Sports metrology. Sports metrology as a scientific discipline

TUTORIAL ON SPORTS METROLOGY

Topic 1. Basics of measurement theory
Topic 2. Measuring systems and their use in physical education and sports
Topic 3. General testing physical fitness involved in physical education and sports
Topic 4. Mathematical statistics, its basic concepts and application to physical culture and sports
Topic 5. Determination of basic statistical indicators (BSI) to characterize populations
Topic 6. Definition confidence interval for the population mean by Student's t-test
Topic 7. Comparison of groups using the Student's method
Topic 8. Functional and correlation relationships
Topic 9. Regression analysis
Topic 10. Determining test reliability
Topic 11. Determining the information content and quality factor of a test
Topic 12. Fundamentals of the theory of estimates and norms
Topic 13. Definition of norms in sports
Topic 14. Quantitative assessment of qualitative characteristics
Topic 15. Control over strength qualities
Topic 16. Monitoring the level of development of flexibility and endurance
Topic 17. Control over the volume and intensity of the load
Topic 18. Monitoring the effectiveness of equipment
Topic 19. Fundamentals of the theory of controlled systems
Topic 20. Comprehensive assessment physical fitness of the subjects

Theoretical information

By measuring(in the broad sense of the word) is the establishment of correspondence between the phenomena being studied, on the one hand, and numbers, on the other.
To results different dimensions could be compared with each other, they must be expressed in the same units. In 1960, the International General Conference on Weights and Measures adopted International system units, abbreviated as SI.
The SI currently includes seven independent from each other main units from which the units of other physical quantities are derived as derivatives. Derived units are determined on the basis of formulas that relate physical quantities to each other.
For example, the unit of length (meter) and the unit of time (second) are basic units, and the unit of speed (meter per second [m/s]) is a derivative. The set of selected basic and derived units formed with their help for one or several areas of measurement is called a system of units (Table 1).

Table 1

Basic SI units

To form multiples and submultiple units special attachments must be used (Table 2).

table 2

Multipliers and prefixes

All derived quantities have their own dimensions.
Dimension is an expression that connects the derived quantity with the basic quantities of the system with a coefficient of proportionality, equal to one. For example, the dimension of speed is equal to , and the dimension of acceleration is equal to
No measurement can be made absolutely accurately. The measurement result inevitably contains an error, the magnitude of which is smaller, the more accurate the measurement method and measuring device.
The main error is is the error of the measurement method or measuring instrument, which occurs under normal conditions of their use.
Additional error - This is the error of a measuring device caused by a deviation of its operating conditions from normal ones.
The value D A=A-A0, equal to the difference between the reading of the measuring device (A) and the true value of the measured quantity (A0), is called absolute error measurements. It is measured in the same units as the measured quantity itself.
Relative error - this is the ratio of the absolute error to the value of the measured quantity:

In cases where it is not the measurement error that is assessed, but the error of the measuring device, for maximum value The measured value is taken to be the limit value of the instrument scale. In this understanding, the greatest permissible value D Pa, expressed as a percentage, determines under normal operating conditions accuracy class of the measuring device.
Systematic is called an error, the value of which does not change from measurement to measurement. Due to this feature, systematic error can often be predicted in advance or, in extreme cases, detected and eliminated at the end of the measurement process.
Taring(from German tarieren) is called checking the readings of measuring instruments by comparison with the readings of standard values ​​​​of measures (standards *) over the entire range possible values measured quantity.
Calibration is called the definition of errors or correction for a set of measures (for example, a set of dynamometers). Both during taring and calibration, a reference signal source is connected to the input of the measuring system instead of the athlete known quantity. For example, when calibrating an installation for measuring forces, loads weighing 10, 20, 30, etc. are alternately placed on the strain gauge platform. kilograms.
Randomization(from the English random - random) is the transformation of a systematic error into a random one. This technique is aimed at eliminating unknown systematic errors. According to the randomization method, the measured value is measured several times. In this case, the measurements are organized so that the constant factor influencing their result acts differently in each case. For example, when studying physical performance, it can be recommended to measure it many times, each time changing the method of setting the load. Upon completion of all measurements, their results are averaged according to the rules of mathematical statistics.
Random errors arise under the influence of various factors that cannot be predicted in advance or accurately taken into account.
Standard - a regulatory and technical document establishing a set of norms, rules, requirements for the object of standardization and approved by the competent authority - the State Committee for Standardization. In sports metrology, the object of standardization is sports measurements.

Name scale (nominal scale)

This is the simplest of all scales. In it, numbers act as labels and serve to detect and distinguish objects under study (for example, the numbering of players on a football team). The numbers that make up the naming scale are allowed to be swapped. There are no more-less relationships in this scale, so some believe that the use of a naming scale should not be considered a measurement. When using a naming scale, only certain mathematical operations can be performed. For example, its numbers cannot be added and subtracted, but you can count how many times (how often) a particular number occurs.

Order scale

There are sports where the athlete’s result is determined only by the place taken in the competition (for example, martial arts). After such competitions, it is clear which of the athletes is stronger and which is weaker. But how much stronger or weaker it is impossible to say. If three athletes took first, second and third places, respectively, then what their differences in sportsmanship are remains unclear: the second athlete may be almost equal to the first, or may be significantly weaker than him and be almost identical to the third. The places occupied in the order scale are called ranks, and the scale itself is called rank or non-metric. In such a scale, its constituent numbers are ordered by rank (i.e., occupied places), but the intervals between them cannot be accurately measured. Unlike the naming scale, the order scale allows not only to establish the fact of equality or inequality of measured objects, but also to determine the nature of inequality in the form of judgments: “more - less”, “better - worse”, etc.
Using order scales, you can measure qualitative indicators that do not have a strict quantitative measure. These scales are used especially widely in the humanities: pedagogy, psychology, sociology. A greater number of mathematical operations can be applied to the ranks of the order scale than to the numbers of the name scale.

Interval scale

This is a scale in which numbers are not only ordered by rank, but also separated by certain intervals. The feature that distinguishes it from the relationship scale described below is that zero point is chosen randomly. Examples can be calendar time (the beginning of chronology in different calendars was set for random reasons), joint angle (the angle at the elbow joint with full extension of the forearm can be taken equal to either zero or 180o), temperature, potential energy of a lifted load, potential electric field and etc.
Interval scale measurement results can be processed by all mathematical methods, except for calculating ratios. Interval scale data provides an answer to the question “how much more?”, but does not allow us to state that one value of a measured quantity is so many times greater or less than another. For example, if the temperature increased from 10° to 20° Celsius, then it cannot be said that it has become twice as warm.

Relationship scale

This scale differs from the interval scale only in that it strictly defines the position of the zero point. Thanks to this, the ratio scale does not impose any restrictions on the mathematical apparatus used to process observational results.
In sports, ratio scales measure distance, strength, speed, and dozens of other variables. The ratio scale also measures those quantities that are formed as differences between numbers measured on the interval scale. Thus, calendar time is counted on a scale of intervals, and time intervals - on a scale of ratios.
When using a ratio scale (and only in this case!) the measurement of any quantity is reduced to experimental determination the ratio of this quantity to another similar one, taken as a unit. By measuring the length of the jump, we find out how many times this length is greater than the length of another body taken as a unit of length (a meter ruler in a particular case); When weighing a barbell, we determine the ratio of its mass to the mass of another body - a single “kilogram” weight, etc. If we limit ourselves only to the use of ratio scales, then we can give another (narrower, more specific) definition of measurement: to measure a quantity means to experimentally find its relation to the corresponding unit of measurement.
Table 3 provides a summary of the measurement scales.

Table 3

Measurement scales.

Scale	Basic Operations	Valid mathematical procedures	Examples
Items	Establishing equality	Number of cases Mode Correlation random events(tetra- and polychoric correlation coefficients)	Numbering of athletes in the team Draw results
About	Establishing "more" or "less" ratios	Median Rank correlation Rank criteria Testing hypotheses using nonparametric statistics	Place taken at competitions Results of ranking of athletes by a group of experts
Intervals	Establishing equality of intervals	All statistical methods except for determining ratios	Calendar dates (times) Joint angle Body temperature
Relationships	Establishing equality of relations	All statistical methods	Length, strength, mass, speed, etc.

