Basic concepts of test theory. Presentation of the basis of the theory of tests in physical culture
basics of test theory
Basic concepts of test theory
A measurement or test performed to determine the condition or ability of an athlete is called test .
Not all measurements can be used as tests, but only those that meet special requirements. These include:
1. standardization (the testing procedure and conditions must be the same in all cases of application of the test);
2. reliability;
3. information content;
4. Availability of a rating system.
Tests that meet the requirements of reliability and information content are called solid or authentic (Greek authentico - in a reliable manner).
The testing process is called testing ; the numerical value obtained as a result of the measurement - test result (or test result). For example, the 100 m run is a test, the procedure for conducting races and timing is testing, and the time of the race is the test result.
Tests based on motor tasks are called motor or motor . Their results can be either motor achievements (time to complete the distance, number of repetitions, distance traveled, etc.), or physiological and biochemical indicators.
Sometimes not one, but several tests are used that have a single final goal (for example, assessing the athlete’s condition during the competitive training period). This group of tests is called complex or battery of tests .
The same test, applied to the same subjects, should give identical results under the same conditions (unless the subjects themselves have changed). However, even with the most stringent standardization and precise equipment, test results always vary somewhat. For example, a subject who has just shown a result of 215 kg in a deadlift dynamometry test, shows only 190 kg when repeated.
2. Test reliability and ways to determine it
Reliability test is the degree of agreement between results when repeated testing of the same people (or other objects) under the same conditions.
Variation in test-retest results is called within-individual, or within-group, or within-class.
Four main reasons cause this variation:
1. Change in the state of the subjects (fatigue, training, learning, change in motivation, concentration, etc.).
2. Uncontrolled changes in external conditions and equipment (temperature, wind, humidity, power supply voltage, presence of unauthorized persons, etc.), i.e. everything that is united by the term “random measurement error”.
3. Changing the state of the person conducting or evaluating the test (and, of course, replacing one experimenter or judge with another).
4. Imperfection of the test (there are tests that are obviously unreliable. For example, if the subjects are making free throws into a basketball basket, then even a basketball player with a high percentage of hits can accidentally make a mistake on the first throws).
The main difference between test reliability theory and measurement error theory is that in error theory the measured value is assumed to be constant, while in test reliability theory it is assumed that it changes from measurement to measurement. For example, if it is necessary to measure the result of a completed attempt in a running long jump, then it is quite definite and cannot change significantly over time. Of course, due to random reasons (for example, unequal tension of the tape measure), it is impossible to measure this result with ideal accuracy (say, up to 0.0001 mm). However, by using a more precise measuring tool (such as a laser meter), their accuracy can be increased to the required level. At the same time, if the task is to determine the preparedness of a jumper at individual stages of the annual training cycle, then the most accurate measurement of the results shown by him will be of little help: after all, they will change from attempt to attempt.
To understand the idea of the methods used to judge the reliability of tests, let's look at a simplified example. Let's assume that it is necessary to compare the standing long jump results of two athletes based on two attempts made. Let us assume that the results of each of the athletes vary within ± 10 cm from average size and are equal to 230 ± 10 cm (i.e. 220 and 240 cm) and 280 ± 10 cm (i.e. 270 and 290 cm), respectively. In this case, the conclusion, of course, will be completely unambiguous: the second athlete is superior to the first (differences between the averages of 50 cm are clearly higher than random fluctuations of ± 10 cm). If, with the same intragroup variation (± 10 cm), the difference between the average values of the subjects (intergroup variation) is small, then it will be much more difficult to draw a conclusion. Let's assume that the average values will be approximately 220 cm (in one attempt - 210, in the other - 230 cm) and 222 cm (212 and 232 cm). In this case, the first subject in the first attempt jumps 230 cm, and the second - only 212 cm; and it seems that the first is significantly stronger than the second. From this example it is clear that the main significance is not intraclass variability itself, but its relationship with interclass differences. The same intraclass variability gives different reliability with equal differences between classes (in the particular case between the studied ones, Fig. 14).
Rice. 14. The ratio of inter- and intraclass variation with high (top) and low (bottom) reliability:
short vertical strokes - data from individual attempts;
Average results of three subjects.
The theory of test reliability is based on the fact that the result of any measurement carried out on a person is the sum of two values:
where: - the so-called true result that they want to record;
Error caused by uncontrolled changes in the state of the subject and random measurement errors.
The true result is understood as the average value of x for an infinitely large number of observations under the same conditions (for this reason, the sign is put at x).
If errors are random (their sum is zero, and in equal attempts they do not depend on each other), then from mathematical statistics it follows:
those. The variance of the results recorded in the experiment is equal to the sum of the variances of the true results and errors.
Reliability factor is called the ratio of the true dispersion to the dispersion recorded in the experiment:
In addition to the reliability coefficient, they also use reliability index:
which is considered as a theoretical correlation coefficient between the recorded test values and the true ones.
The concept of a true test result is an abstraction (it cannot be measured experimentally). Therefore, we have to use indirect methods. The most preferable method for assessing reliability is analysis of variance followed by calculation of intraclass correlation coefficients. Analysis of variance makes it possible to decompose the experimentally recorded variation in test results into components determined by the influence of individual factors. For example, if you register the results of the subjects in some test, repeating this test in different days, and make several attempts every day, periodically changing experimenters, then variations will occur:
a) from subject to subject;
b) from day to day;
c) from experimenter to experimenter;
d) from attempt to attempt.
Analysis of variance makes it possible to isolate and evaluate these variations.
Thus, in order to assess the practical reliability of the test, it is necessary, firstly, to perform an analysis of variance, and secondly, to calculate the intraclass correlation coefficient (reliability coefficient).
With two attempts, the value of the intraclass correlation coefficient practically coincides with the values of the usual correlation coefficient between the results of the first and second attempts. Therefore, in such situations, the usual correlation coefficient can be used to assess reliability (it estimates the reliability of one rather than two attempts).
Speaking about the reliability of tests, it is necessary to distinguish between their stability (reproducibility), consistency, and equivalence.
Under stability test understand the reproducibility of results when repeated after a certain time under the same conditions. Retesting is usually called retest.
Consistency The test is characterized by the independence of the test results from the personal qualities of the person conducting or evaluating the test.
When selecting a test from a certain number of similar tests (for example, sprinting at 30, 60 and 100 m), the degree of agreement of the results is assessed using the parallel forms method. The correlation coefficient calculated between the results is called equivalence coefficient.
If all the tests included in a test suite are highly equivalent, it is called homogeneous. This entire complex measures one particular property of human motor skills (for example, a complex consisting of standing long, up and triple jumps; the level of development of speed-strength qualities is assessed). If there are no equivalent tests in the complex, that is, the tests included in it measure different properties, then it is called heterogeneous (for example, a complex consisting of deadlift dynamometry, Abalakov jump, 100 m run).
The reliability of tests can be increased to a certain extent by:
a) more stringent standardization of testing;
b) increasing the number of attempts;
c) increasing the number of evaluators (judges, experiments) and increasing the consistency of their opinions;
d) increasing the number of equivalent tests;
e) better motivation of the subjects.
Example 10.1.
To determine the reliability of the standing triple jump results in assessing the speed-strength capabilities of sprinters, if the sample data are as follows:
Solution:
1. Enter the test results into the worksheet: 
2. Substitute the results obtained into the formula for calculating the rank correlation coefficient:
3. Determine the number of degrees of freedom using the formula:
Conclusion: the calculated value obtained Therefore, with confidence in 99% we can say that the standing triple jump test is reliable.
Basic concepts of test theory.
A measurement or test taken to determine an athlete's condition or ability is called a test. Any test involves measurement. But not every change serves as a test. The measurement or test procedure is called testing.
A test based on motor tasks is called motor. There are three groups of motor tests:
- 1. Control exercises, in which the athlete is tasked to show maximum results.
- 2. Standard functional tests, during which the task, the same for everyone, is dosed either according to the amount of work performed, or according to the magnitude of physiological changes.
- 3. Maximum functional tests, during which the athlete must show maximum results.
High quality testing requires knowledge of measurement theory.
Basic concepts of measurement theory.
Measurement is the identification of correspondence between the phenomenon being studied, on the one hand, and numbers, on the other.
The fundamentals of measurement theory are three concepts: measurement scales, units of measurement and measurement accuracy.
Measurement scales.
A measurement scale is a law by which a numerical value is assigned to a measured result as it increases or decreases. Let's look at some of the scales used in sports.
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 changed by metas. 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 scale, names, only some mathematical operations can be carried out. For example, its numbers cannot be added or subtracted, but you can count how many times (how often) a particular number appears.
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 the difference in their sportsmanship is remains unclear: the second athlete may be almost equal to the first, or may be 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 is less,” “better is worse,” etc.
Using order scales, you can measure qualitative indicators that do not have a strict quantitative measure. These scales are especially widely used in humanities: pedagogy, psychology, sociology.
