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6APPLICATION METHODOLOGY OF VARIOUS MEASUREMENT METHODS WHEN ESTIMATING INDICES OF ELITE WORLD-CLASS ATHLETES A.M. Gafarov, professor, Dr.Tech., Honored worker of science
A.S. Gatamov, associate professor, Honored worker of physical culture and sport, Honored trainer of the Republic of Azerbaijan, two-time world and European champion in karate, 7th Dan Black Belt
Academy of the Ministry of Emergency Situations of the Republic of Azerbaijan
Key words: methodology, measurement, athlete, accuracy, error, fixation, strikes, measurement methods.
Introduction. Measuring techniques and methods are the main sources providing sports professionals, trainers, athletes etc. with necessary statistical data. The development of one or another sport and the necessary results for the near and distant future cannot be predicted without statistical data.
Types of measurement are determined by physical nature of the measured value, required accuracy of measurement, required speed of measurement, conditions and mode of measurements etc. Types of measurements can be distinguished according to their purpose: control, diagnostic and prognostic, laboratory and technical, reference and verifying, absolute and relative etc. [1].
The purpose of the research was to use various measurement methods and techniques in the evaluation of physical data of world-class athletes.
Materials and methods. Direct measurements are the most common, the essence of this type of measurement is that the desired values are allocated from the experimental data using the experimental comparison. In addition, the indirect, cumulative, collaborative and other measurement methods are applied.
Direct measurements are the basis of more complex measurements. In accordance with Interstate Standardization Recommendations 29-99 the following methods of direct measurement are distinguished: method of direct estimation, direct comparison method,
complementary measurement method, differential method, null method, substitution method. In relevant literature other measurement methods are sometimes mentioned such as measurements with single observations are ordinary measurements, and those with multiple observations are statistical measurements. If a measured value is recorded directly by some measuring means, then it is an absolute method. If measuring means only capture a deviation of a value, then it is a relative measurement method [2]. The above is by no means a complete list of measurement methods. Currently there are over forty of them. The following activities are to be carried out for accomplishing measurements: analysis of measurement task with allocation of possible sources of error, choice of measurements accuracy indicators, choice of the number of measurements, choice of the method and means of measurement, initial data formulation for errors calculation, calculation of individual components and overall error, calculation of accuracy indicators and their comparison with chosen ones [3].
These issues relate to research measurement methods and can be of great importance in the training of elite world-class athletes that widely use statistical material obtained using various measurement techniques and methods in their formation.
When using measurement techniques and methods it is important to assess their accuracy. The term "accuracy of measurement" is used for qualitative comparison of measuring operations. The concept of an error on a measurement is used for quantitative assessment of a measured parameter. The increase of the error promotes lower accuracy. Numerous factors affect the accuracy of measurements. Any error of measurement depends on the conditions of the measurement process. Currently over twenty-five kinds of measurement errors are distinguished.
Depending on the form of expression absolute, relative and reduced measurement errors are distinguished, while systematic, random and gross errors are distinguished by the nature of manifestation, causes and possibility of elimination. Systematic errors remain constant or change consistently in repeated measurements of the same parameter. Random errors vary in repeated measurements of the same parameter at random. Gross errors occur because of
erroneous actions of the operator conducting the measurements, malfunction of measurement means or abrupt changes of the measurement conditions.
Knowing the value of a constant systematic error, it is possible to eliminate or compensate it. Similar measures can be taken to compensate a systematic consistently changing error, if we know the law of its change.
It is much more difficult to identify and compensate random errors. They occur as a result of a large number of manifestations of unrelated random factors. Fixation of different strikes of athletes by judges during competitions and coaches during the training process can be qualified as such errors. Change of random errors is studied using fundamental principles of the probability theory and mathematical statistics. Classification of errors as systematic and random is relative to some extent. One and the same error in different cases can occur either as systematic or as random. For example, in strike fixation at karate competitions actions of a poorly trained judge can be classified as random, and those of an unfair one - as systematic errors.
Results and discussion. Random errors cannot be eliminated completely, but their impact can be reduced by processing measurements results. To accomplish this, the distribution law, mathematical expectations, standard deviation, confidence probability and confidence interval must be known.
If the distribution law of the parameter and the error is not known, but the standard deviation of the measurement error is, then confidence intervals are based on the Chebyshev's inequality [4]: .(1)
Where, arithmetic mean value of the measured parameter;
- Chebyshev's coefficient; °T- standard deviation of the arithmetic mean of measurement; x - true value of the measured value. According to the formula (1)
Where, - the probability that a single random value of a series of measurements under any distribution law will not differ from an average value by more than half of the confidence interval A . Where, .
It is known that measurements of the same parameter by the same method do not provide identical results. In such cases convergence and reproducibility can serve as an objective measure of statistical basis. Convergence is similarity of results of parameters obtained by one method on identical stands and under the same conditions. Reproducibility is similarity of results obtained under different conditions.
According to [4] under the confidential probability F = the convergence is defined as r=2,77 oc, and reproducibility as R=27 or.
Here oc and or - the standard deviation of measurement results under the conditions of
convergence and reproducibility respectively.
= = (Gcx = Engl GC? GB = Engl Gr)(2)
Wliere, and - results of individual measurements under the conditions of convergence; y± and y= - results of individual measurements under the conditions of reproducibility.
x 2 ; ^ ~ 2~ - mean values.
The values of r and R are defined in the standards.