Progress

TASK 1.
Define in SI units:
a) power (N) electric current, if its voltage is U=1kV, power I=500 mA;
b) the average speed (V) of an object, if during the time t=500 ms it covered a distance S=10 cm;
c) the current strength (I) flowing in a conductor with a resistance of 20 kOhm, if a voltage of 100 mV is applied to it.
Solution:

Conclusion:

Conclusion:

TASK 4.
Determine the exact value of the deadlift strength indicator for the subject, if the maximum scale value of the deadlift dynamometer is Fmax = 450 kg, the accuracy class of the KTP device = 1.5%, and the shown result is Fmeas = 210 kg.
Solution:

or

Conclusion:

TASK 5.
Randomize your resting heart rate by measuring it three times over 15 seconds.
P1= ; р2= ; р3= .
Solution:


Conclusion:

Control questions

1. Subject and tasks of sports metrology.
2. The concept of measurement and units of measurement.
3. Measurement scales.
4. Basic, additional, derived SI units.
5. Dimension of derived quantities.
6. The concept of measurement accuracy and errors.
7. Types of errors (absolute, relative, systematic and random).
8. The concept of instrument accuracy class, calibration, calibration and randomization.

Theoretical part

When improving sports technique, we choose the technical performance of an exercise by an outstanding athlete as the standard technique (often the technique of the world record holder is taken as the standard). Wherein great importance has not an external picture of the athlete’s movements, but the internal content of the movement (efforts applied to the support or apparatus). Therefore, a sports result largely depends on how accurately we copy efforts, the rate of change of efforts, which in turn depends on the ability of our analyzers to perceive and evaluate these parameters. Due to the fact that the accuracy of hardware recording of various biomechanical parameters significantly exceeds the resolution of our analyzers, it becomes possible to use devices as an addition to our senses.
The electrotensometry method allows you to register and measure the efforts developed by an athlete when performing various physical exercises.

Composition of a complex measuring system is a list of all elements included in it and aimed at solving the measurement problem (Fig. 1).


Fig.1. Diagram of the composition of the measuring system.

Progress

1. Obtain a tensogram of your standing jump. The recorder pen deflects in proportion to the forces on the platform (Fig. 2).
2. Draw an isoline (zero line).
3. Process the tensogram, highlighting the phases of the exercise:

function PlayMyFlash(cmd, arg)( if (cmd=="play") (Tenzo_.GotoFrame(arg); Tenzo_.Play();) else Tenzo_.TGotoFrame(cmd, 2); Tenzo_.TPlay(cmd); )

Weight!!! Hooked!!! Repulsion!!! Flight and landing!!!;

F0!!! Fmin!!! Fmax!!! Flight phase
Developed force phase Pull-off phase

Rice. 2. Tensogram of a standing jump:

1. F0 - weight of the subject;
2. t0 - beginning of the squat;
3. Repulsion
4. F min - minimum developed force when squatting;
5. Fmax - maximum developed force during repulsion;
6. - repulsion phase;
7. - flight phase.

4. Determine the vertical force scale using the formula
:
5. Determine the time scale along the horizontal axis using the formula:

6. Determine the time of repulsion from the strain gauge platform using the formula:
(3)
7. Determine the time of development of maximum force using the formula:
(4)
8. Determine the flight time using the formula:
(5)

(For highly qualified athletes with good jump technique, the flight time is 0.5 s or more).

9. Determine the minimum developed force using the formula:
(6)
10. Determine the maximum developed force using the formula:
(7)
(Highly skilled long jumpers have a maximum take-off force of up to 1000 kg).
11. Determine the force gradient using the formula:

(8)
The force gradient is the rate of change of force per unit time.

12. Determine the force impulse using the formula:
(9)
An impulse of force is the action of a force over a period of time.
P=
The height of the jump according to Abalakov directly depends on the magnitude of the force impulse, and, therefore, we can talk about a correlation between the indicators of the force impulse and the performance of the Abalakov test.

Control questions

9. What is the composition of the measuring system?
10. What is the structure of the measuring system?
11. What is the difference between a simple measuring system and a complex one?
12. Types of telemetry and their application in physical education and sports.

Theoretical information

Word test translated from English means “test” or “test”. This term first appeared in scientific literature at the end of the last century, and wide use received after the publication in 1912 by the American psychologist E. Thorndike of his work on the application of test theory in pedagogy.
In sports metrology test refers to a measurement or test conducted to determine the condition or characteristics of an athlete that satisfies the following specific metrological requirements:
1. Standardization- compliance with a set of measures, rules and requirements for the test, i.e. the procedure and conditions for conducting tests must be the same in all cases of their use. They try to unify and standardize all tests.
2. Information content- this is the property of a test to reflect the quality of the system (for example, an athlete) for which it is used.
3. Reliability test - the degree of agreement between results when repeated testing of the same people under the same conditions.
4. Availability of a rating system.

Progress

1. Statement of the testing problem. Each student must be tested on all 10 proposed tests and write down their results in their own row of group table 4.
2. Testing of each subject is carried out in the following sequence:
Test 1. Weight measured on medical scales, which are pre-balanced to zero using movable balances. The weight value (P) is measured on the scale with an accuracy of 1 kg and recorded in column 3 of the table.

Test 2. Height is measured using a stadiometer. The height value (H) is measured on a centimeter scale with an accuracy of 1 cm and is recorded in column 4 of the table.

Test 3. The Quetelet index, which characterizes the weight-height ratio, is calculated by dividing the weight of the subject in grams by the height in centimeters. The result is recorded in column 5.
Test 4. By palpation in the area of ​​the radial or carotid artery, the heart rate in a state of relative rest (HRSp) is measured for 1 minute and recorded in column 6. Then the subject performs 30 full squats (tempo - one squat per second) and immediately after the load the heart rate is measured for 10 s . After 2 minutes of rest, the recovery heart rate is measured for 10 seconds. Then the results are recalculated in 1 minute and recorded in columns 7 and 8.
Test 5. The Ruffier index is calculated using the formula:

R=

Test 6. A back dynamometer measures the maximum strength of the back extensor muscles with an accuracy of ± 5 kg. When performing the test, the arms and legs should be straight, the dynamometer handle should be level knee joints. The result is written in column 10.
Test 7. The level of flexibility is measured in linear units according to the method of N.G. Ozolin in its own modification using a specially designed device. The subject sits on the mat, resting his feet on the crossbar of the device, with his hands extended forward, he grabs the handle of the measuring tape; the back and arms form an angle of 90°. The length of the tape pulled out of the device is recorded. When the subject is tilted forward all the way, the length of the tape is measured again. The flexibility indicator is calculated in conventional units using the formula:

The results are entered in column 11.
Test 8. In front of the subject on the table lies a board divided into 4 squares (20x20 cm). The subject touches the squares with his hand in the following sequence: upper left - lower right - lower left - upper right (for right-handers). The number of correctly completed movement cycles in 10 seconds is taken into account. The results are entered in column 12.
Test 9. To determine the level of speed, a measuring complex is used, consisting of a contact platform, an interface, a computer and a monitor. The subject runs in place with a high hip lift for 10 seconds (tapping test). Immediately after the end of the run, a histogram of the parameters of the support and non-support phases is constructed on the monitor screen, data on the number of step cycles, average values ​​of the support time and flight time in ms are displayed. The main criterion for assessing the level of development of speed is the support time, since this parameter is more stable and informative. The results are entered in column 13.
Test 10. To assess speed and strength qualities, a modification of the Abalakov test is used using a measuring complex. At the command from the monitor, the subject performs a standing jump on the contact platform with a wave of his arms. After landing, the flight time in ms and the jump height in cm are calculated in real time. The criterion for evaluating the results of this test is the flight time, since a straight line has been identified between this indicator and the jump height functional dependence. The results are entered in column 14.
3. At the end of the lesson, each student dictates his results to the whole group. Thus, each student fills out a table of GPT results for the entire subgroup, which will be used in the future as experimental material for mastering methods for processing test results and for completing individual tasks on RGR.