A larger number can be applied to the ranks of the order scale mathematical operations, than to the numbers of the naming 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 ratio scale described below is that the zero point is chosen arbitrarily. Examples include 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 180°), 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. These interval scales provide an answer to the question: “how much more,” but do 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 C, 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 the experimental determination of 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); By 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 find experimentally its relation to the corresponding unit of measurement.
Units of measurement.
In order for the results of different measurements to 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 (from the initial letters of the words System International). Currently, the preferred application of this system has been established in all areas of science and technology, in the national economy, as well as in teaching.
The SI currently includes seven basic units independent from each other (see table 2.1.)
Table 1.1.
From the indicated basic units, 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) is a derivative.
In addition to the basic ones, the SI distinguishes two additional units: the radian, a unit of plane angle, and the steradian, a unit of solid angle (angle in space).
Accuracy of measurements.
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. For example, using a regular ruler with millimeter divisions, it is impossible to measure length with an accuracy of 0.01 mm.
Basic and additional error.
Basic error is the error of a measurement method or measuring instrument that occurs under normal conditions of use.
Additional error is the error of a measuring device caused by deviation of its operating conditions from normal ones. It is clear that instruments designed to operate at room temperature will not give accurate readings if used in the summer at a stadium under the scorching sun or in the winter in the cold. Measurement errors can occur when the voltage of the electrical network or battery power supply is lower than normal or is not constant in value.
Absolute and relative errors.
The value E = A--Ao, equal to the difference between the reading of the measuring device (A) and the true value of the measured quantity (Ao), is called the absolute measurement error. It is measured in the same units as the measured quantity itself.
In practice, it is often convenient to use not the absolute, but the relative error. The relative measurement error is of two types - real and reduced. The actual relative error is the ratio of the absolute error to the true value of the measured quantity:
A D =---------* 100%
The given relative error is the ratio of the absolute error to the maximum possible value of the measured quantity:
Up =----------* 100%
Systematic and random errors.
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.
The method for eliminating systematic error depends primarily on its nature. Systematic measurement errors can be divided into three groups:
errors of known origin and known magnitude;
errors of known origin but unknown magnitude;
errors of unknown origin and unknown magnitude. The most harmless are the errors of the first group. They are easily removed
by introducing appropriate corrections to the measurement result.
The second group includes, first of all, errors associated with the imperfection of the measurement method and measuring equipment. For example, the error in measuring physical performance using a mask for collecting exhaled air: the mask makes breathing difficult, and the athlete naturally demonstrates physical performance that is underestimated compared to the true one measured without a mask. The magnitude of this error cannot be predicted in advance: it depends on the individual abilities of the athlete and his state of health at the time of the study.
Another example of a systematic error in this group is an error associated with imperfect equipment, when a measuring device knowingly overestimates or underestimates the true value of the measured value, but the magnitude of the error is unknown.
Errors of the third group are the most dangerous; their occurrence is associated both with the imperfection of the measurement method and with the characteristics of the object of measurement - the athlete.
Random errors arise under the influence of various factors that cannot be predicted in advance or accurately taken into account. Random errors cannot be eliminated in principle. However, using the methods of mathematical statistics, it is possible to estimate the magnitude of the random error and take it into account when interpreting the measurement results. Without statistical processing, measurement results cannot be considered reliable.
The problem of testing human physical fitness developed in the theory and methodology of physical education, sports metrology, anthropomotorics, biomechanics, sports medicine and other sciences. Over approximately 130-140 years of the history of this problem, a huge and varied material has been accumulated, which has always aroused and continues to arouse great interest not only from scientists, but also from physical education teachers, coaches, students, and their parents.
The first article devoted to the problem under consideration is introductory. It reveals the basics of the theory of tests and testing, without familiarization with which it is difficult for a teacher to solve the problems of using tests in the practice of his work. Let us name at least some of the issues that arise. What is a "test"? What is the classification of tests? Why and is it necessary to test the physical fitness of students? How to determine the level (high, medium, low) of development of physical qualities and preparedness? What is considered the norm when testing and how to set it? If a teacher came up with a new motor test or battery of tests to determine the physical fitness of children, then what should he pay attention to or what necessary conditions (requirements, criteria) should he fulfill? Testing the physical condition of students requires mandatory familiarization of the teacher with elementary methods of mathematical statistics. Which ones?
In our articles we will also present historical information about the emergence of tests and the theory of testing human physical fitness. Let's say when and where the first tests appeared, including batteries of tests to assess physical fitness. What are the most common tests to determine the conditioning (strength, speed, endurance, flexibility) and coordination abilities of children school age? Which batteries (programs) of tests for assessing the physical fitness of children and adolescents are the most popular in different countries? We will also discuss such an important practical problem as the relationship between test results and grades (grades) in the subject “ Physical Culture" More specifically, if a student consistently shows high level, does this automatically mean an excellent grade in our subject? And so on.
In this article we will discuss: 1) testing tasks; 2) the concept of “test” and classification of motor (motor) tests; 3) criteria for the quality factor of motor tests; 4) organization of testing of physical fitness of school-age children.
1. Testing tasks. Testing human motor abilities is one of the most important areas of activity of scientists and teachers in the field of physical education and sports. It helps solve a number of complex pedagogical problems in identifying the levels of development of conditioning and coordination abilities, assessing the quality of technical and tactical readiness. Based on the test results, it is possible to compare the preparedness of both individual students and entire groups of students living in different regions and countries; carry out appropriate selection for practicing one or another sport, for participation in competitions; carry out fairly objective control over the education (training) of schoolchildren and young athletes; identify the advantages and disadvantages of the means used, teaching methods and forms of organizing classes; finally, to substantiate the norms (age-specific, individual) for the physical fitness of children and adolescents.
a) teach schoolchildren themselves to determine the level of their physical fitness and plan the necessary sets of physical exercises for themselves;
b) encourage students to further improve their physical condition
(forms);
c) know not so much the initial level of development of motor ability, but its change over a certain time;
d) stimulate students who have achieved high results, but not so much for the high level of physical fitness achieved, but for the implementation of the planned increase in personal results.
Experts emphasize that the traditional approach to testing, when data from standardized tests and standards are compared with the results shown, causes a negative attitude among many students, especially those with low and average levels of physical fitness. Testing should help increase the interest of schoolchildren, bring them joy, and not lead to the development of an inferiority complex. In this regard, we propose the following approaches:
1) the student’s test results are determined not based on comparison with standards, but on the basis of changes that have occurred over a certain period of time;
2) all components of the test are modified, lightweight versions of the exercises are used (the tasks that make up the content of the test must be easy enough so that the likelihood of their successful completion is high);
3) zero scores or those with a minus sign are excluded; only positive results are eligible.
So, when testing, it is important to bring together scientific (theoretical) tasks and personally significant, positive motives for the student to participate in this procedure.
2. The concept of “test” and classification of motor (motor) tests. The term test translated from in English means trial, test. Tests are used to solve many scientific and practical problems. Among the ways to assess a person’s physical condition (observation, expert assessments) the method of tests (in our case - motor, or motor) is the main method used in sports metrology and other scientific disciplines - “the study of movements”, the theory and methodology of physical education.
Test is a measurement or test taken to determine a person's ability or condition. There can be a lot of such measurements, including based on the use of a wide variety of physical exercises. However, not every physical exercise or test can be considered a test. Only those tests (samples) that meet special requirements and in accordance with which must be:
a) the purpose of using any test (or tests) is determined;
b) a standardized methodology for measuring test results and a testing procedure have been developed;
c) the reliability and information content of the tests was determined;
d) the ability to present test results in the appropriate assessment system has been implemented.
The system of using tests in connection with a given task, organizing conditions, performing tests by subjects, evaluating and analyzing the results is called testing. The numerical value obtained during measurements is test result.
For example, the standing long jump is a test; procedure for performing jumps and measuring results - testing; jump length - test result.
The tests used in physical education are based on motor actions (physical exercises, motor tasks). Such tests are called motor, or motor.
Currently, there is no unified classification of motor tests. There is a known classification of tests according to their structure and preferred indications (see Table 1).
Distinguish unit And complex tests. Unit test serves to measure and evaluate one trait (coordination or conditioning ability). Since the structure of each coordination or conditioning ability is complex, such a test usually evaluates only one component of this ability (for example, balance ability, simple reaction speed, arm muscle strength).
By using educational test evaluates the ability for motor learning (by the difference between the final and initial estimates for a certain period of training in movement techniques).
Test series makes it possible to use the same test for a long time, when the measured ability improves significantly. At the same time, the test tasks consistently increase in difficulty. Unfortunately, this type of single test is not yet widely used both in science and in practice.
By using complex test evaluate several signs or components of different abilities or the same ability (for example, jumping up from a place - with a wave of the arms, without a wave of the arms, to a given height). Based on such a test, you can obtain information about the level of speed-strength abilities (based on the height of the jump), coordination abilities (based on the accuracy of differentiation of power efforts, the difference in the height of the jump with and without a swing of the arms).
