Training of students’ special endurance in ping pong sport circles

Purpose: to test experimentally influence of aerobic trainings (cross country training and basic aerobic) on students’ special endurance in sport oriented groups (sport circles, ping pong). Material: 106 first year students (n=53 – control group and n=53 – experimental) participated in experiment. For determination of temporal series’ trends R-S analysis was used. Prognostication of mistakes’ quantity per one set was fulfilled with the help of exponential smoothing method. Results: it was shown that exponential smoothing method permits to prognosticate by one set ahead with rather high accuracy. As initial predictor we found mean quantity of mistakes in all sets. It permits to average all internal and external factors, which influence on the next predicting indicators. Such approach increases confidence of mistakes’ calculation in prognostication. Criteria of prognostication methodic for possible indicators’ values were also determined. Conclusions: the recommended time distribution in program is as follows: ping pong − 75%; cross country training and basic aerobic – 25%.


Introduction
The problem of students' physical education improvement has bee being an objects of specialists' attention already for many years [3,21,23]. Analysis of literature sources shows that physical training level, psychic and moral potentials of most students is still rather low [11,22]. It points at worsening of young generation's physical, psychic and mental development [7,24], progressing of motor functioning deficit [10]. All these witness about demand in seeking new ways for improvement of students' physical, psychic and moral condition [27,28]. Besides, it is noted that it is important to train physical qualities [4]. The supplied facts witness that students understand importance of endurance influence and its significance in preparation for labor activity. Students also understand that just this quality is the worst in most of them [4,10]. The authors recommend approaches to correcting academic program for sport oriented groups (sport circles' training). Improvement of students' physical fitness has been being regarded by many scientists recent years [3,5,9]. Their works are devoted to physical endurance. But there is deficit of works on special endurance training in sport oriented groups (sport circles' ping pong trainings). Besides, there are a few researches on special endurance training by cross country race means and with the help of basic aerobic in sport circles' trainings [5,9]. An addition to solution of the mentioned problems could be study of dynamic processes with the help of fractal geometry [17,20,25,27]. The authors note that there is no universal model, which could be used for dynamic processes' description.
The purpose of the research is to determine influence of aerobic trainings (cross country training and basic aerobic) on students' special endurance in sport oriented groups (sport circles, ping pong).

Material and methods
Participants: 106 first year students (n=53control group and n=53 -experimental) participated in experiment. All participants gave written consent for participation in this experiment.
Organization of the research: the experiment was being fulfilled during academic year -from October 2015 to June 2016. Control group students were trained by program of higher educational establishments for sport oriented groups (sport circles' trainings, ping pong). Experimental group students were trained by the worked out by us program. This program combines special sport trainings (ping pong -75 %) and aerobic trainings (cross country training and basic aerobic -25 %). As the base we took higher educational program for sport oriented groups (sport circles' trainings, ping pong). Additionally, every forth training of this program included aerobic loads (cross country training and basic aerobic). Up to the middle of December experimental group students trained cross country race in the fresh air. Then the trainings were conducted in gym. With it every forth training included basic aerobic elements. At the end of March trainings again started in the fresh air, with cross country race at every forth class. At the beginning and at the end of experiment we conducted ping pong competitions. It permitted to test students' endurance [14]. Every pair of students played five sets. The quantity of made mistakes was registered in each set.
Statistical analysis: statistical and comparative analyses of the received data were fulfilled for testing of special endurance at the beginning and at the end of experiment. The method of pair regression was used for this purpose [8]. Besides, Fisher's F criterion and Student's t criterion were used. Analysis of pair regression linear equation was fulfilled also [15,17,26]. We calculated linear coefficients of pair correlation, determination and approximation mean error [2,6,25]. Besides, we assessed statistical significance of regression and correlation 02 53 parameters [12,13,29]; found excessive regression and calculated confidence intervals [16].