TOPIC 4. MATHEMATICAL STATISTICS, ITS BASIC CONCEPTS AND APPLICATION TO PHYSICAL EDUCATION AND SPORTS

1. The emergence and development of mathematical statistics
Since ancient times, in each state, the relevant authorities have collected information on the number of residents by gender, age, employment in various fields labor, the presence of various soldiers, weapons, money, tools, means of production, etc. All these and similar data are called statistical. With the development of the state and international relations there was a need to analyze statistical data, their forecasting, processing, assessing the reliability of conclusions based on their analysis, etc. Mathematicians began to be involved in solving such problems. Thus, in mathematics there was formed new area- mathematical statistics, studying general patterns statistical data or phenomena and the relationships between them.
The scope of application of mathematical statistics has spread to many, especially experimental, sciences. This is how economic statistics, medical statistics, biological statistics, statistical physics etc. With the advent of high-speed computers, the possibility of using mathematical statistics in various fields of human activity is constantly increasing. Its application to the field of physical culture and sports is expanding. In this regard, the basic concepts, provisions and some methods of mathematical statistics are discussed in the course “ Sports metrology" Let us dwell on some basic concepts of mathematical statistics.
2. Statistics
Currently, the term “statistical data” refers to all collected information that is subsequently subjected to statistical processing. In various literature they are also called: variables, options, quantities, dates, etc. All statistics can be divided into: high quality, difficult to measure (available, not present; more, less; strong, weak; red, black; male, female, etc.), and quantitative, which can be measured and represented as a number of general measures (2 kg, 3 m, 10 times, 15 s, etc.); accurate, the size or quality of which is beyond doubt (in a group of 6 people, 5 tables, wooden, metal, male, female, etc.), and close, the size or quality of which is in doubt (all measurements: height 170 cm, weight 56 ​​kg, 100 m run result - 10.3 s, etc.; related concepts - blue, light blue, wet, wet, etc. ); certain (deterministic), the reasons for the appearance, non-appearance or changes of which are known (2 + 3 = 5, a stone thrown upward will necessarily have a vertical speed equal to 0, etc.), and random, which may appear or not appear, or not all the reasons for which changes are known (whether it will rain or not, a girl or a boy will be born, the team will win or not, in the 100 m race - 12.2 s, the load taken is harmful or not). In most cases in physical culture and sports we are dealing with approximate random data.
3. Statistical characteristics, populations
General property, inherent in several statistical data, they are called statistical sign . For example, the height of the team players, the result of the 100 m run, the sport they belong to, heart rate, etc.
Statistical aggregate name several statistical data combined into a group with at least one statistical characteristic. For example, 7.50, 7.30, 7.21, 7.77 are the long jump results in meters for one athlete; 10, 12, 15, 11, 11 - results of five students doing pull-ups on the crossbar, etc. Number of data in statistical population call her volume and denote n. The following aggregates are distinguished:
infinite - n (mass of the planets of the Universe, number of molecules, etc.);
final - n - final number;
large - n > 30;
small - n 30;
general - containing all the data determined by the statement of the problem;
sample - parts of general populations.
For example, let the height of students aged 17-22 in the Russian Federation be population, then the growth of KSAPC students, all students of the city of Krasnodar or second-year students is a sample.
4. Curve normal distribution
When analyzing the distribution of measurement results, an assumption is always made about the distribution that the sample would have if the number of measurements were very large. This distribution (of a very large sample) is called the population distribution or theoretical, and the distribution of the experimental series of measurements is empirical.
Theoretical distribution Most measurement results are described by the normal distribution formula, which was first found by the English mathematician Moivre in 1733:


This mathematical expression of the distribution allows you to obtain a normal distribution curve in the form of a graph (Fig. 3), which is symmetrical about the grouping center (usually the value, mode or median). This curve can be obtained from a distribution polygon with an infinite number of observations and intervals. The shaded area of ​​the graph in Figure 3 shows the percentage of measurement results that are between the values ​​x1 and x2.

Rice. 3. Normal distribution curve.
By introducing the notation called normalized or standardized deviation, we obtain an expression for the normalized distribution:

Figure 4 shows a graph of this expression. It is notable for the fact that for it =0 and s =1 (normalization result). The entire area contained under the curve is equal to 1, i.e. it reflects 100% of the measurement results. For the theory of pedagogical assessments and especially for the construction of scales, the percentage of results that lie in different ranges of variation, or fluctuation, is of interest.
function PlayMyFlash(cmd)( Norm_.SetVariable("Counter", cmd); Norm_.GotoFrame(2); Norm_.Play(); )

1 !!! 1,96 !!! 2 !!! 2,58 !!! 3 !!! 3,29 !!!

Fig.4. Normalized distribution curve with percentage expression of distributions of relative and accumulated particulars:
under the first x-axis - average standard deviation;
under the second (lower) is the accumulated percentage of results.

To assess the variation in measurement results, the following relationships are used:

5. Types of presentation of statistical data
After the sample has been determined and its statistical data (options, dates, elements, etc.) have become known, there is a need to present this data in a form convenient for solving the problem. In practice, many different types of presentation of statistical data are used. The most commonly used are the following:
a) text view;
b) tabular view;
c) variation series;
d) graphical view.
If, during statistical processing of a population, it does not matter in what sequence the data is recorded, then it is convenient to arrange these data (options) in accordance with their value or in ascending order xi ~ 2, 3, 3, 5, 5, 6, 6, 6, 6, 7 (non-decreasing set), or descending xi ~ 7, 6, 6, 6, 6, 5, 5, 3, 3, 3, 2 (non-increasing set). This process is called ranking . And the place of each option in the ranked series is called rank .

Subject: Graphic image variation series
Target: learn to build graphs (histogram and polygon) of frequency distributions in a variation series and draw conclusions from them about the homogeneity of a group for a given characteristic.
Theoretical information
The analysis of variation series is simplified by graphical representation. Let's look at the main graphs of the variation series.
1. Polygon distribution (Fig. 5-I). On the graph, this is a curve reflecting the average values ​​of classes along the abscissa (X) axis, and the frequency of accumulation of values ​​in each class along the ordinate (Y) axis.
2. bar chart distribution (Fig. 5 -II). Schedule made in rectangular system coordinates and reflecting along the ordinate axis (Y) the frequency of accumulation of values ​​in the class, and along the abscissa axis (X) - the boundaries of classes.
Graphical representation measurement results not only significantly facilitate the analysis and identification of hidden patterns, but also allow you to correctly select subsequent statistical characteristics and methods.
EXAMPLE 4.1.
Construct graphs of the variation series of 20 subjects studied in terms of high jump testing results, if the sample data are as follows:
xi, cm ~ 185, 170, 190, 170, 190, 178, 188, 175, 192, 178, 176, 180, 185, 176, 180, 192, 190, 190, 192, 194.
Solution:
1. We rank the variation series in non-decreasing order:
xi, cm ~ 170,170, 174, 176, 176, 178, 178, 180, 180, 185, 185, 188, 190, 190, 190, 190, 192, 192, 192, 194.
2. Determine the minimum and maximum value of the option and calculate the range of the variation series using the formula:
R=Xmax - Xmin (1)
R=194-170=24 cm
3. Calculate the number of classes using the Sturges formula:
(2)
N=1+3.31 H 1.301=5.30631 5
4. We calculate the interval of each class using the formula:
(3)