Test profile consists of several separate tests on the basis of which several different physical abilities are assessed (heterogeneous test profile), or multiple manifestations of the same physical ability (homogeneous test profile). Test results can be presented in the form of a profile, which makes it possible
Forms of tests and possibilities of their use (according to D.-D. Blume, 1987)
Table 1
| Type | Measurable ability | Sign of structure | Example |
| Unit test | |||
| Elementary test containing one motor task | One Test Objective, One Final Test Score | Balance test, tremometer, connection test, rhythm test, landing accuracy jump | |
| Practice test | One ability or aspect (component) of an ability | One or more test tasks. One final test score (teaching period) | General Study Test |
| Test series | One ability or aspect (component) of an ability | One test problem with options or several problems of increasing difficulty | Test for assessing the ability to connect (communication) |
| Complex test | |||
| Complex test containing one task | Multiple abilities or aspects (components) of one ability | One test task, multiple final grades | Jump test |
| Reusable task test | Multiple test tasks running sequentially, multiple final evaluations | Reusable reaction test | |
| Test profile | Multiple abilities or aspects of one ability | Multiple tests, multiple final assessments | Coordinating star |
| Test battery | Multiple abilities or aspects of one ability | Multiple tests, one test score | Test battery for assessing motor learning ability |
quickly compare individual and group results.
Test battery also consists of several separate tests, the results of which are combined into one final score, considered in one of the rating scales (more on this in the second article). As in the test profile, here we distinguish homogeneous And heterogeneous batteries.
homogeneous battery, or homogeneous profile are used in assessing all components of a complex ability (eg, responsiveness). In this case, the results of individual tests must be closely interrelated (correlated).
A heterogeneous test profile or a heterogeneous battery serves to assess a complex (set) of various motor abilities. For example, such test batteries are used to assess strength, speed and endurance abilities - these are batteries of physical fitness tests.
In tests reusable tasks subjects perform motor tasks sequentially and receive separate marks for each solution of a motor task. These assessments may be closely related to each other. Through appropriate statistical calculations, additional information about the abilities being assessed can be obtained. An example is the sequentially performed jump test tasks (Table 2).
The definition of motor tests states that they serve to assess motor abilities and partially motor skills. Therefore, in the most general form, conditioning tests, coordination tests and tests for assessing motor abilities and skills (movement techniques) are distinguished. This systematization is, however, still too general.
Classification of motor tests according to their predominant indications stems from the systematization of physical (motor) abilities. In this regard, there are conditioning tests(to assess strength: maximum, speed, strength endurance; to assess endurance; to assess speed abilities; to assess flexibility: active and passive) and coordination tests(to estimate coor
dination abilities related to individual independent groups motor actions that measure special coordination abilities; to assess specific coordination abilities - the ability to balance, spatial orientation, response, differentiation of movement parameters, rhythm, rearrangement of motor actions, coordination (communication), vestibular stability, voluntary muscle relaxation.
A large number of tests have been developed to assess motor skills in various sports. They are given in the relevant textbooks and manuals and are not discussed in this article.
Thus, each classification serves as a kind of guideline for selecting (or creating) the type of tests that best suits the testing objectives.
3. Quality criteria for motor tests. As noted above, the concept of “motor test” meets its purpose if the test satisfies the relevant basic criteria: reliability, stability, equivalence, objectivity, information content, as well as additional criteria: standardization, comparability and economy.
Tests that meet the requirements of reliability and information content are called good or authentic (reliable).
Reliability of a test refers to the degree of accuracy with which it assesses a particular motor ability, regardless of the requirements of the person assessing it. Reliability is the extent to which results are consistent when the same people are tested repeatedly under the same conditions; it is the stability or stability of an individual's test result when a test exercise is repeated. In other words, a student in a group of subjects, based on the results of repeated testing (for example, jumping indicators, running time, throwing distance), consistently retains his ranking place.
The reliability of the test is determined using correlation-statistical analysis by calculating the reliability coefficient. In this case, various methods are used to judge the reliability of the test.
The stability of the test is based on the relationship between the first and second attempts, repeated after a certain time under the same conditions by the same experimenter. The method of repeated testing to determine reliability is called retest. The stability of the test depends on the type of test, the age and gender of the subjects, and the time interval between test and retest. For example, performance on conditioning tests or morphological features at short time intervals they are more stable than the results of coordination tests; For older students, the results are more stable than for younger ones. A retest is usually carried out no later than one week later. At longer intervals (for example, after a month), the stability of even such tests as the 1000 m run or standing long jump becomes noticeably lower.
Test equivalence lies in the correlation of the test result with the results of other tests of the same type. For example, the equivalence criterion is used when it is necessary to choose which test more adequately reflects speed abilities: running 30, 50, 60 or 100 m.
This or that attitude towards equivalent (homogeneous) tests depends on many reasons. If it is necessary to increase the reliability of assessments or study conclusions, then it is advisable to use two or more equivalent tests. And if the task is to create a battery containing a minimum of tests, then only one of the equivalent tests should be used.
Table 2 Sequentially performed tasks of the jump test (according to D.-D. Blume, 1987)
| №№ | Test objective | Result evaluation | Ability |
| Jump to maximum height without swinging arms | Height, cm | Jumping force | |
| Jump to maximum height with arm swing | Height, cm | Jumping power and connection ability | |
| Jump to maximum height with arm swing and hop | Height, cm | Connectivity and jumping strength | |
| 10 jumps with arm swings at a distance equal to 2/3 of the maximum jump height, as in problem 2 | Sum of deviations from a given mark | Ability to differentiate power parameters of movements | |
| The difference between the results of solving one problem and two problems | ... cm | Ability to connect (communication) |
Such a battery, as noted, is heterogeneous, since the tests included in it measure different motor abilities. An example of a heterogeneous test battery is the 30 m run, pull-ups, bending forward, and 1000 m run. Other examples of such complexes will be presented in a separate publication.
The reliability of tests is also determined by comparing the average scores of even and odd attempts included in the test. For example, the average accuracy of throwing a ball at a target from 1, 3, 5, 7 and 9 attempts is compared with the average accuracy of throws from 2, 4, 6, 8 and 10 attempts. This method of assessing reliability is called the doubling method, or splitting, and it is used primarily when assessing coordination abilities and in the event that the number of attempts that form the test result is at least six.
Under objectivity(consistency) of a test refers to the degree of consistency of results obtained on the same subjects by different experimenters (teachers, judges, experts).
a) testing time, place, weather conditions;
b) unified material and hardware support;
c) psychophysiological factors (volume and intensity of load, motivation);
d) presentation of information (precise verbal statement of the test task, explanation and demonstration).
Compliance with these conditions creates the so-called objectivity of the test. They also talk about interpretive objectivity, concerning the degree of independence of interpretation of test results by different experimenters.
In general, as experts note, the reliability of tests can be increased in various ways: more stringent standardization of testing (see above), increasing the number of attempts, the best motivation subjects, an increase in the number of evaluators (judges, experts), an increase in the consistency of their opinions, and an increase in the number of equivalent tests.
There are no fixed values for test reliability indicators. In most cases, the following recommendations are used: 0.95-0.99 - excellent reliability; 0.90-0.94 - good; 0.80-0.89 - acceptable; 0.70-0.79 - bad; 0.60-0.69 - doubtful for individual assessments, the test is only suitable for characterizing a group of subjects. Information content of a test is the degree of accuracy with which it measures the motor ability or skill being assessed. In foreign and domestic literature, instead of the word “informativeness,” the term “validity” is used (from the English validity - validity, reality, legality). In fact, in relation to information content, the researcher answers two questions: what does this particular test (battery of tests) measure and what is the degree of measurement accuracy.
Distinguish validity logical (substantive), empirical (based on experimental data) and predictive. More detailed information on this topic is contained in the now classic textbooks for students of physical education universities (Sports Metrology / Edited by V.M. Zatsiorsky. - M.: FiS, 1982. - P. 73-80; Godik M.A. Sports metrology. - M.: FiS, 1988), as well as in a number of modern manuals.
Important additional test criteria, as noted, are standardization, comparability and efficiency.
The essence rationing is that, based on the test results, it is possible to create standards that are of particular importance for practice (this will be discussed in a separate article).
Comparability test is the ability to compare results obtained from one test or several forms of parallel (homogeneous) tests. In practical terms, the use of comparable motor tests reduces the likelihood that, as a result of regular use of the same test, the degree of skill is assessed not only and not so much as the level of ability. At the same time, comparable test results increase the reliability of the conclusions.
The essence efficiency as a criterion for the quality of the test is that conducting the test does not require a long time, large material costs and the participation of many assistants. For example, a battery of six tests to determine physical fitness, recommended in the “Comprehensive program of physical education for students in grades I-XI” (M.: Prosveshcheniye, 2005-2006), can be carried out by a teacher with two assistants in one lesson, examining 25-30 children .
