intergroup numerical difference, in which Liberos recorded much lower values of body height (ATV) and range of hand (RAR) in relation to all other groups. The reasons probably lie in the fact that the longitudinal dimension of Liberos is lower, and constitution of players at this position adapted to the requirements of the game for the defense, for which body height and range of hands are not essential. Authors Janković, Đurković & Rešetar (2009) agree with this statement and in their discussion of requirements and selection of such a player the authors emphasize motor predispositions such as exceptional agility and coordination, balance, depth perception and width of the space, fast of reaction time, etc. When it comes to maximum reach with one hand (MDOH1RM) and maximum reach with two hands (MDOH2RM) variables, what dominates is the longitudinal dimension of the skeleton, especially the length of the upper and lower extremities, and the assumption is that the first intergroup, and then the statistical difference appeared in the (passive) of the musculoskeletal system. To perform the maximum reach with one or two hands what is needed above all is flexibility, both in general and specific, so flexibility of upper and lower extremities can be one of the possible reasons for the difference found. Previous research (Iashvili, 1982) shows that active flexibility has a very high correlation (r = 0.81) with the level of performance. Based on that, the occurrence of differences in the domain of body size probably influenced flexibility of the shoulder belt and joints, which participate in the performance of these tasks. What is especially significant for the differences found is the so called static-active flexibility such as the ability to obtain and maintain extended position in a particular joint (or joints) using at the same time only agonists and synergists muscles, while antagonistic muscle groups are stretched (Kurz, 1991). Preconditions for static-active flexibility and good working muscles are elasticity of muscle tissue, elasticity of tendons and ligaments, skin elasticity, and the ability of muscles (the active part of the locomotor system) of contraction and relaxation, to contribute to a greater range of motion. RESULTS OF THE POST HOC ANALYSIS – Tukey HSD test The analysis was performed only for those variables from the physical dimension where statistically significant differences between the studied groups were found. Post hoc analysis of body dimensions cadets female volleyball players From an overview in Table 8 it can be concluded that in Body height variables (ATV), a statistically significant difference was found between the Side Hitters (174.47) and Liberos groups (166.00). There were statistically significant differences between Setters (175.44) and Liberos groups (166.00). There were statistically significant differences between Opposites (176.09) and Liberos groups (166.00). Also, a statistically significant difference was found between Middle Blockers (178.15) and Liberos groups (166.00). No statistically significant differences were observed between the other groups for this variable (r = 0507), at the level of p = 0.05. Table 8. Post Hoc analysis – Body height (ATV)

Body height (ATV)

Tukey HSD metod
KATEGORY N Subset for alpha = 0.05

1

2

Liberos

5

166.00

Side Hitters

17

174.47

Setters

9

175.44

Opposites

11

176.09

Middle Blockers

13

178.15

Sig.

1.000

0.507

Based on the data in Table 9 it can be concluded that when looking at Range of hands (RAR) variable statistically significant difference was found between Setters (174.33) and Liberos groups (166.20). There were statistically significant differences between Side Hitters (175.41) and Liberos groups (166.20). There were statistically significant differences between Opposites (176.45) and Liberos groups (166.20). A statistically significant difference was found between Middle Blockers (178.69) and Liberos groups (166.20). The differences observed between the other groups were not statistically significance for this variable (r = 0.475), at the level of p = 0.05. Table 9. Post Hoc analysis – Range of hands (RAR)

Range of hands (RAR)

Tukey HSD metod
KATEGORY N Subset for alpha = 0.05

1

2

Liberos

5

166.20

Setters

9

174.33

Side Hitters

17

175.41

Opposites

11

176.45

Middle Blockers

13

178.69

Sig.

1.000

0.475

With an overview of Table 10, it can be concluded that Maximum reach with one hand from a place (MDOH1RM) variable shows statistically significant difference between Side Hitters (225.24) and Liberos groups (211.40). Then, there were statistically significant differences between Setters (228.00) and Liberos groups (211.40). There were statistically significant differences between Opposites (228.82) and Liberos groups (211.40). A statistically significant difference was found between Middle Blockers (230.31) and Liberos groups (211.40). The differences observed between the other groups were not statistically significance for this variable (r = 0.500), at the level of p = 0.05. Table 10. Post Hoc analysis – Maximum reach with one hand from a place (MDOH1RM)

Maximum reach with one hand from a place (MDOH1RM)

Tukey HSD metod
KATEGORY N Subset for alpha = 0.05

1

2

Liberos

5

211.40

Side Hitters

17

225.24

Setters

9

228.00

Opposites

11

228.82

Middle Blockers

13

230.31

Sig.