5. Compile a table of class boundaries.

Source: " Sports metrology» , 2016

SECTION 2. ANALYSIS OF COMPETITIVE AND TRAINING ACTIVITIES

CHAPTER 2. Analysis of competitive activity -

2.1 Statistics International Federation ice hockey (IIHF)

2.2 Corsi statistics

2.3 Fenwick statistics

2.4 PDO statistic

2.5 FenCIose statistics

2.6 Assessing the quality of a player’s competitive activity (QoC)

2.7 Assessment of the quality of competitive activity of partners on the link (QoT)

2.8 Analysis of the predominant use of a hockey player

CHAPTER 3. Analysis of technical and tactical readiness -

3.1 Analysis of the effectiveness of technical and tactical actions

3.2 Analysis of the volume of technical actions performed

3.3 Analysis of the versatility of technical actions

3.4 Assessing tactical thinking

CHAPTER 4. Accounting for competitive and training loads

4.1 Accounting outside loads

4.2 Accounting inside loads

SECTION 3. CONTROL OF PHYSICAL DEVELOPMENT AND FUNCTIONAL STATE

6.1 Methods for determining body composition

6.2.3.2 Formulas for estimating body fat mass

6.3.1 Physical Basics method

6.3.2 Integral research methodology

6.3.2.1 Interpretation of study results.

6.3.3 Regional and multisegmental techniques for assessing body composition

6.3.4 Method safety

6.3.5 Method reliability

6.3.6 Indicators of highly qualified hockey players

6.4 Comparison of results obtained from bioimpedance analysis and caliperometry

6.5.1 Measurement procedure

6.6 Composition of muscle fibers???

7.1 Classical methods for assessing an athlete’s condition

7.2 Systematic comprehensive monitoring of the athlete’s condition and readiness using Omegawave technology

7.2.1 Practical implementation of the concept of readiness in Omegawave technology

7.2.LI Central nervous system readiness

7.2.1.2 Cardiac and autonomic nervous system readiness

7.2.1.3 Availability of energy supply systems

7.2.1.4 Neuromuscular system readiness

7.2.1.5 Readiness of the sensorimotor system

7.2.1.6 Readiness of the whole organism

7.2.2. Results..

SECTION 4. Psychodiagnostics and psychological testing In sports

CHAPTER 8. Basics of psychological testing

8.1 Classification of methods

8.2 Study structural components hockey player personality

8.2.1 Study of sports orientation, anxiety and level of aspirations

8.2.2 Assessment of typological properties and characteristics of temperament

8.2.3 Characteristics of individual aspects of the athlete’s personality

8.3 Comprehensive personality assessment

8.3.1 Projective techniques

8.3.2 Analysis of the characterological characteristics of the athlete and coach

8.4 Study of the athlete’s personality in the system of public relations

8.4.1 Sociometry and team assessment

8.4.2 Measuring the coach-athlete relationship

8.4.3 Group personality assessment

Overall assessment psychological stability and reliability of the athlete 151

8.4.5 Methods for assessing volitional qualities.....154

8.5 Study of mental processes......155

8.5.1 Sensation and perception155

8.5.2 Attention.157

8.5.3 Memory..157

8.5.4 Features of thinking158

8.6 Diagnosis of mental conditions159

8.6.1 Assessment of emotional states.....159

8.6.2 Assessment of the state of neuropsychic stress..160

8.6.3 Color test Luther161

8.7 Main causes of errors in psychodiagnostic studies.....162

Conclusion.....163

Literature.....163

SECTION 5. PHYSICAL FITNESS CONTROL

CHAPTER 9. The problem of feedback in training management

in modern professional hockey171

9.1 Characteristics of the surveyed population...173

9.1.1 Place of work..173

9.1.2 Age..174

9.1.3 Coaching experience175

9.1.4 Current position..176

9.2 Analysis of results survey questionnaire trainers professional clubs and National teams..177

9.3 Analysis of methods for assessing the functional readiness of athletes.... 182

9.4 Analysis of test results183

9.5 Conclusions.....186

CHAPTER 10. Functional motor abilities.187

10.1 Mobility.190

10.2 Stability.190

10.3 Testing functional motor abilities191

10.3.1 Evaluation criteria191

10.3.2 Interpretation of results.191

10.3.3 Tests for qualitative assessment functional motor abilities.192

10.3.4 Protocol of results of testing of functional motor abilities.202

CHAPTER 11. Power abilities.205

11.1 Metrology of force abilities207

11.2 Tests to assess strength abilities....208

11.2.1 Tests to assess absolute (maximum) muscle strength.209

11.2.1.1 Tests to assess absolute (maximum) muscle strength using dynamometers.209

11.2.1.2 Maximum tests to assess absolute muscle strength using a barbell and maximum weights.214

11.2.1.3 Protocol for assessing absolute muscle strength using barbell and non-maximum weights218

11.2.2 Assessment tests speed-strength abilities and power.....219

11.2.2.1 Tests to assess speed-strength abilities and power using a barbell.219

11.2.2.2 Tests to evaluate speed-strength abilities and power using medicine balls.222

11.2.2.3 Tests to assess speed-strength abilities and power using bicycle ergometers229

11.2.2.4 Tests to assess speed-strength abilities and power using other equipment234

11.2.2.5 Jump tests to assess speed-strength abilities and power.....236

11.3 Tests to assess the special power abilities of field players.... 250

CHAPTER 12. Speed ​​abilities......253

12.1 Metrology of speed abilities.....255

12.2 Tests to assess speed abilities..256

12.2.1 Tests to evaluate reaction speed...257

12.2.1.1 Evaluation of a simple reaction......257

12.2.1.2 Evaluation of the choice response from several signals258

12.2.1.3 Assessing the speed of response to a specific tactical situation......260

12.2.1.4 Assessing response to a moving object261

12.2.2 Tests for assessing the speed of single movements261

12.2.3 Tests for assessing maximum frequency of movements.261

12.2.4 Tests for assessing the speed manifested in holistic motor actions264

12.2.4.1 Tests to evaluate starting speed265

12.2.4.2 Tests to evaluate distance speed..266

12.2.5 Tests to evaluate braking speed.26“

12.3 Tests to evaluate the special speed abilities of field players. . 26*

12.3.1 Test protocol for skating 27.5/30/36 meters face and back forward to assess the power of the anaerobic-alactate energy supply mechanism.. 2“3

Tests for assessing the capacity of the anaerobic-alactate energy supply mechanism..273

ON Tests to evaluate the special speed abilities of goalkeepers277

12.4.1 Tests to evaluate a goalkeeper's reaction time.277

12.4.2 Tests to assess the speed exhibited in the holistic motor actions of goalkeepers..279

CHAPTER 13. Endurance.281

13.1 Endurance metrology.283

13.2 Tests to assess endurance285

13.2.1 Direct method for assessing endurance...289

13.2.1.1 Maximum tests for assessing speed endurance and the capacity of the anaerobic-alactate energy supply mechanism. . 290

13.2.1.2 Maximum tests for assessing regional speed-strength endurance.292

13.2.1.3 Maximum tests for assessing speed and speed-strength endurance and the power of the anaerobic-glycolytic energy supply mechanism...295

13.2.1.4 Maximum tests for assessing speed and speed-strength endurance and the capacity of the anaerobic-glycolytic energy supply mechanism...300

13.2.1.5 Maximum tests for assessing global strength endurance.301

13.2.1.6 Maximum tests to assess VO2max and general (aerobic) endurance.316

13.2.1.7 Maximum tests to assess PANO and general (aerobic) endurance.320

13.2.1.8 Maximum tests for assessing heart rate and general (aerobic) endurance.323

13.2.1.9 Maximum tests to assess general (aerobic) endurance. . 329

13.2.2 Indirect method for assessing endurance (tests with submaximal power loads)330

13.3 Tests to evaluate the special endurance of field players336

13.4 Tests to evaluate the special endurance of goalkeepers341

CHAPTER 14. Flexibility.343

14.1 Metrology of flexibility345

14.1.1 Factors affecting flexibility.....345

14.2 Tests for assessing flexibility.346

CHAPTER 15. Coordination abilities..353

15.1 Metrology of coordination abilities.355

15.1.1 Classification of types of coordination abilities357

15.1.2 Criteria for assessing coordination abilities..358

5.2 Tests to assess coordination abilities.359

15.2.1 Control of coordination of movements.....362

15.2.2 Monitoring the ability to maintain body balance (balance)......364

15.2.3 Monitoring the accuracy of estimation and measurement of movement parameters. . . 367

15.2.4 Control of coordination abilities in their complex manifestation. . 369

15.3 Tests to assess the special coordination abilities and technical readiness of field players.382

15.3.1 Tests to evaluate skating technique and puck handling. . 382

15.3.1.1 Control of cross-step skating technique382

15.3.1.2 Control of the ability to change direction on skates. . 384

15.3.1.3 Control of technique for performing turns on skates387

15.3.1.4 Control of the technique of transitions from skating face forward to running backwards and vice versa.388

15.3.1.5 Control of stick and puck handling technique392

15.3.1.6 Control of special coordination abilities in their complex manifestation

15.3.2 Tests to evaluate braking technique and the ability to quickly change directions

15.3.3 Gestures for assessing the accuracy of shots and passes of the puck

15.3.3.1 Control of throw accuracy

15.3.3.2 Monitoring the accuracy of puck passes

15.4 Tests to evaluate the special coordination abilities and technical readiness of goalkeepers

15.4.1 Control of movement technique with an additional step

15.4.2 Checking the T-slide technique

15.4.3 Control of cross-sliding movement technique on shields

15.4.4 Evaluation of puck bounce control technique

15.4.5 Control of special coordination abilities of goalkeepers in their complex manifestation

CHAPTER 16. Interrelationships in the manifestation of various types of physical abilities on and off the ice

16.1 The relationship between speed, power and speed-power abilities of hockey players on and off the ice

16.1.1 Organization of the study

16.1.2 Analysis of the relationship between speed, power and speed-power abilities of hockey players on and off the ice

16.2 Relationship between various indicators of coordination abilities

16.2.1 Organization of the study

16.2.2 Analysis of the relationship between various indicators of coordination abilities

17.1 Optimal comprehensive battery for testing GPT and SPT

17.2 Data analysis

17.2.1 Planning training based on calendar features

17.2.2 Drawing up a test report

17.2.3 Personalization

17.2.4 Monitoring progress and assessing the effectiveness of the training program

Introduction to the subject of sports metrology

Sports metrology is the science of measurements in physical education and sports, its task is to ensure the unity and accuracy of measurements. The subject of sports metrology is comprehensive control in sports and physical education, as well as the further use of the obtained data in the training of athletes.