Results
For prognostication it is necessary to analyze temporal series and find if the studied system is persistent or non persistent; if its behavior is caused by determinate non linear law or it is completely occasional. In work [26] it was mentioned that any assessment method of change in time prognostication requires consideration of their temporal series' fractal attributes. Different fractal structures in different systems cause fractal behavior of such systems' indicators. For prognostication of such systems' behavior (determination of changes' tendencies) Hurst's method is used [13]. In works [16,16] algorithm of Hurst's indicator is given, which characterizes such attributes. After determination of Hurst's indicator methodic of possible series' values prognostication is chosen depending on its persistence. The following formula (T -time) is in the base of this method: Hurst found more general equation (1): (R/S) n = c*n H , (2) Where R -range of deviations, S -standard deviation, с -constant, n -quantity of measurements, H -Hurst's indicator (from 0 to 1). If to take logarithm from expression (2) we shall receive the following: Ln(R/S) n = Ln(c) +H*Ln(n), (3).
It permits to find Hurst's indicator (H) through building dependence Ln(R/S) n on Ln(n) and determine inclination of trend line with the help of simple regression.
Algorithm of Hurst's indicator determination (fractal method, based on R/S analysis or method of standardized range) is as follows: temporal series of length M is transformed in temporal series of length =M-1 by logarithmic relations N t = Ln(M t+1 /M t ), t=1,2,3…..M-1. Temporal series N t is divided into a number of adjoining sub-periods of length n =2,3…N. Deviation for every sub-period from mean value (accumulated deviations) is calculated in the following way: Where n -length of sub-period, which changes from 2 to the length of temporal series t; M -mean value of elements in sub-period; е u -specific element of subperiod; u -number of sub-period's element. On every iteration we calculate deviations' range X u,n: Standardizing of range we find by division on standard deviation S, which is found by n values of sub-period. Then we find logarithm R/S and n and on the base of the received data build graph of linear regression. By graph of Ln (R/S) on Ln (n) function, we find inclination with method of linear approximation. Tangent of linear graph inclination angle is exactly Hurst's indicator. Hurst's indicator is connected with fractal dimension span of D curve by relation: Where D is fractal dimension span of the curve, indicator Н can be from 0 to 1. For system's analyzing Hurst's indicator can take the following values: 1. 0 ≤ Н < 0.5 or 1.5 < D ≤ 2 temporal series is not persistent ("pink noise"): one can observe economic system's bent to constant change of tendency (increase is replaced by drops and vice versa). The closer its value is to zero the more changeable is series. Such systems are often called "return to average".
2. H = 0.5 or D = 1.5 -numerical series is absolutely occasional ("white noise"): there is full absence of long statistic dependence (occasional behavior of economic indicator); 3. 0.5 < H ≤ 1 or 1<D<1.5 -persistent temporal series ("black noise"), in which a trend is observed, as well as tendency to increasing or falling down of indicator (both in the past and in the future), The higher indicator is the more often indicator' rising is followed by rising (falling down -by falling down).
Distinction of Hurst's indicator from 0.5 is a particular reflection of processes' fractal attributes, which cause temporal series. Application of persistence (or non persistence) permits to comparatively easy and reliably prognosticate future development of the studied process on the base of his history data. In works [2,26] it was found that these attributes are valid even in case of relatively short temporal series. That is why we regard application of R/S indicator for analysis of mean quantity of mistakes in ping pong, made by experimental group students in October (see table 1). According to algorithm of Hurst's indicator determination we construct a table for finding this indicator's parameters. By the data of Ln(R/S) and Ln(n) temporal series Y (see table 1) we find equation of linear regression: Y= 0.1253x + 0.2486, R2 = 0.8751. Thus, standardized rage R/S -is increasing value and can be described by linear regression equation in logarithmic form: Ln(R/S)=0.1253*Ln(n)+0.2486. From this equation we find that H = 0.1253 and D= 2-0.1253 = 1.8747.
It means that this numerical series can be prognosticated.
In similar way we find equation of standardized range for temporal series of experimental groups (May) and control group (October and May). In Such type of numerical series is often called "return to average". That is why for prognostication exponential smoothing can be chosen. This method permits to choose as initial prognostication value mean quantity of mistakes in all sets. It means that it is possible to average all internal and external factors, influencing on the next prognostication indicators. It raises confidence of errors' calculation in prognostication. As coefficient of smoothing (α= 0.1-0.9) we choose the value under which mean square difference between model and actual indicators would be minimal.
For exponential smoothing we take the following formula (7): Where α is smoothing coefficient, A t -actual value, F tprevious prognostication value, F t+1 -next prognostication value. Minimal value of mean square deviations of model and actual indicators for experimental data in October 2015 is given in table 5. Table 5 data show that for prognostication of mistakes' quantity in sixth set (October 2015) coefficient α shall be chosen as equal to 0.9 (at minimal σ).
In the same way we can prognosticate for experimental group May data and control group data in October and May (see tables 6,7,8).
So, prognosis of mistakes' quantity for sixth set of experimental group in May is: Prognosis of mistakes' quantity for sixth set of control group in May is: F 6 = 0.9* 5.79+ (1-0.9)*5.3485 = 5.7459.
Mean relative error (ε), percentage of all predicted values does not exceed 10%: Table 3. Parameters of Hurst's indicator determination in control group (ping pong in October) 2015  Where n is quantity of sets, A i -actual values, F ipredicted values.