Organization of testing of physical fitness of school-age children. The second important problem of testing motor abilities (recall that the first - the selection of informative tests - was discussed earlier) is the organization of their use.
The physical education teacher must determine when it is best to organize testing, how to carry it out in the classroom, and how often testing should be carried out.
Save testing are established in accordance with the school curriculum, which provides for mandatory testing of students’ physical fitness twice a day. It is advisable to carry out the first testing in the second or third week of September (after educational process will return to normal), and the second - two weeks before the end of the school year (at a later date there may be organizational difficulties caused by upcoming exams and holidays).
Knowledge of annual changes in the development of motor abilities of schoolchildren allows the teacher to make appropriate adjustments to the process of physical education for the next academic year. However, the teacher can and should conduct more frequent testing and exercise so-called operational control. This procedure it is advisable to perform, for example, in order to determine changes in the level of speed, strength abilities and endurance under the influence of athletics lessons during the first quarter, etc. For this purpose, the teacher can use tests to assess the coordination abilities of children at the beginning and at the end of mastering educational material school curriculum, for example, in sports games, to identify changes in the development indicators of these abilities.
It should be taken into account that the variety of pedagogical problems being solved does not make it possible to provide the teacher with a unified testing methodology, the same rules for conducting tests and evaluating test results. This requires experimenters (teachers) to demonstrate independence in solving theoretical, methodological and organizational testing issues.
Testing in class must be linked to its content. In other words, the test (or tests) used, subject to the appropriate requirements for it as a research method, should (should) be organically included in the planned physical exercises. If, for example, schoolchildren need to determine the level of development of speed abilities or endurance, then the necessary tests should be scheduled in that part of the lesson in which the tasks of developing the corresponding physical abilities will be solved.
Test frequency is largely determined by the pace of development of specific physical abilities, age, gender and individual characteristics their development.
For example, to achieve a significant increase in speed, endurance or strength, several months of regular exercise (training) are required. At the same time, to obtain a significant increase in flexibility or individual coordination abilities, only 4-12 workouts are required. If you start from scratch, you can achieve improvement in one or another physical quality in a shorter period of time. But to improve the same quality, when it reaches a high level in a student, it takes more time. In this regard, the teacher must study more deeply the features of the development and improvement of various motor abilities in children at different age and gender periods.
When assessing the general physical fitness of students, as noted, you can use a wide variety of test batteries, the choice of which depends on the specific testing objectives and the availability of necessary conditions. However, due to the fact that the test results obtained can only be assessed by comparison, it is advisable to choose tests that are widely represented in the theory and practice of physical education of children. For example, rely on those recommended in the “Comprehensive program of physical education for students in grades I-XI of a comprehensive school” (M.: Prosveshcheniye, 2004-2006).
To compare the general level of physical fitness of a student or group of students using a set of tests, they resort to converting test results into points or scores (we’ll talk about this in more detail in the next article). The change in the amount of points during repeated testing makes it possible to judge the progress of both an individual child and a group of children.
Physical education at school, 2007, No. 6
Introduction
Relevance. The problem of testing a person's physical fitness is one of the most developed in the theory and methodology of physical education. Over the past decades, a huge and varied amount of material has been accumulated: defining testing tasks; conditionality of test results by various factors; development of tests to assess individual conditioning and coordination abilities; test programs characterizing the physical fitness of children and adolescents from 11 to 15 years old, adopted in Russian Federation, in other CIS countries and in many foreign countries.
Testing the motor qualities of schoolchildren is one of the most important and basic methods of pedagogical control.
It helps solve a number of complex pedagogical problems: identify levels of development of conditioning and coordination abilities, assess the quality of technical and tactical readiness. Based on the test results you can:
compare the preparedness of both individual students and entire groups living in different regions and countries;
conduct sports selection for practicing one or another sport, for participation in competitions;
carry out in to a large extent objective control over the education (training) of schoolchildren and young athletes;
identify the advantages and disadvantages of the means used, teaching methods and forms of organizing classes;
finally, to substantiate the norms (age-specific, individual) for the physical fitness of children and adolescents.
Along with scientific tasks in practice in different countries, testing tasks boil down to the following:
teach schoolchildren themselves to determine the level of their physical fitness and plan the necessary sets of physical exercises for themselves;
encourage students to further improve their physical condition (shape);
to know not so much the initial level of development of motor ability, but its change over a certain time;
encourage students who have achieved high results, but not so much for a high level, but for the planned increase in personal results.
In this work we will rely on those tests that are recommended in the “Comprehensive program of physical education for students in grades 1–11 of a comprehensive school” prepared by V.I. Lyakh and G.B. Maxson.
Purpose of the study: to substantiate the methodology for testing the physical qualities of primary school students.
Research hypothesis: the use of testing is an accurate, informative method for determining the development of physical qualities.
Object of study: testing as a method of pedagogical control.
Subject of research: testing the qualities of students.
Chapter 1. VIEWS ABOUT THE THEORY OF PHYSICAL FITNESS TESTS
1.1 Brief historical information about the theory of testing motor abilities
People have been interested in measuring human motor achievements for a long time. The first information about measuring the distance over which long jumps were made dates back to 664 BC. e. On XXIX Olympic Games in ancient times at Olympia, Chionis from Sparta jumped a distance of 52 feet, which is approximately 16.66 m. It is clear that here we're talking about about jumping repeatedly.
It is known that one of the founders of physical education, J. Ch. F. Guts-Muts, 1759-1839, measured the motor achievements of his students and made accurate records of their results. And for improving their achievements, he awarded them “prizes” - oak wreaths (G. Sorm, 1977). In the thirties of the XIX century. Eiselen, an employee of the famous German teacher F. L. Yahn, based on the measurements taken, compiled a table for determining achievements in jumping. As you can see, it contains three gradations (Table 1).
Table 1. - Results in jumps (in cm) for men (source: K. Mekota, P. Blahus, 1983)
elementary
Through the goat
Note that already in the middle of the 19th century. in Germany, when determining the length or height of a jump, it was recommended to take into account body parameters.
Accurate measurements of sporting achievements, including record ones, are carried out with mid-19th century, and regularly since 1896, since the Olympic Games of our time.
For quite a long time people have been trying to measure strength abilities. The first interesting information on this matter dates back to 1741, when, using simple instruments, it was possible to measure the strength of the wrestler Thomas Topham. He lifted a weight whose mass exceeded 830 kg (G. Sorm, 1977). The strength capabilities of the students were already measured by Guts-Muts and Jan, using simple strength meters. But the first dynamometer, the progenitor of the modern dynamometer, was designed by Reiniger in France in 1807. In the practice of physical education of gymnasium students in Paris, it was used by F. Amoros in 1821. In the 19th century. To measure strength, we also used lifting the body while hanging on a bar, bending and straightening the arms in support, and lifting weights.
The forerunners of modern batteries of tests to determine physical fitness are sports and gymnastic all-around events. The first is the ancient pentathlon, introduced into practice at the XVIII Olympic Games of antiquity in 708 BC. e. It included discus throwing, javelin throwing, jumping, running and wrestling. The decathlon as we know it was first included in the competition program at the III Olympic Games (St. Louis, USA, 1904), and the modern pentathlon at the V Olympic Games (Stockholm, Sweden, 1912). The composition of exercises in these competitions is heterogeneous; the athlete needs to demonstrate preparedness in different disciplines. So, he must be physically versatile.
Probably, taking this idea into account, around the same time (beginning of the 20th century), sets of exercises were introduced into practice for children, youth and adults, which comprehensively determined a person’s physical fitness. For the first time, such complex tests were introduced in Sweden (1906), then in Germany (1913) and even later - in Austria and the USSR (Russia) - the “Ready for Labor and Defense” complex (1931).
The predecessors of modern motor tests arose in late XIX- beginning of the 20th century In particular, D. A. Sargent introduced the “strength test” into practice at Harvard University, which, in addition to dynamometry and spirometry, included pushing up the arms, raising and lowering the body. Since 1890, this test has been used in 15 US universities. The Frenchman G. Hebert created a test, the publication of which appeared in 1911. It includes 12 motor tasks: running at different distances, standing and running jump, throw, repeated lifting of a 40-kilogram projectile (weight ), swimming and diving.
Let us briefly look at the sources of information that discuss the results scientific research doctors and psychologists. Research by doctors until the end of the 19th century. were most often focused on changing external morphological data, as well as identifying asymmetry. Anthropometry used for these purposes kept pace with the use of dynamometry. Thus, the Belgian doctor A. Quetelet, having conducted extensive research, published a work in 1838, according to which the average results of the backbone (spine) of 25-year-old women and men are 53 and 82 kg, respectively. In 1884, the Italian A. Mosso studied muscle endurance. To do this, he used an ergograph, which allowed him to observe the development of fatigue with repeated bending of the finger.
Modern ergometry dates back to 1707. At that time, a device was created that made it possible to measure pulse per minute. The prototype of today's ergometer was designed by G. A. Him in 1858. Cycloergometers and treadmills were created later, in 1889-1913.