Fundamentals of integrated control metrology

The preparation of an athlete is a controlled process. Its most important attribute is Feedback. The basis of its content is comprehensive control, which gives trainers the opportunity to receive objective information about the work done and the functional changes that it caused. This allows you to make the necessary adjustments to the training process.

Comprehensive control includes pedagogical, medical-biological and psychological sections. An effective preparation process is possible only with the integrated use of all sections of control.

Managing the process of training athletes

Managing the process of training athletes includes five stages:

1. collecting information about the athlete;
2. analysis of the received data;
3. development of strategy and preparation of training plans and training programs;
4. their implementation;
5. monitoring the effectiveness of programs and plans, making timely adjustments.

Hockey specialists receive a large amount of subjective information about players’ readiness during training and competitive activities. Undoubtedly, the coaching staff also needs objective information about individual aspects of preparedness, which can only be obtained in specially created standard conditions.

This problem can be solved by using a testing program consisting of the minimum possible number of tests to obtain the maximum useful and comprehensive information.

Types of control

Main types pedagogical control are:

• Stage control- evaluates steady states hockey players and is carried out, as a rule, at the end of a certain stage of preparation;

• Current control- monitors the speed and nature of the recovery processes, as well as the condition of athletes as a whole based on the results of a training session or a series of them;

• Operational control - gives an express assessment of the player’s condition at a given specific moment: between tasks or at the end of a training session, between entering the ice during a match, as well as during a break between periods.

The main methods of control in hockey are pedagogical observations and testing.

Basics of measurement theory

“Measurement of a physical quantity is an operation that results in determining how many times this quantity is greater (or less) than another quantity taken as a standard.”

Measurement scales

There are four main measurement scales:

Table 1. Characteristics and examples of measurement scales

	Characteristics	Mathematical methods
Items	Objects are grouped and groups are designated by numbers. The fact that the number of one group is greater or less than another does not say anything about their properties, except that they are different	Number of cases Tetrachoric and polychoric correlation coefficients	Athlete Role number, etc.
	The numbers assigned to objects reflect the amount of property they own. It is possible to establish a ratio of “more” or “less”	Rank correlation Rank tests Hypothesis testing of nonparametric statistics	Results of ranking athletes in the test
Intervals	There is a unit of measurement with which objects can not only be ordered, but also numbers can be assigned to them so that different differences reflect different differences in the amount of the property being measured. The zero point is arbitrary and does not indicate the absence of a property	All statistical methods except for determining ratios	Body temperature, joint angles, etc.
Relationships	The numbers assigned to objects have all the properties of an interval scale. There is an absolute zero on the scale, which indicates complete absence of a given property of an object. The ratio of numbers assigned to objects after measurements reflect the quantitative relationships of the property being measured.	All statistical methods	Length and weight of the body Force of movement Acceleration, etc.

Accuracy of measurements

In sports, two types of measurements are most often used: direct (the desired value is found from experimental data) and indirect (the desired value is derived based on the dependence of one value on the others being measured). For example, in the Cooper test, the distance is measured (direct method), and the MIC is obtained by calculation (indirect method).

According to the laws of metrology, any measurements have an error. The task is to reduce it to a minimum. The objectivity of the assessment depends on the accuracy of the measurement; Based on this, knowledge of measurement accuracy is a prerequisite.

Systematic and random measurement errors

According to the theory of errors, they are divided into systematic and random.

The magnitude of the former is always the same if measurements are carried out by the same method using the same instruments. The following groups of systematic errors are distinguished:

• the cause of their occurrence is known and quite accurately determined. This may include changing the length of the tape measure due to changes in air temperature during the long jump;
• the cause is known, but the magnitude is not. These errors depend on the accuracy class of the measuring devices;
• the cause and magnitude are unknown. This case can be observed in complex measurements, when it is simply impossible to take into account everything possible sources errors;
• errors related to the properties of the measurement object. This may include the level of stability of the athlete, the degree of fatigue or excitement, etc.

To eliminate systematic errors, measuring devices are first checked and compared with standards or calibrated (the error and the amount of corrections are determined).

Random errors are those that are simply impossible to predict in advance. They are identified and taken into account using probability theory and mathematical apparatus.

Absolute and relative measurement errors

The difference, equal to the difference between the indicators of the measuring device and the true value, is the absolute measurement error (expressed in the same units as the measured value):

x = x source - x measurement, (1.1)

where x is the absolute error.

When testing, there is often a need to determine not the absolute, but the relative error:

X rel =x/x rel * 100% (1.2)

Basic test requirements

A test is a test or measurement conducted to determine an athlete's condition or ability. Tests satisfying the following requirements may be used as tests:

• having a goal;

• the testing procedure and methodology have been standardized;

• the degree of their reliability and information content was determined;

• there is a system for evaluating results;

• the type of control is indicated (operational, current or stage-by-stage).

All tests are divided into groups depending on the purpose:

1) indicators measured at rest (body length and weight, heart rate, etc.);

2) standard tests using non-maximal load (for example, running on a treadmill 6 m/s for 10 minutes). Distinctive feature of these tests is a lack of motivation to achieve the highest possible result. The result depends on the method of setting the load: for example, if it is set by the magnitude of shifts in medical and biological indicators (for example, running at a heart rate of 160 beats/min), then the physical values ​​of the load are measured (distance, time, etc.) and vice versa.

3) maximum tests with a high psychological attitude to achieve the maximum possible result. IN in this case values ​​of various functional systems(MOC, heart rate, etc.). The motivation factor is the main disadvantage of these tests. It is extremely difficult to motivate a player who has a signed contract to achieve maximum results in control exercise.

Standardization of measurement procedures

Testing can be effective and useful to a coach only if it is used systematically. This makes it possible to analyze the degree of progress of hockey players, evaluate the effectiveness of the training program, and also normalize the load depending on the dynamics of the athletes’ performance

f) general endurance (aerobic energy supply mechanism);

6) rest intervals between attempts and tests must be until the subject fully recovers:

a) between repetitions of exercises that do not require maximum effort - at least 2-3 minutes;

b) between repetitions of exercises with maximum effort - at least 3-5 minutes;

7) motivation to achieve maximum results. Achievement this condition can be quite difficult, especially when it comes to professional athletes. Here everything largely depends on charisma and leadership qualities

The word “metrology” translated from Greek means “the science of measurements” (metro - measure, logos - teaching, science). Any science begins with measurements, therefore the science of measurements, methods and means of ensuring their unity and the required accuracy is fundamental in any field of activity.

Sports metrology- the science of measurement in physical education and sports. The specificity of sports metrology is that the object of measurement is a living system - a person. In this regard, sports metrology has a number of fundamental differences from the field of knowledge that considers traditional classical measurements of physical quantities. The specifics of sports metrology are determined by following features measurement object:

• Variability is the inconstancy of variables that characterize physiological state a person and the results of his sports activities. All indicators (physiological, morpho-anatomical, psychophysiological, etc.) are constantly changing, so multiple measurements are required with subsequent statistical processing of the information received.
• Multidimensionality - the need for simultaneous measurement large number variables characterizing physical state and the result of sports activity.
• Qualitativeness is the qualitative nature of a number of measurements in the absence of an exact quantitative measure.
• Adaptability is the ability to adapt to new conditions, which often masks the true result of a measurement.
• Mobility is a constant movement in space, characteristic of most sports and significantly complicating the measurement process.
• Controllability is the ability to purposefully influence the athlete’s actions during training, depending on objective and subjective factors.

Thus, sports metrology not only deals with traditional technical measurements of physical quantities, but also solves important problems of managing the training process:

• used as a tool for measuring biological, psychological, pedagogical, sociological and other indicators characterizing the activity of an athlete;
• represents the source material for biomechanical analysis motor actions of the athlete.

Subject of sports metrology- comprehensive control in physical education and sports, including monitoring the athlete’s condition, training loads, exercise technique, sports results and the athlete’s behavior in competitions.