Different methods are used while processing the results of measurements, such as multiple direct equally accurate measurements, unequal measurements, indirect measurements, joint and cumulative measurements, dynamic measurements, etc.
While carrying out multiple direct equally accurate measurements, the value calculated as the confidence interval is
Ar=
. (3)
(I EMBED Equation, DSMT4 3ElEÎ)a +
3 a™
[(a eMBED Equation, Dssan mmm}* +
Where, A - the value of a random error;
s - Student's coefficient;
(Engl mm) - an error of measurement method. With a clear allocation of a residual error the value can be determined in accordance with the state standard (GOST) 8.207-76. The final result can be formulated as x= a ±Az. (4)
The method of unequal measurements should be used when checking the state of readiness of athletes on various parameters, changing the training location, registering the physical data of athletes using different equipment, measuring parameters of athletes with different accuracy, changing the conditions of training sessions and competitions, conducting research with the help of various coaches and sports professionals to determine the level of readiness of athletes for competitions.
To determine the probable value of a sports parameter with the help of unequal measurements data the definition of "weight" of the measurement Si can be adopted
Where, and the amount and dispersion of the i series of equally accurate measurements.
If unequal measurements have led to results ■ ■ ^rv where xi - the arithmetic mean of a
number of equally accurate measurements^ ^ m ), then the most probable value of the parameter in question will be its weighted average ¥ L
.(6)
Single measurements are performed without repeated observations. For an updated estimation of the possibility of using single measurements in sports technologies the total error of single measurements should be compared with the total error of multiple
0 yj
measurements, in the presence of random A and residual components Single measurements are sufficient if the residual error exceeds the random one.
Then the measurement result is recorded in the form of, the probability being P=0,95. This is
0
achieved when A .
Where, - the result recorded by measuring means;
- the total measurement error defined by a class of accuracy of measurement method
(Engl. mm) and method error. The method of indirect measurement can be used in determining the effect of individual factors on the overall performance of an athlete. In this case the studied factors may be mutually independent and interdependent. For example, evaluation of the force of arm and leg strikes of a karateka, measurement of the force of arm strikes carried out in different directions: straight strikes, strikes from the bottom up, from top to bottom, side strikes, same kinds of leg strikes, etc.
Indirect measurements require a functional relation: y-fO-i,::,,.^.....(7)
Where, .....arguments of function J that are to be subject to direct
measurements
In this case the error in defining y depends on the errors in the measurements of the arguments.
For independent arguments the absolute error is defined by the formula:
(8)
The relative error is formulated as:
(9)
Standard deviation is characterized by the following functional connection
Sy -
' * (wj +(0 +■ '4 iS
Where, partial derivatives &Xi. are calculated at ^ = x2. = — * a value
determined by the Student's coefficients for one and the same value of confidential probability.
In the absence of a functional connection of type (7) it is possible to use experimental values and
■ -A\or .(11)
Where, 4y - change of the function caused by the change of the E" ~ argument; V and xi- the average values of the function and the argument respectively.
The final result has the form of y = i 4>F with the P probability. In case of mutual dependence of arguments paired correlation coefficients are defined. With simultaneous measurements of two or more parameters (e.g. in determining the force of a strike of an athlete using his arms and legs at the same time) the method of joint measurement can be used. A mandatory condition for this method is that the measurement equation for these parameters must form a system of linear independent equations. For the two measured parameters x and y the system of linear equations is the following: ft.;... ,..&,.)= 0 ■ .iSi^V) = 0 (12)
Where, A . . .- results of direct and indirect measurements;
i, lV . . -:";s, os... - physical constants or constant MM (measuring means).
If the number of equations is exceeded by the number of unknowns, the system is solved by the least-squares method and x, y and the standard deviation ff are found. Confidence intervals for the true values of x and y are based on the t-distribution.
While measuring similar parameters, for example, while determining the force of several direct strikes carried out by athletes during training sessions, the method of measurements in a closed series can be used. The mathematical techniques of measurement in a closed series and of joint measurement are the same.
If it is not possible to ignore the change in the parameter being measured in time, then one should use the method of dynamic measurement. For example, it can be used in determining the response of an athlete to his opponent's action, the change of the strike force of an athlete depending on the time, the impact of uninformative parameters on the quality of used techniques, the impact of technical characteristics of measuring systems elements (sensors, amplifiers, converters, transformers, etc.) on the accuracy of defined parameters. In case of dynamic measurements it is necessary to select analytical expressions for approximation of found or specified parameters of an athlete, to find analytical dependencies describing the process in question, to identify dynamic errors, etc. Dynamic errors are mainly determined by an experiment-calculated method. Conclusion. Proceeding from the conducted studies, various methods, techniques and means of measurement can be successfully applied to the evaluation of indices of world-class athletes.
References
1. Gafarov, A.M. Fundamentals of metrology / A.M. Gafarov, V.A. Gafarov. - Baku: Nauka, 2008, 312 P. (In Russian)
2. RIG29-99. Recommendations on intergovernmental standardization of National Measurement Assurance System. Basic terms and definitions. - Moscow. -Metrologiya. (In Russian)
3. Sergeev, A.G. Metrology. - Moscow: Logos, 2004. - 288 P. (In Russian)
4. Sergeev, A.G. Metrology, standardization, certification / A.G. Sergeev, M.V. Latyshev, V.V. Teregerya. - Moscow: Logos, 2005. - 560 P. (In Russian)
Corresponding author: Aydin.qafarov@baku.az