At the end of the 19th - beginning of the 20th centuries. Systematic research by psychologists begins. Reaction time is being studied, and tests are being developed to determine motor coordination and rhythm. The concept of “reaction time” was introduced into science by the Austrian physiologist S. Exner in 1873. Students of the founder of experimental psychology W. Wundt in the laboratory created in 1879 in Leipzig carried out extensive measurements of idle time and complex reactions. The first tests of motor coordination included tapping and different types aiming. One of the first attempts to study aiming is the test of X. Frenkel, proposed by him in 1900. Its essence was to hold forefinger in all kinds of holes, rings, etc. This is a prototype of modern tests “for static and dynamic tremor.”
Trying to determine musical talent, in 1915, S. E. Seashore investigated the ability to rhythm.
The theory of testing dates back, however, to the end of the 19th and beginning of the 20th centuries. It was then that the foundations of mathematical statistics were laid, without which modern test theory cannot do. On this path, undoubted merits belong to the geneticist and anthropologist F. Galton, the mathematicians Pearson and U. Youle, and the mathematician-psychologist S. Spearman. It was these scientists who created a new branch of biology - biometrics, which is based on measurements and statistical methods, such as correlation, regression, etc. Created by Pearson (1901) and Spearman (1904), a complex mathematical-static method - factor analysis - allowed English scientist Bart (S. Burt) applied it in 1925 to the analysis of the results of motor tests of students in London schools. As a result, physical abilities such as strength, speed, agility and endurance were identified. A factor called “general physical fitness” also stood out. Somewhat later, one of the most famous works American scientist McCloy (S.N. McCloy, 1934) - “Measurement of general motor abilities.” By the beginning of the 40s. scientists come to the conclusion about the complex structure of human motor abilities. Using various motor tests in combination with the use of parallel developed mathematical models (single- and multivariate analysis), the testing theory has firmly incorporated the concepts of five motor abilities: strength, speed, motor coordination, endurance and flexibility.
Motor tests in former USSR were used to develop control standards for the “Ready for Labor and Defense” complex (1931). There is a well-known test of motor abilities (mainly coordination of movements), which was proposed for children and youth by N. I. Ozeretsky (1923). Work on measuring the motor abilities of children and youth appeared around the same time in Germany, Poland, Czechoslovakia and other countries.
Significant advances in the development of the theory of testing human physical fitness occurred in the late 50s and 60s. XX century The founder of this theory is most likely the American McCloy, who co-authored with M. D. Young in 1954 published the monograph “Tests and Measurement in Health Care and Physical Education,” which was subsequently relied upon by many authors of similar works .
The book “Structure and Measurement of Physical Abilities” by the famous American researcher E.A. was and still is of great theoretical importance. Fleishman (1964). The book not only reflects the theoretical and methodological issues of the problem of testing these abilities, but also outlines specific results, options for approaches, studies of reliability, informativeness (validity) of tests, and also presents important factual material according to the factor structure of motor tests of various motor abilities.
Great importance for the theory of testing physical abilities there are books by V.M. Zatsiorsky “Physical Qualities of an Athlete” (1966) and “Cybernetics, Mathematics, Sports” (1969).
Brief historical information on physical fitness testing in the former USSR can be found in the publications of E.Ya. Bondarevsky, V.V. Kudryavtsev, Yu.I. Sbrueva, V.G. Panaeva, B.G. Fadeeva, P.A. Vinogradova and others.
Conventionally, three stages of testing in the USSR (Russia) can be distinguished:
Stage 1 - 1920-1940 - a period of mass examinations in order to study the main indicators of physical development and the level of motor readiness, the emergence on this basis of the standards of the “Ready for Labor and Defense” complex.
Stage 2 -- 1946-1960 -- study of motor readiness depending on morphofunctional characteristics in order to create the prerequisites for a scientific and theoretical substantiation of their relationship.
Stage 3 - from 1961 to the present - a period of comprehensive studies of the physical condition of the population depending on the climatic and geographical characteristics of the country's regions.
Research carried out during this period shows that the indicators of physical development and motor fitness of people living in different regions of the country are determined by the influence of biological, climatic-geographical, socio-economic and other both constant and variable factors. According to the developed unified comprehensive program, consisting of four sections (physical fitness, physical development, functional state of the main body systems, sociological information), a comprehensive survey of the physical condition of the population was carried out in 1981 of different ages and gender of various regions of the USSR.
Somewhat later, our experts noted that the level of physical development and preparedness of a person has been studied for more than 100 years. However, despite the relatively large number of works in this direction, it is not possible to conduct a deep and comprehensive analysis of the data obtained, since the studies were carried out with different contingents, during different seasonal periods, using different methods, testing programs and mathematical and statistical processing of the information received .
In this regard, the main emphasis was placed on developing a methodology and organizing a unified data collection system, taking into account metrological and methodological requirements and creating a data bank on a computer.
In the mid-80s. last century, a massive all-Union survey was conducted of about 200,000 people from 6 to 60 years old, which confirmed the conclusions of the previous study.
From the very beginning of the emergence of scientific approaches to testing human physical fitness, researchers have sought to obtain answers to two main questions:
what tests should be selected to assess the level of development of a specific motor (physical) ability and the level of physical fitness of children, adolescents and adults;
How many tests are needed to obtain minimal and at the same time sufficient information about a person’s physical condition?
There are no common ideas in the world on these issues yet. At the same time, ideas about test programs (batteries) characterizing the physical fitness of children and adolescents from 6 to 17 years old, adopted in different countries, are becoming increasingly closer.
1.2 The concept of “test” and classification of motor (motor) tests
The term test translated from English means “sample, test.”
Tests are used to solve many scientific and practical problems. Among other methods of assessing a person’s physical condition (observation, expert assessments), the test method (in our case, motor or motor) is the main method used in sports metrology and other scientific disciplines (“the study of movements,” theory and methods of physical education) .
A test is a measurement or test taken to determine a person's ability or condition. There can be a lot of such measurements, including based on the use of a wide variety of physical exercises. However, not every physical exercise or test can be considered a test. Only those tests (samples) that meet special requirements can be used as tests:
the purpose of any test (or tests) must be defined;
A standardized test measurement methodology and testing procedure should be developed;
it is necessary to determine the reliability and information content of the tests;
test results can be presented in the appropriate evaluation system.
The system of using tests in accordance with the task, organization of conditions, performance of tests by subjects, evaluation and analysis of results is called testing, and the numerical value obtained during measurements is the result of testing (test). For example, the standing long jump is a test; jumping procedure and measurement of results - testing; jump length is the test result.
The tests used in physical education are based on motor actions (physical exercises, motor tasks). Such tests are called movement or motor tests.
Currently, there is no unified classification of motor tests. There is a known classification of tests according to their structure and their primary indications (Table 2).
As follows from the table, a distinction is made between single and complex tests. A single test is used to measure and evaluate one trait (coordination or conditioning ability). Since, as we see, the structure of each coordination or conditioning ability is complex, such a test, as a rule, evaluates only one component of such an ability (for example, the ability to balance, the speed of a simple reaction, the strength of the arm muscles).
Table 2. - Forms of tests and possibilities of their use (according to D.D. Blume, 1987)
Measurable ability
Sign of structure
Unit test
Elementary test containing one motor task
One ability or aspect (component) of an ability
One Test Objective, One Final Test Score
Balance test, tremometry, connectivity test, rhythm test
Practice test
One or more test tasks. One final test score
General Study Test
Test series
One test task with options or several tasks of increased difficulty
Test for assessing the ability to connect (communication)
Complex test
Complex test containing one task
Multiple abilities or aspects (components) of one ability
One test task, multiple final grades
Jump test
Reusable task test
Multiple test tasks running sequentially, multiple final evaluations
Reusable reaction test
Test profile
Multiple tests, multiple final assessments
Coordination task
Test battery
Multiple tests, one test score
Test battery for assessing movement learning ability
Using a training test, the ability for motor learning is assessed (based on the difference between the final and initial scores for a certain period of training in movement techniques).
A test series makes it possible to use the same test over a long period of time, when the ability to be measured improves significantly. At the same time, the test tasks consistently increase in difficulty. Unfortunately, this type of test is not yet sufficiently used both in science and in practice.
Using a complex test, several signs or components of different or the same ability are assessed, for example, jumping up from a place (with a wave of the arms, without a wave of the arms, to a given height). Based on this test, you can obtain information about the level of speed-strength abilities (based on the height of the jump), coordination abilities (based on the accuracy of differentiation of power efforts, the difference in the height of the jump with and without a swing of the arms).
A test profile consists of individual tests that assess either several different physical abilities (heterogeneous test profile) or different manifestations of the same physical ability (homogeneous test profile). Test results can be presented in profile form, allowing comparison of individual and group results.