Purpose of sports metrology- implementation of comprehensive control to achieve maximum sports results and maintain the health of the athlete against the backdrop of high loads.

During sports pedagogical research and during the training process, many different parameters are measured. All of them are divided into four levels:

1. Single - reveal one value separate property studied biological system(for example, simple motor reaction time).
2. Differential - characterize one property of the system (for example, speed).
3. Complex - relate to one of the systems (for example, physical fitness).
4. Integral - reflect the total effect of functioning various systems(e.g. sportsmanship).

The basis for determining all of these parameters are single parameters that are complexly related to parameters of more high level. In sports practice, the most common parameters are those used to assess basic physical qualities.

2. Structure of sports metrology

Sections of sports metrology are presented in Fig. 1. Each of them constitutes an independent field of knowledge. On the other hand, they are closely related to each other. For example, in order to assess the level of speed-strength readiness of a track and field sprinter at a certain stage of training using an accepted scale, it is necessary to select and conduct appropriate tests (standing high jump, triple jump, etc.). During the tests, it is necessary to measure physical quantities (height and length of the jump in meters and centimeters) with the required accuracy. For this purpose, contact or non-contact measuring instruments can be used

Rice. 1. Sections of sports metrology

For some sports, the basis of complex control is the measurement of physical quantities (in athletics, weightlifting, swimming, etc.), for others - quality indicators (in rhythmic gymnastics, figure skating, etc.). In both cases, to process the measurement results, the appropriate mathematical apparatus is used, which makes it possible to draw correct conclusions based on the measurements and assessments.

Questions for self-control

1. What is sports metrology and what are its specifics?
2. What are the subject, purpose and objectives of sports metrology?
3. What parameters are measured in sports practice?
4. What sections does sports metrology include?

Methods of sports metrology.

The role of sports metrology in physical culture and sports.

Measurement of physical quantities.

Parameters measured in physical culture and sports

Measurement scales

Accuracy of measurements.

1.1. Subject and objectives of the course “Sports Metrology”

IN everyday practice of humanity and each individual, measurement is a completely normal procedure. Measurement, along with calculation, is directly related to the material life of society, since it developed in the process of practical exploration of the world by man. Measurement, like counting and calculation, has become integral part social production and distribution, the objective starting point for the emergence of mathematical disciplines, and primarily geometry, and hence a necessary prerequisite for the development of science and technology.

At the very beginning, at the moment of their emergence, measurements, no matter how different they were, were naturally of an elementary nature. So, calculus of many objects certain type was based on comparison with the number of fingers. The measurement of the length of certain objects was based on comparison with the length of a finger, foot or step. This accessible method was initially literally “experimental computing and measuring technology.” It has its roots in the distant era of the “childhood” of humanity. Whole centuries passed before the development of mathematics and other sciences, the emergence of measuring technology, caused by the needs of production and trade, communications between by individuals and peoples, has led to the emergence of well-developed and differentiated methods and technical means in various fields of knowledge.

Now it is difficult to imagine any human activity in which measurements would not be used. Measurements are carried out in science, industry, agriculture, medicine, trade, military affairs, labor and environmental protection, everyday life, sports, etc. Thanks to measurements, control is possible technological processes, industrial enterprises, training of athletes and the national economy as a whole. The requirements for measurement accuracy, speed of obtaining measurement information, and measurement of a complex of physical quantities have sharply increased and continue to increase. The number of complex measuring systems and measuring and computing complexes is increasing.

Measurements at a certain stage of their development led to the emergence of metrology, which is currently defined as “the science of measurements, methods and means of ensuring their unity and the required accuracy.” This definition indicates practical orientation metrology, which studies the measurements of physical quantities and the elements that form these measurements and develops the necessary rules and regulations. The word “metrology” is made up of two ancient Greek words: “metro” - measure and “logos” - doctrine, or science.

Modern metrology includes three components: legal metrology, fundamental (scientific) and practical (applied) metrology.

Sports metrology is the science of measurement in physical education and sports. It should be considered as a specific application to general metrology, as one of the components of practical (applied) metrology. However, as an academic discipline, sports metrology goes beyond the scope of general metrology due to the following circumstances. In physical education and sports, some of the physical quantities (time, mass, length, strength), on the problems of unity and accuracy, which metrologists focus on, are also subject to measurement. But most of all, specialists in this industry are interested in pedagogical, psychological, social, biological indicators, which in their content cannot be called physical. General metrology practically does not deal with the methodology of their measurements, and therefore there is a need to develop special measurements, the results of which comprehensively characterize the preparedness of athletes. A feature of sports metrology is that it interprets the term “measurement” in the broadest sense, since in sports practice it is not enough to measure only physical quantities. In physical culture and sports, in addition to measuring length, height, time, mass and other physical quantities, it is necessary to evaluate technical skill, expressiveness and artistry of movements and similar non-physical quantities.

Subject of sports metrology are comprehensive control in physical education and sports and the use of its results in planning the training of athletes and athletes.

Along with the development of fundamental and practical metrology, the formation of legal metrology took place.

Legal metrology is a section of metrology that includes complexes of interrelated and interdependent general rules, as well as other issues that require regulation and control by the state, aimed at ensuring the uniformity of measurements and the uniformity of measuring instruments.

Legal metrology serves as a means of state regulation of metrological activities through laws and legislative provisions that are put into practice through the State Metrological Service and metrological services government agencies management and legal entities. The field of legal metrology includes testing and type approval of measuring instruments and their verification and calibration, certification of measuring instruments, state metrological control and supervision of measuring instruments.

Metrological rules and norms of legal metrology are harmonized with the recommendations and documents of the relevant international organizations. Thus, legal metrology contributes to the development of international economic and trade relations and promotes mutual understanding in international metrological cooperation.

Sports metrology methods

The main method of sports metrology is complex control. There are three main forms of monitoring the athlete’s condition:

A) Stage-by-stage control, the purpose of which is to assess the stage-by-stage condition of the athlete;

B) Current control, the main task of which is to determine everyday, current fluctuations in the athlete’s condition;

C) Operational control, the purpose of which is a rapid assessment of the athlete’s condition at the moment.

Final goal comprehensive control – to obtain reliable and reliable information for managing the process of physical education and sports training.

In all cases of control, some measurements or tests are used to judge the athlete’s condition. Their construction and selection must satisfy certain requirements, which are considered in the so-called test theory . After testing has been carried out, its results must be evaluated. An analysis of various assessment methods is given in the so-called valuation theory . Test theory and assessment theory are those sections of sports metrology that are of general importance for all specific types of control used in the process of training an athlete.

In addition, methods of mathematical statistics, also used in sports metrology, provide significant assistance in data analysis. These methods are used to analyze the results of mass repeated measurements. The results of such measurements always differ from each other due to numerous factors that cannot be controlled and vary from one measurement to another. Mass measurements of homogeneous objects with qualitative commonality reveal certain patterns. Using statistical methods There are three stages of research:

A) statistical observation, which is a systematic, scientifically based collection of data characterizing the object being studied;

B) statistical summary and grouping, which is an important preparatory part for statistical data analysis;

C) analysis of statistical material, which is the final stage of the statistical approach.

Related information.

"Sports Metrology"

Subject, tasks and content of “Sports Metrology”, its place among other academic disciplines.

Sports metrology- is the science of measurement in physical education and sport. It should be considered as a specific application of general metrology, the main task of which, as is known, is to ensure the accuracy and uniformity of measurements.

Thus, The subject of sports metrology is complex control in physical education and sports and the use of its results in planning the training of athletes and athletes. The word "metrology" translated from ancient Greek means "the science of measurements" (metron - measure, logos - word, science).

The main task of general metrology is to ensure the uniformity and accuracy of measurements. Sports metrology as a scientific discipline is part of general metrology. Its main tasks include:

1. Development of new measurement tools and methods.

2. Registration of changes in the condition of those involved under the influence of various physical activities.

3. Collection of mass data, formation of assessment systems and norms.

4. Processing of the obtained measurement results in order to organize effective control and management of the educational and training process.

However, as an academic discipline, sports metrology goes beyond general metrology. Thus, in physical education and sports, in addition to ensuring the measurement of physical quantities, such as length, mass, etc., pedagogical, psychological, biological and social indicators are subject to measurement, which cannot be called physical in their content. General metrology does not deal with the methodology of their measurements and, therefore, special measurements have been developed, the results of which comprehensively characterize the preparedness of athletes and athletes.