Quantity of mistakes (Y) Nt=Ln(Yi+1/ Yi) Deviation from mean value
The data of experimental group comparative analysis (October 2015 and May 2016) are shown in fig. 1.
As we can see experimental group data are rather better at the end of experiment: in first set -by 0.22; in second set -by 0.55 and in the third set -by 1.09; in the forth set -by 1.02 and the fifth -by 1.9. Prognosis for sixth set in October was 7.023, and for May -5.1474. Here we also see improvement by 1.8756.
Comparative analysis of control group data for October and May is given in fig. 2.
As we can see the data of control group also improved by the end of experiment: in the first set -by 0.31%; in the second -by 0.68%; in the third -by 0.85%; in the forthby 1.02% and in the fifth -by 1.36%. Prognosis for sixth set in October was 7.0699, and for May -5.74595. Here we also see improvement by 1.324.
Comparative analysis of experimental and control Quantity of made mistakes groups data for October is shown in fig. 3.
As we see the quantity of mad mistakes at the beginning of experiment (October) is nearly equal: in the first set, in experimental group the quantity of mistakes is less by 0.01; in the second -by 0.11; in the third set the quantity of mistakes was higher by 0.11; in the forth set -by 0.07; in the fifth set it was less by 0.06. In predicted sixth set it was less by0.0469.
Comparative analysis of experimental and control groups data for May is shown in fig. 4.
At the end of experiment (May) the quantity of made mistakes in first two sets was nearly equal: in the first set in experimental group it was higher by 0.08; in the second set -by 0.02. Starting from third set experimental group results are rather different from control group: in the third set quantity of made mistakes was less by 0.13; in the forth set -less by 0.36; in the fifth -by 0.60. In predicted sixth set it was less by 0.5985.

Discussion
For the first time: we proved effectiveness of methodological approach to working out of students' physical education programs for sport oriented groups, which combines commonly accepted means of physical qualities' training with special endurance trainings methods; we substantiated physical education program for students of sport oriented groups (sport circles trainings, ping pong), combined with aerobic exercises This program showed that experimental group students improved their general endurance. Though, they can lag behind in technical tactic training (sportsmanship). It is connected with the fact that every forth training contained aerobic loads (cross country, basic aerobic) instead of ping pong practicing. After experiment data of the fulfilled analysis witness that the chosen strategy was correct: experimental group special endurance results highly differ from those of control group (see fig.  4). Experimental group students made less quantity of mistakes; they became more attentive, concentrated and responsible in important moments of game. Our results point that aerobic loads in physical culture lessons did not influence negatively on students' technical-tactic fitness (see fig. 1). It should be noted that at the end of experiment control group results were better in first two sets (see fig.  4) than experimental group results. It is connected with better technical tactic fitness in control group: they had more special fitness trainings. However, from the third set (in spite of less quantity of technical-tactic trainings) experimental group students demonstrate better results (see fig. 4). It results from their better special endurance.
The received results supplement the data about influence of aerobic exercises on special endurance [5,9]. It means that with correct correlation of trainings by physical education program for students' sport oriented groups (sport circles trainings) and at the cost of aerobic loads (cross country training and basic aerobic) it is possible to significantly improve students' special endurance.