The test battery also consists of several individual tests, the results of which are combined into one final score, considered in one of the rating scales (see Chapter 2). As in the test profile, a distinction is made between homogeneous and heterogeneous batteries. The homogeneous battery, or homogeneous profile, finds application in assessing all components of a complex ability (eg, reaction ability). In this case, the results of individual tests must be closely interrelated (must correlate).
In tests of multiple tasks, subjects perform motor tasks sequentially and receive separate marks for each solution of a motor task. These assessments may be closely related to each other. Through appropriate statistical calculations one can obtain Additional information about the abilities being assessed. An example is the sequentially solved jump test tasks (Table 3).
Table 3. - Sequentially solved jump test tasks
Test objective
Result evaluation
Ability
Maximum jump without swinging arms
Jumping force
Maximum jump up with arm swing
Jumping power and connection ability
Maximum jump up with a wave of arms and a jump
Connectivity and jumping strength
10 jumps with arm swings at a distance equal to 2/3 of the maximum jump height, as in problem 2
Sum of deviations from a given mark
Ability to differentiate power parameters of movements
The difference between the results for solving one problem and two problems
Ability to connect (communication)
(according to D.D. Blume, 1987)
The definition of motor tests states that they assess motor abilities and partly motor skills. In the most general form, there are conditioning tests, coordination tests and tests for assessing motor abilities and skills (movement techniques). This systematization is, however, still too general. The classification of motor tests according to their primary indications follows from the systematization of physical (motor) abilities.
In this regard, there are:
1) condition tests:
to assess strength: maximum, speed, strength endurance;
to assess endurance;
to assess speed abilities;
to assess flexibility - active and passive;
2) coordination tests:
to assess coordination abilities related to individual independent groups of motor actions that measure special coordination abilities;
to assess specific coordination abilities - abilities for balance, orientation in space, response, differentiation of movement parameters, rhythm, restructuring of motor actions, coordination (communication),
vestibular stability, voluntary muscle relaxation.
The concept of “tests for assessing motor skills” in this work are not considered. Examples of tests are given in Appendix 2.
Thus, each classification is a kind of guidelines for selecting (or creating) the type of tests that are more consistent with testing tasks.
1.3 Quality criteria for motor tests
The concept of “motor test” serves its purpose when the test satisfies the relevant requirements.
Tests that meet the requirements of reliability and information content are called good or authentic (reliable).
Reliability of a test refers to the degree of accuracy with which it assesses a specific motor ability, regardless of the requirements of the person assessing it. Reliability is the extent to which results are consistent when the same people are tested repeatedly under the same conditions; is the stability or stability of an individual's test result when re-execution control exercise. In other words, a child in a group of subjects, based on the results of repeated testing (for example, jumping performance, running time, throwing distance), consistently retains its ranking place.
The reliability of the test is determined using correlation-statistical analysis by calculating the reliability coefficient. In this case, various methods are used to judge the reliability of the test.
The stability of the test is based on the relationship between the first and second attempts, repeated after a certain time under the same conditions by the same experimenter. The method of repeated testing to determine reliability is called retest. The stability of the test depends on the type of test, the age and gender of the subjects, and the time interval between test and retest. For example, performance on conditioning tests or morphological traits over short time intervals is more stable than performance on coordination tests; Older children have more stable results than younger ones. A retest is usually carried out no later than a week later. At longer intervals (for example, after a month), the stability of even such tests as the 1000 m run or standing long jump becomes noticeably lower.
Test equivalence lies in the correlation of the test result with the results of other tests of the same type (for example, when it is necessary to choose which test more adequately reflects speed abilities: running 30, 50, 60 or 100 m).
The attitude towards equivalent (homogeneous) tests depends on many reasons. If it is necessary to increase the reliability of assessments or research conclusions, then it is advisable to use two or more equivalent tests. And if the task is to create a battery containing a minimum of tests, only one of the equivalent tests should be used. Such a battery, as noted, is heterogeneous, since the tests included in it measure different motor abilities. An example of a heterogeneous battery of tests is the 30 m run, pull-up, forward bend, and 1000 m run.
The reliability of tests is also determined by comparing the average scores of even and odd attempts included in the test. For example, the average accuracy of shots on target from 1, 3, 5, 7 and 9 attempts is compared with the average accuracy of shots from 2, 4, 6, 8 and 10 attempts. This method of assessing reliability is called the doubling or splitting method. It is used primarily when assessing coordination abilities and in the event that the number of attempts that form the test result is at least 6.
The objectivity (consistency) of a test is understood as the degree of consistency of results obtained on the same subjects by different experimenters (teachers, judges, experts).
To increase the objectivity of testing, it is necessary to comply with standard test conditions:
testing time, location, weather conditions;
unified material and hardware support;
psychophysiological factors (volume and intensity of load, motivation);
presentation of information (precise verbal statement of the test task, explanation and demonstration).
This is the so-called objectivity of the test. They also talk about interpretive objectivity, which concerns the degree of independence in the interpretation of test results by different experimenters.
In general, as experts note, the reliability of tests can be increased in various ways: more stringent standardization of testing (see above), an increase in the number of attempts, better motivation of subjects, an increase in the number of evaluators (judges, experts), an increase in the consistency of their opinions, an increase in the number of equivalent tests .
There are no fixed values for test reliability indicators. In most cases, the following recommendations are used: 0.95--0.99 - excellent reliability; 0.90--0.94 - good; 0.80--0.89 - acceptable; 0.70--0.79 - bad; 0.60-- 0.69 - doubtful for individual assessments, the test is only suitable for characterizing a group of subjects.
The validity of a test is the degree of accuracy with which it measures the motor ability or skill being assessed. In foreign (and domestic) literature, instead of the word “informativeness”, the term “validity” is used (from the English validity - validity, reality, legality). In fact, when talking about information content, the researcher answers two questions: what does this particular test (battery of tests) measure and what is the degree of accuracy of the measurement?
There are several types of validity: logical (substantive), empirical (based on experimental data) and predictive (2)
Important additional test criteria are standardization, comparability and efficiency.
The essence of standardization is that, based on test results, it is possible to create standards that are of particular importance for practice.
Test comparability is the ability to compare results obtained from one or more forms of parallel (homogeneous) tests. In practical terms, the use of comparable motor tests reduces the likelihood that, as a result of regular use of the same test, the degree of skill is assessed not only and not so much as the level of ability. At the same time, comparable test results increase the reliability of the conclusions.
The essence of economy as a criterion for the quality of a test is that conducting the test does not require a long time, large material costs and the participation of many assistants.
Conclusion
The predecessors of modern motor tests arose in the late 19th and early 20th centuries. Since 1920, mass examinations have been carried out in our country to study the main indicators of physical development and the level of motor readiness. Based on this data, the standards of the “Ready for Labor and Defense” complex were developed.
The testing theory has firmly incorporated the concepts of five motor abilities: strength, speed, coordination, endurance and flexibility. A number of different test batteries have been developed to evaluate them.
Among the methods of assessing a person’s physical condition, the test method is the main one. There are single and complex tests. Also, in connection with the systematization of physical (motor) abilities, tests are classified into conditioning and coordination.
All tests must meet specific requirements. The main criteria include: reliability, stability, equivalence, objectivity, information content (validity). Additional criteria include: standardization, comparability and efficiency.
Therefore, when choosing certain tests, all these requirements must be met. To increase the objectivity of tests, one should adhere to more stringent standardization of testing, an increase in the number of attempts, better motivation of subjects, an increase in the number of evaluators (judges, experts), an increase in the consistency of their opinions, and an increase in the number of equivalent tests.
Chapter 2. Objectives, methods and organization of the study
2.1 Research objectives:
1. Learn about the theory of data testing literary sources;
2. Analyze the methodology for testing physical qualities;
3. Compare the indicators of motor readiness of students in grades 7a and 7b.
2.2 Research methods:
1. Analysis and synthesis of literary sources.
Carried out throughout the study. Solving these problems at a theoretical level is carried out by studying literature on: theory and methodology of physical education and sports, education of physical qualities, sports metrology. 20 literary sources were analyzed.
2. Verbal influence.
Instructions were provided on the sequence of performing motor tests and a motivational conversation to set the mood for achieving a better result.
3. Testing physical qualities.
30 meter run (from a high start),
shuttle run 3 x 10 meters,
standing long jump,
6 minute run (m),
forward bend from a sitting position (cm),
pull-ups on the bar (girls on low).
4. Methods of mathematical statistics.
Used to carry out calculations that were used in comparative analysis students of grades 7a and 7b.
2.3 Organization of the study
At the first stage, in April 2009, an analysis of scientific and methodological literature was carried out:
· studying the content of physical education programs for general education students
CHAPTER 3. STATISTICAL PROCESSING OF TESTING RESULTS
Statistical processing of test results allows, on the one hand, to objectively determine the results of the subjects, on the other hand, to assess the quality of the test itself, test tasks, in particular, to assess its reliability. The problem of reliability has received a lot of attention in classical test theory. This theory has not lost its relevance today. Despite the appearance, more modern theories, the classical theory continues to maintain its position.