The use of mathematical statistics methods in sports metrology made it possible to obtain a more accurate understanding of the objects being measured, compare them and evaluate the measurement results.

In the practice of physical education and sports, measurements are carried out in the process of systematic control (French: checking something), during which various indicators of competitive and training activity, as well as the condition of athletes, are recorded. Such control is called comprehensive.

This makes it possible to establish cause-and-effect relationships between loads and results in competitions. And after comparison and analysis, develop a program and plan for training athletes.

Thus, the subject of sports metrology is complex control in physical education and sports and the use of its results in planning the training of athletes and athletes.

Systematic monitoring of athletes allows us to determine the measure of their stability and take into account possible measurement errors.

2. Scales and units of measurement. SI system.

Name scale

Actually, measurements that meet the definition of this action are not made in the naming scale. Here we're talking about about grouping objects that are identical according to a certain characteristic and assigning designations to them. It is no coincidence that another name for this scale is nominal (from the Latin word nome - name).

The designations assigned to objects are numbers. For example, track and field athletes-long jumpers in this scale can be designated by the number 1, high jumpers - 2, triple jumpers - 3, pole vaulters - 4.

With nominal measurements, the introduced symbolism means that object 1 only differs from objects 2, 3 or 4. However, how different and in what way exactly cannot be measured on this scale.

Order scale

If some objects have a certain quality, then ordinal measurements allow us to answer the question of differences in this quality. For example, a 100m race is

determination of the level of development of speed-strength qualities. The athlete who won the race has a higher level of these qualities at the moment than the one who came second. The second, in turn, is higher than the third, etc.

But most often the order scale is used where qualitative measurements are impossible in the accepted system of units.

When using this scale, you can add and subtract ranks or perform any other mathematical operations on them.

Interval scale

The dimensions in this scale are not only ordered by rank, but also separated by certain intervals. The interval scale has units of measurement (degree, second, etc.). The measured object here is assigned a number equal to the number of units of measurement it contains.

Here you can use any statistical methods, except for determining relationships. This is due to the fact that the zero point of this scale is chosen arbitrarily.

Relationship scale

In a ratio scale, the zero point is not arbitrary, and therefore, at some point in time, the quality being measured may be zero. In this regard, when evaluating measurement results on this scale, it is possible to determine “how many times” one object is larger than another.

In this scale, one of the units of measurement is taken as a standard, and the measured value contains as many of these units as how many times it is larger than the standard. The measurement results in this scale can be processed by any methods of mathematical statistics.

Basic SI Units Unit

Quantity Dimension Name Designation

Russian international

Length L Meter m m

Weight M Kilogram kg kg

Time T Second s S

Electric power current Ampere A A

Temperature Kelvin K K

Quantity of things Mole mole mol

Luminous intensity Candella CD cd

3.Measurement accuracy. Errors and their types and methods of elimination.

No measurement can be made absolutely accurately. The measurement result inevitably contains an error, the magnitude of which is smaller, the more accurate the measurement method and measuring device.

Basic error is the error of a measurement method or measuring device that occurs under normal conditions of use.

Additional error- this is the error of a measuring device caused by a deviation of its operating conditions from normal ones.

The value D A=A-A0, equal to the difference between the reading of the measuring device (A) and the true value of the measured value (A0), is called the absolute measurement error. It is measured in the same units as the measured quantity itself.

Relative error is the ratio of the absolute error to the value of the measured quantity:

Systematic is an error whose value does not change from measurement to measurement. Due to this feature, systematic error can often be predicted in advance or, in extreme cases, detected and eliminated at the end of the measurement process.

Calibration (from German tarieren) is the checking of the readings of measuring instruments by comparison with the readings of standard values ​​of measures (standards*) over the entire range of possible values ​​of the measured quantity.

Calibration is the determination of errors or corrections for a set of measures (for example, a set of dynamometers). Both during calibration and calibration, a source of a reference signal of a known magnitude is connected to the input of the measuring system instead of the athlete.

Randomization (from the English random - random) is the transformation of a systematic error into a random one. This technique is aimed at eliminating unknown systematic errors. According to the randomization method, the measured value is measured several times. In this case, the measurements are organized so that the constant factor influencing their result acts differently in each case. For example, when studying physical performance, it can be recommended to measure it many times, each time changing the method of setting the load. Upon completion of all measurements, their results are averaged according to the rules of mathematical statistics.

Random errors arise under the influence of various factors that cannot be predicted in advance or accurately taken into account.

4.Fundamentals of probability theory. Random event random value, probability.

Probability theory- probability theory can be defined as a branch of mathematics in which the patterns inherent in mass random phenomena are studied.

Conditional probability - conditional probability PA(B) of event B is the probability of event B, found under the assumption that event A has already occurred.

Elementary event- events U1, U2, ..., Un, forming a complete group of pairwise incompatible and equally possible events, will be called elementary events.

Random event - an event is called random if it objectively may or may not occur in a given test.

Event - the result (outcome) of a test is called an event.

Any random event has some degree of possibility, which in principle can be measured numerically. In order to compare events according to the degree of their possibility, you need to associate a certain number with each of them, which is larger, the greater the possibility of the event. We will call this number the probability of the event.

When characterizing the probabilities of events with numbers, it is necessary to establish some kind of unit of measurement. As such a unit, it is natural to take the probability of a reliable event, i.e. an event that must inevitably occur as a result of experience.

The probability of an event is a numerical expression of the possibility of its occurrence.

In some simple cases, the probabilities of events can be easily determined directly from the test conditions.

Random value- this is a quantity that, as a result of experiment, takes on one of many values, and the appearance of one or another value of this quantity cannot be accurately predicted before its measurement.

5. General and sample populations. Sample size. Disorganized and ranked sample.

In sample observation, the concepts of “general population” are used - the studied set of units to be studied according to characteristics of interest to the researcher, and “sample population” - some part of it randomly selected from the general population. This sample is subject to the requirement of representativeness, i.e. When studying only part of a population, the findings can be applied to the entire population.

The characteristics of the general and sample populations can be the average values ​​of the characteristics being studied, their variances and standard deviations, mode and median, etc. The researcher may also be interested in the distribution of units according to the characteristics being studied in the general and sample populations. In this case, the frequencies are called general and sample, respectively.

The system of selection rules and methods of characterizing units of the population under study constitutes the content of the sampling method, the essence of which is to obtain primary data from observing a sample with subsequent generalization, analysis and distribution to the entire population in order to obtain reliable information about the phenomenon under study.

The representativeness of the sample is ensured by observing the principle of random selection of population objects in the sample. If the population is qualitatively homogeneous, then the principle of randomness is implemented by simple random selection of sample objects. Simple random sampling is a sampling procedure that provides each unit in the population with the same probability of being selected for observation for any sample of a given size. Thus, the purpose of the sampling method is to infer the meaning of characteristics of a population based on information from a random sample from that population.

Sample size - in an audit - the number of units selected by the auditor from the population being audited. Sample called disordered, if the order of the elements in it is not significant.

6. Basic statistical characteristics of the position of the center of the row.

Indicators of the position of the distribution center. These include power average in the form of arithmetic mean and structuralaverages – mode and median.

Arthmetic mean for a discrete distribution series is calculated by the formula:

Unlike the arithmetic mean, calculated on the basis of all options, the mode and median characterize the value of a characteristic in a statistical unit occupying a certain position in the variation series.

Median ( Me) -characteristic value y statistical unit, standing in the middle of the ranked series and dividing the totality into two equal parts.

Fashion (Mo) is the most common value of the characteristic in the aggregate. Mode is widely used in statistical practice when studying consumer demand, price registration, etc.

For discrete variation series Mo And Me are selected in accordance with the definitions: mode - as the value of a feature with the highest frequency : the position of the median with an odd population size is determined by its number, where N is the volume of the statistical population. If the volume of the series is even, the median is equal to the average of the two options located in the middle of the series.

The median is used as the most reliable indicator typical values ​​of a heterogeneous population, since it is insensitive to extreme values ​​of the characteristic, which may differ significantly from the main array of its values. In addition, the median finds practical application due to a special mathematical property: Consider the definition of mode and median using the following example: There is a range of distribution of site workers by skill level.

7. Basic statistical characteristics of dispersion (variations).

The homogeneity of statistical populations is characterized by the amount of variation (dispersion) of a characteristic, i.e. discrepancy between its values ​​in different statistical units. To measure variation in statistics, absolute and relative indicators are used.