1.000

0.500

With an overview of Table 11, it can be concluded that Maximum reach one of the two hands (MDOH2RM) variable shows statistically significant difference between Side Hitters (222.88) and Liberos groups (209.20). Statistically significant differences were also found between the Setters (226.00) and Liberos groups (209.20). There were statistically significant differences between Opposites (226.55) and Liberos groups (209.20). A statistically significant difference was found between Middle Blockers (228.38) and Liberos groups (209.20). The differences observed between the other groups were not statistically significance for this variable (r = 0.440), at the level of p= 0.05. Table 11. Post Hoc analysis – Maximum reach with two hand from a place (MDOH2RM)

Maximum reach with two hand from a place (MDOH2RM)

Tukey HSD metod
KATEGORY

N

Subset for alpha = 0.05

1

2

Liberos

5

209.20

Side Hitters

17

222.88

Setters

9

226.00

Opposites

11

226.55

Middle Blockers

13

228.38

Sig.

1.000

0.440

Considering all the facts outlined above as well as the assumptions in the discussion, based on the results of a post hoc analysis, it can be concluded that the statistically significant differences appeared mainly between the Liberos group and other groups of specialists. In models looking at body size there were differences in body height (ATV) and range of hand (RAR), the maximum reach with one hand from a place (MDOH1RM), maximum reach with two hands from a place (MDOH2RM). The reasons for the appearance of the difference between Liberos and players of other groups can be found only in the specialization of their playing positions, which came to the fore in the realization of the tests applied in this study. The study which was conceptualized on a similar idea, was conducted by Trajković, Milanović, Sporiš & Radisavljević (2011) with the aim to examine the differences in body composition when young elite volleyball players performing jumps. The players were categorized as middle blockers (n=7), rightside hitters (n=5), outside hitters (n=8), servicers (n=6) and liberos (n=2). Middle blockers and rightside hitters are the highest (201.57 ± 4.92 cm, 203.00 ± 4.41 cm) and heaviest (86.14 ± 6.79 kg, 91.60 ± 6.69 kg) in the selection of players. The lowest values of height and body mass were found in liberos. A statistically significant difference was found between the positions for height and body weight, as well as for maximum reach. CONCLUSIONS Based on the obtained results, statistically significant differences in four of the five offered tests were shown. Specific, significant differences for body size by cadet female volleyball players were identified. A more refined analysis showed that these differences appeared between the Liberos and the other specialist groups.

APPLICATIONS IN SPORT
Scientific and theoretical significance of this study lies in the fact that there are not many authors that are still exploring volleyball, or studies conducted on a sample of male or female volleyball players in relation to their role in the team, especially at the cadet age. The research presents an exploration of what previous practice has shown, which is that when it comes to female volleyball players, there are certain differences in body size and specific motor abilities that were treated in this study and that efficiency of realization is directly and indirectly affected by factors from space, not only motorics, but also from the overall area of anthropological status of female volleyball players. In terms of practical application of the results, especially in the planning and programming of training, it is important to point out that this research is a contribution to determining the principles of functioning of an integrated system, which consists of female volleyball players, and volleyball activity areas (female volleyball players, coaches and their inter-relationships). This study also provides to apply the principles by which it is possible to define the characteristics of volleyball activities, as a result of structural, morphological, motoric, functional and other analyzes. Finally, the purpose of this research is to provide a comprehensive analysis of the personal characteristics of female volleyball players individually (skills, qualities and characteristics, which allow achieving high volleyball sport results). Based on the results, volleyball coaches can plan and implement effective training of technical and tactical elements. Given that there was not much research conceptualized in this way, the results will be extremely important for future research in the area of physical dimensions, especially for the study of dimensions such as maximum reach with one hand and maximum reach with two hands by male or female volleyball players. The knowledge about structure and level of physical dimensions in (cadets) female volleyball players would allow teachers of physical education a better realization of the program of volleyball in physical education, in terms of a better use of current physical parameters for improvement of motor skills, and easier application of volleyball in recreation and leisure time.

ACKNOWLEDGMENTS
None

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Footnotes:
[1] According to the existing propositions of contest and volleyball player age definition, there are four standard categories (age groups): pioneers (players up to 12 years), cadets (players who are 14-16 years old), juniors (players who are 16-18 years old) and seniors (players older than 18). Young volleyball players can compete with older players if they are mentally and physically healthy for the competition and with the consent of a specialist in sports medicine (retrieved: Odbojkaški savez Srbije. Serbian Volleyball Federation. SRB, 2014. www.ossrb.org. March 19, 2014.).
[2] Skewness – symmetric.
[3] Kurtosis – flattened.
[4] In: Bala, G. (1986). Logičke osnove za analizu podataka iz istraživanja u fizičkoj kulturi. [The logical basis for the analysis of data from studies in physical education]. Novi Sad: solo edition of author. Serbia.