3.1. BASIC PROVISIONS OF CLASSICAL TEST THEORY
3.2. TEST RESULTS MATRIX
3.3. GRAPHICAL REPRESENTATION OF TEST SCORE
3.4. MEASURES OF CENTRAL TENDENCY
3.5. NORMAL DISTRIBUTION
3.6. VARIATION OF TEST SCORES OF SUBJECTS
3.7. CORRELATION MATRIX
3.8. TEST RELIABILITY
3.9. TEST VALIDITY
LITERATURE
BASIC PROVISIONS OF CLASSICAL TEST THEORY
The creator of the Classical Theory of mental tests is the famous British psychologist, author of factor analysis, Charles Edward Spearman (1863-1945) 1. He was born on September 10, 1863, and served in the British Army for a quarter of his life. For this reason, he received his PhD degree only at the age of 41 2. Charles Spearman carried out his dissertation research at the Leipzig Laboratory of Experimental Psychology under the direction of Wilhelm Wundt. At that time, Charles Spearman was strongly influenced by the work of Francis Galton on testing human intelligence. Charles Spearman's students were R. Cattell and D. Wechsler. Among his followers are A. Anastasi, J. P. Guilford, P. Vernon, C. Burt, A. Jensen.
Huge contribution Lewis Guttman (1916-1987) contributed to the development of classical test theory 3.
The classical test theory was first presented comprehensively and completely in the fundamental work of Harold Gulliksen (Gulliksen H., 1950) 4 . Since then, the theory has been somewhat modified, in particular, the mathematical apparatus has been improved. Classical test theory in a modern presentation is given in the book Crocker L., Aligna J. (1986) 5. Among domestic researchers, V. Avanesov (1989) 6 was the first to describe this theory. In the work of Chelyshkova M.B. (2002) 7 provides information on the statistical justification of the quality of the test.
Classical test theory is based on the following five basic principles.
1. The empirically obtained measurement result (X) is the sum of the true measurement result (T) and the measurement error (E) 8:
X = T + E (3.1.1)
The values of T and E are usually unknown.
2. The true measurement result can be expressed as expected value E(X):
3. The correlation of true and false components across the set of subjects is zero, that is, ρ TE = 0.
4. The erroneous components of any two tests do not correlate:
5. The erroneous components of one test do not correlate with the true components of any other test:
In addition, the basis of classical test theory is formed by two definitions - parallel and equivalent tests.
PARALLEL tests must meet the requirements (1-5), the true components of one test (T 1) must be equal to the true components of the other test (T 2) in each sample of subjects answering both tests. It is assumed that T 1 =T 2 and, in addition, are equal to the variance s 1 2 = s 2 2.
Equivalent tests must meet all the requirements of parallel tests with one exception: the true components of one test do not have to be equal to the true components of another parallel test, but they must differ by the same constant With.
The condition for the equivalence of two tests is written as follows:
where c 12 is the constant between the results of the first and second tests.
Based on the above provisions, a theory of test reliability has been constructed 9,10.
that is, the variance of the resulting test scores is equal to the sum of the variances of the true and error components.
Let's rewrite this expression as follows:
(3.1.3)
The right side of this equality represents the reliability of the test ( r). Thus, the reliability of the test can be written as:
Based on this formula, various expressions were subsequently proposed for finding the test reliability coefficient. The reliability of the test is its most important characteristic. If reliability is unknown, test results cannot be interpreted. The reliability of a test characterizes its accuracy as a measuring instrument. High reliability means high repeatability of test results under the same conditions.
In classical test theory, the most important problem is determining the true test score of the subject (T). The empirical test score (X) depends on many conditions - the level of difficulty of the tasks, the level of preparedness of the test takers, the number of tasks, testing conditions, etc. In a group of strong, well-prepared subjects, test results will usually be better. than in a group of poorly trained subjects. In this regard, the question remains open about the magnitude of the measure of difficulty of tasks on population subjects. The problem is that real empirical data are obtained from completely random samples of subjects. As a rule, these are study groups that represent a multitude of students who interact quite strongly with each other in the learning process and study in conditions that are often not repeated for other groups.
We'll find s E from equation (3.1.4)
Here the dependence of the measurement accuracy on the standard deviation is explicitly shown s X and on the reliability of the test r.
Send your good work in the knowledge base is simple. Use the form below
Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.
Posted on http://www.allbest.ru/
1. BASIC CONCEPTS
A test is a measurement or test conducted to determine the condition or ability of an athlete. The testing process is called testing: the resulting numerical value is the result of testing (or test result). For example, the 100m run is a test, the procedure for conducting races and timing is testing, the running time is the test result.
Tests based on motor tasks are called motor (or motor) tests. In these tests, the results can be either motor achievements (time to complete the distance, number of repetitions, distance traveled, etc.), or physiological and biochemical indicators. Depending on this, as well as on the task facing the subject, three groups of motor tests are distinguished (Table A).
Table A. Types of motor tests.
|
Test name |
Task for the athlete |
Test results |
||
|
Test exercises |
Motor achievement |
1500m run, running time |
||
|
Standard functional tests |
The same for everyone, dosed either: a) according to the amount of work performed, or: b) according to the magnitude of physiological changes |
Physiological or biochemical indicators during standard work Motor indicators during a standard amount of physiological changes |
Registration of heart rate during standard work 1000 km/min Running speed at heart rate 160 beats/min, PVC sample (170) |
|
|
Maximum functional tests |
Show maximum result |
Physiological or biochemical indicators |
Determination of maximum oxygen debt or maximum oxygen consumption |
Sometimes not one, but several tests are used that have a single final goal (for example, assessing the athlete’s condition during the competitive training period). Such a group is called a complex or battery of tests. Not all measurements can be used as tests. To do this, they must meet special requirements. These include: 1) test reliability; 2) information content of the test; 3) the presence of a rating system (see the next chapter); 4) standardization - the testing procedure and conditions must be the same in all cases of application of the test. Tests that meet the requirements of reliability and information content are called good or authentic tests.
2. TEST RELIABILITY
2.1 Concept of test reliability
physical treadmill testing
Test reliability is the degree to which results agree when repeated testing of the same people (or other objects) under the same conditions. Ideally, the same test administered to the same subjects under the same conditions should produce the same results. However, even with the most stringent standardization of testing and precise equipment, test results always vary somewhat. For example, an athlete who has just bench-pressed 55 kg on a wrist dynamometer will only show 50 kg in a few minutes. Such variation is called intra-individual or (using the more general terminology of mathematical statistics) intra-class variation. It is caused by four main reasons:
change in the state of the subjects (fatigue, training, learning, change in motivation, concentration, etc.);
uncontrolled changes in external conditions and equipment (temperature and humidity, power supply voltage, presence of unauthorized persons, wind, etc.);
change in the state of the person conducting or evaluating the test, replacement of one experimenter or judge with another;
imperfection of the test (there are tests that are obviously unreliable, for example, free throws into a basketball basket before the first miss; even an athlete with a high percentage of hits can accidentally make a mistake on the first throws).
The following simplified example will help understand the idea of the methods used to judge the reliability of tests. Let's assume that they want to compare the standing long jump results of two athletes based on two attempts performed. If you want to draw accurate conclusions, you cannot limit yourself to recording only the best results. Let us assume that the results of each of the athletes vary within ± 10 cm from the average value and are equal to 220 ± 10 cm (i.e. 210 and 230 cm) and 320 ± 10 cm (i.e. 310 and 330 cm), respectively. In this case, the conclusion, of course, will be completely unambiguous: the second athlete is superior to the first. The difference between the results (320 cm - 220 cm = 100 cm) is clearly greater than random fluctuations (±10 cm). It will be much less certain
Rice. 1. The ratio of inter- and intraclass variation with high (top) and low (bottom) reliability.
Short vertical strokes - data from individual attempts, X and A" 2, X 3 - average results of three subjects
conclusion if, for the same intraclass variation (equal to ±10 cm), the difference between subjects (interclass variation) will be small. Let's say the average values will be 220 cm (in one attempt 210 cm, in another 230 cm) and 222 (212 and 232 cm). Then it may happen, for example, that in the first attempt the first athlete jumps 230 cm, and the second only 212, and the impression will be created that the first is significantly stronger than the second.
The example shows that the main significance is not intraclass variability itself, but its relationship with interclass differences. The same intraclass variation gives different reliability with different differences between classes (in the particular case of subjects, Fig. 1).
The theory of test reliability is based on the fact that the result of any measurement carried out on a person - X ( - is the sum of two quantities:
X^Hoo + Heh, (1)
where X x is the so-called true result that they want to record;
X e - an error caused by an uncontrolled variation in the state of the subject, introduced by a measuring device, etc.
By definition, the true result is understood as the average value of X^ for an infinitely large number of observations under identical conditions (that’s why the infinity sign oo is put at X).