To absolute indicators of variation relate:

Range of variation R is the simplest indicator of variation:

This indicator represents the difference between the maximum and minimum values ​​of the characteristics and characterizes the dispersion of the elements of the population. The range captures only the extreme values ​​of a characteristic in the aggregate, does not take into account the repeatability of its intermediate values, and also does not reflect deviations of all variants of the characteristic values.

The range is often used in practical activities, for example, the difference between max and min pensions, wages in various industries, etc.

Average linear deviationd is a more strict characteristic of the variation of a trait, taking into account the differences of all units of the population being studied. Average linear deviation represents arithmetic mean of absolute values deviations of individual options from their arithmetic mean. This indicator is calculated using the simple and weighted arithmetic average formulas:

In practical calculations, the average linear deviation is used to assess the rhythm of production and the uniformity of supplies. Since modules have poor mathematical properties, in practice other indicators of the average deviation from the mean are often used - dispersion and standard deviation.

Standard deviation represents the mean square of the deviations individual values sign from their arithmetic mean:

8. Reliability of differences in statistical indicators.

IN statistics the quantity is called statistically significant, if the probability of its random occurrence is small, that is null hypothesis may be rejected. A difference is said to be "statistically significant" if there is evidence that would be unlikely to occur if the difference were assumed not to exist; this expression does not mean that the difference must be large, important, or significant in the general sense of the word.

9.Graphic representation of variation series. Polygon and distribution histogram.

Graphs are a visual form of displaying distribution series. Linear graphs and planar diagrams constructed in a rectangular coordinate system are used to depict series.

For a graphical representation of attribute distribution series, various diagrams are used: bar, line, pie, figured, sector, etc.

For discrete variation series, the graph is the distribution polygon.

A distribution polygon is a broken line connecting points with coordinates or where is the discrete value of the attribute, is the frequency, is the frequency. A polygon is used to graphically represent a discrete variation series, and this graph is a type of statistical broken line. In a rectangular coordinate system, the variants of the attribute are plotted along the x-axis, and the frequencies of each variant are plotted along the ordinate axis. At the intersection of the abscissa and ordinate, the points corresponding to the given distribution series are recorded. By connecting these points with straight lines, we get a broken line, which is a polygon, or an empirical distribution curve. To close a polygon, the extreme vertices are connected to points on the x-axis, spaced one division apart on the accepted scale, or to the midpoints of the previous (before the initial) and subsequent (behind the last) intervals.

To depict interval variation series, histograms are used, which are stepped figures consisting of rectangles, the bases of which are equal to the width of the interval, and the height is equal to the frequency (frequency) of an equal-interval series or the distribution density of an unequal-interval ) variation series. In this case, the intervals of the series are plotted on the abscissa axis. On these segments, rectangles are constructed, the height of which along the ordinate axis on the accepted scale corresponds to the frequencies. At equal intervals along the abscissa axis, rectangles are laid close to each other, with equal bases and ordinates proportional to the weights. This stepped polygon is called a histogram. Its construction is similar to the construction of bar charts. The histogram can be converted into a distribution polygon, for which the midpoints of the upper sides of the rectangles are connected by straight segments. Two extreme points rectangles are closed along the x-axis in the middle of the intervals, similar to the closure of a polygon. In case of inequality of intervals, the graph is constructed not according to frequencies or frequencies, but according to the distribution density (the ratio of frequencies or frequencies to the value of the interval), and then the heights of the graph rectangles will correspond to the values ​​of this density.

When constructing graphs of distribution series, the ratio of scales along the abscissa and ordinate axis is of great importance. In this case, it is necessary to be guided by the “golden ratio rule”, according to which the height of the graph should be approximately two times less than its base

10.Normal distribution law (essence, meaning). The normal distribution curve and its properties. http://igriki.narod.ru/index.files/16001.GIF

A continuous random variable X is called normally distributed if its distribution density is equal to

where m - expected value random variable;

σ2 - dispersion of a random variable, a characteristic of the dispersion of the values ​​of a random variable around the mathematical expectation.

The condition for the emergence of a normal distribution is the formation of a characteristic as the sum of a large number of mutually independent terms, none of which is characterized by exceptionally large variances compared to other ones.

The normal distribution is limiting; other distributions approach it.

The mathematical expectation of the random variable X is distributed according to the normal law, equal to

mx = m, and variance Dx = σ2.

The probability of a random variable X, distributed according to a normal law, falling in the interval (α, β) is expressed by the formula

where is the tabulated function

11. Three sigma rule and its practical application.

When considering the normal distribution law, an important special case stands out, known as the three-sigma rule.

Those. the probability that a random variable will deviate from its mathematical expectation by an amount greater than triple the standard deviation is practically zero.

This rule is called the three sigma rule.

In practice, it is believed that if the three-sigma rule is satisfied for any random variable, then this random variable has a normal distribution.

12.Types of statistical relationships.

Qualitative analysis of the phenomenon being studied allows us to identify the main cause-and-effect relationships of this phenomenon and establish factorial and effective characteristics.

Relationships studied in statistics can be classified according to a number of criteria:

1) By the nature of the dependence: functional (hard), correlation (probabilistic) Functional connections are connections in which each value of the factor characteristic corresponds to a single value of the resulting characteristic.

With correlation connections, a separate value of a factor characteristic may correspond to different values ​​of the resulting characteristic.

Such connections appear with a large number of observations, through a change in the average value of the resulting characteristic under the influence of factor characteristics.

2) By analytical expression: rectilinear, curvilinear.

3) In direction: forward, reverse.

4) According to the number of factor characteristics that influence the resulting characteristic: single-factor, multi-factor.

Objectives of statistical study of relationships:

Establishing the presence of a direction of communication;

Quantitative measurement of the influence of factors;

Measuring the tightness of a connection;

Assessing the reliability of the data obtained.

13.Main tasks of correlation analysis.

1. Measuring the degree of connectivity of two or more variables. Our general knowledge about objectively existing causal relationships must be complemented by scientifically based knowledge about quantitative degree of dependence between variables. This paragraph implies verification already known connections.

2. Detection of unknowns causal connections . Correlation analysis does not directly reveal causal relationships between variables, but it establishes the strength of these relationships and their significance. The causal nature is clarified using logical reasoning that reveals the mechanism of connections.

3. Selection of factors that significantly influence the trait. The most important factors are those that most strongly correlate with the characteristics being studied.

14.Correlation field. Forms of relationship.

Sample data analysis aid. If the values ​​of two characteristics xl are given. . . xn and yl. . . yn, then when compiling a map, points with coordinates (xl, yl) (xn... yn) are plotted on the plane. The location of the points allows us to make a preliminary conclusion about the nature and form of the dependence.

To describe the cause-and-effect relationship between phenomena and processes, the division of statistical characteristics is used, reflecting individual aspects of interrelated phenomena, on factorial and effective.Signs that cause changes in other related features are considered factorial., being the causes and conditions of such changes. Effective signs are those that change under the influence of factor factors..

The forms of manifestation of existing relationships are very diverse. The most common types are: functional and statistical connections.

Functionalcall such a relationship in which a certain value of a factor characteristic corresponds to one and only one value of the resultant. Such a connection is possible when provided that the behavior of one characteristic (resultative) is influenced by only the second sign (factorial) and no others. Such connections are abstractions; in real life they are rare, but are widely used in the exact sciences and in First of all, in mathematics. For example: the dependence of the area of ​​a circle on radius: S=π∙ r 2

The functional connection is manifested in all cases of observation and for each specific unit of the studied population. In mass phenomena they manifest themselves statistical relationships in which a strictly defined value of a factor characteristic is associated with a set of values ​​of the resultant. Such connections take place if the resultant sign is affected by several factorial, and one or more are used to describe the relationship determining (taken into account) factors.

A strict distinction between functional and statistical relationships can be obtained by formulating them mathematically.

The functional relationship can be represented by the equation:
due to uncontrollable factors or measurement errors.

An example of a statistical relationship is the dependence of the cost per unit of production on the level of labor productivity: the higher the labor productivity, the lower the cost. But the cost per unit of production, in addition to labor productivity, is also influenced by other factors: the cost of raw materials, materials, fuel, general production and general business expenses, etc. Therefore, it cannot be argued that a change in labor productivity by 5% (increase) will lead to a similar reduction in cost. The opposite picture may also be observed if the cost price is influenced to a greater extent by other factors - for example, prices for raw materials and supplies increase sharply.