If the errors are random (their sum is zero, and in different attempts they do not depend on each other), then from mathematical statistics it follows:
O/ = Ooo T<З е,
i.e., the dispersion of the results recorded in the experiment (st/ 2) is equal to the sum of the dispersions of the true results ((Xm 2) and errors (0 e 2).
Ooo 2 characterizes idealized (i.e., error-free) interclass variation, and e 2 characterizes intraclass variation. The influence of o e 2 changes the distribution of test results (Fig. 2).
By definition, the reliability coefficient (Hz) is equal to the ratio of the true variance to the variance recorded in the experiment:
In other words, r p is simply the proportion of true variation in the variation that is recorded in experience.
In addition to the reliability coefficient, the reliability index is also used:
which is considered as a theoretical correlation coefficient between the recorded test values and the true ones. They also use the concept of standard error of reliability, which is understood as the standard deviation of the recorded test results (X () from the regression line connecting the value of X g with the true results (X") - Fig. 3.
2.2 Reliability assessment based on experimental data
The concept of a true test result is an abstraction. Hoe cannot be measured experimentally (after all, it is impossible in reality to carry out an infinitely large number of observations under identical conditions). Therefore, we have to use indirect methods.
The most preferable method for assessing reliability is analysis of variance followed by calculation of the so-called intraclass correlation coefficients.
Analysis of variance, as is known, makes it possible to decompose the experimentally recorded variation in test results into components due to the influence of individual factors. For example, if we register the results of subjects in any test, repeating this test on different days, and making several attempts on each day, periodically changing experimenters, then a variation will occur:
a) from subject to subject (interindividual variation),
b) from day to day,
c) from experimenter to experimenter,
d) from attempt to attempt.
Analysis of variance makes it possible to isolate and evaluate the variations caused by these factors.
A simplified example shows how this is done. Let’s assume that the results of two attempts were measured in 5 subjects (k = 5, n = 2)
The results of variance analysis (see the course in mathematical statistics, as well as Appendix 1 to the first part of the book) are given in the traditional form in table. 2.
table 2
Reliability is assessed using the so-called intraclass correlation coefficient:
where r "i is the intraclass correlation coefficient (reliability coefficient, which, in order to distinguish it from the usual correlation coefficient (r), is denoted with an additional prime (r")\
n -- number of attempts used in the test;
n" - the number of attempts for which the reliability assessment is carried out.
For example, if they want to estimate the reliability of the average of two attempts based on the data given in the example, then
If we limit ourselves to only one attempt, then the reliability will be equal to:
and if you increase the number of attempts to four, the reliability coefficient will also increase slightly:
Thus, in order to assess reliability, it is necessary, firstly, to perform an analysis of variance and, secondly, to calculate the intraclass correlation coefficient (reliability coefficient).
Some difficulties arise when there is a so-called trend, i.e. a systematic increase or decrease in results from attempt to attempt (Fig. 4). In this case, more complex methods for assessing reliability are used (they are not described in this book).
For the case of two attempts and the absence of a trend, the values of the intraclass correlation coefficient practically coincide with the values of the usual correlation coefficient between the results of the first and second attempts. Therefore, in such situations, the usual correlation coefficient can be used to assess reliability (it estimates the reliability of one rather than two attempts). However, if the number of retries in a test is more than two, and especially if complex test designs are used,
Rice. 4. A series of six attempts, of which the first three (left) or the last three (right) are subject to the trend
(for example, 2 attempts per day for two days), calculation of the intraclass coefficient is necessary.
The reliability coefficient is not an absolute indicator characterizing the test. This coefficient may vary depending on the population of subjects (for example, it may be different for beginners and skilled athletes), testing conditions (whether repeated attempts are carried out one after another or, say, at intervals of one week) and other reasons. Therefore, it is always necessary to describe how and on whom the test was carried out.
2.3 Reliability in test practice
The unreliability of experimental data reduces the magnitude of estimates of correlation coefficients. Since no test can correlate more with another test than with itself, the upper limit for estimating the correlation coefficient here is no longer ±1.00, but the reliability index
g (oo = Y~g and
To move from estimating correlation coefficients between empirical data to estimating the correlation between true values, you can use the expression
where r xy is the correlation between the true values of X and Y;
1~xy -- correlation between empirical data; HzI^ - assessment of the reliability of X and Y.
For example, if r xy = 0.60, r xx = 0.80 and r yy = 0.90, then the correlation between the true values is 0.707.
The given formula (6) is called the reduction correction (or the Spearman-Brown formula), it is constantly used in practice.
There is no fixed reliability value for a test to be considered acceptable. It all depends on the importance of the conclusions drawn from the application of the test. And yet, in most cases in sports, the following approximate guidelines can be used: 0.95--0.99 --¦ excellent reliability, 0.90-^0.94 - - good, 0.80--0.89 - acceptable, 0.70--0.79 - bad, 0.60--0.69 - doubtful for individual assessments, the test is suitable only for characterizing a group of subjects.
You can achieve some improvement in test reliability by increasing the number of retries. Here is how, for example, in the experiment the reliability of the test (throwing a 350 g grenade with a running start) increased as the number of attempts increased: 1 attempt - 0.53, 2 attempts - 0.72, 3 attempts - 0.78, 4 attempts -- 0.80, 5 attempts -- 0.82, 6 attempts -- 0.84. The example shows that if at first reliability increases quickly, then after 3-4 attempts the increase slows down significantly.
With several repeated attempts, the results can be determined in different ways: a) by the best attempt, b) by the arithmetic mean, c) by the median, d) by the average of two or three best attempts, etc. Research has shown that in most cases The most reliable is to use the arithmetic mean, the median is somewhat less reliable, and the best attempt is even less reliable.
When talking about the reliability of tests, a distinction is made between their stability (reproducibility), consistency, and equivalence.
2.4 Test stability
Test stability refers to the reproducibility of results when repeated after a certain time under the same conditions. Repeated testing is usually called a retest. The test stability assessment scheme is as follows: 1
In this case, two cases are distinguished. In one, a retest is carried out in order to obtain reliable data on the condition of the subject during the entire time interval between the test and retest (for example, to obtain reliable data on the functional capabilities of skiers in June, they are measured twice with an interval of one week). In this case, accurate test results are important and reliability should be assessed using analysis of variance.
In another case, it may be important only to preserve the order of the subjects in the group (whether the first remains first, the last remains among the last). In this case, stability is assessed by the correlation coefficient between test and retest.
The stability of the test depends on:
type of test
contingent of subjects,
time interval between test and retest. For example, morphological characteristics at small
time intervals are very stable; tests for accuracy of movements (for example, throwing at a target) have the least stability.
In adults, test results are more stable than in children; among athletes they are more stable than among those who do not engage in sports.
As the time interval between test and retest increases, test stability decreases (Table 3).
2.5 Test consistency
The consistency of the test is characterized by the independence of the test results from the personal qualities of the person conducting or evaluating the test." Consistency is determined by the degree of agreement of the results obtained on the same subjects by different experimenters, judges, and experts. In this case, two options are possible:
The person administering the test only evaluates the test results without influencing its performance. For example, different examiners may evaluate the same written work differently. Judges’ assessments in gymnastics, figure skating, boxing, manual timing indicators, electrocardiogram or radiograph assessments by different doctors, etc. often differ.
The person performing the test influences the results. For example, some experimenters are more persistent and demanding than others and are better at motivating subjects. This affects results (which themselves can be measured quite objectively).
Test consistency is essentially the reliability of the test's scores when different people administer the test.
1 Instead of the term “consistency,” the term “objectivity” is often used. This use of words is unfortunate, since the coincidence of the results of different experimenters or judges (experts) does not at all indicate their objectivity. Together they can consciously or unconsciously make mistakes, distorting the objective truth.
2.6 Test equivalence
Often a test is the result of a selection from a certain number of similar tests.
For example, throwing a basketball basket can be done from different points, sprinting can be done over a distance of, say, 50, 60 or 100 m, pull-ups can be done on rings or a bar, with an overhand or underhand grip, etc.
In such cases, the so-called parallel forms method can be used, when subjects are asked to perform two versions of the same test and then the degree of agreement between the results is assessed. The testing scheme here is as follows:
The correlation coefficient calculated between test results is called the equivalence coefficient. The attitude towards test equivalence depends on the specific situation. On the one hand, if two or more tests are equivalent, their combined use increases the reliability of the estimates; on the other hand, it may be useful to leave only one equivalent test in the battery - this will simplify testing and only slightly reduce the information content of the test set. The solution to this issue depends on reasons such as the complexity and cumbersomeness of the tests, the degree of required testing accuracy, etc.
If all the tests included in a test suite are highly equivalent, it is called homogeneous. This entire complex measures one property of human motor skills. Let's say a complex consisting of standing long, vertical and triple jumps is likely to be homogeneous. On the contrary, if there are no equivalent tests in the complex, then all the tests included in it measure different properties. Such a complex is called heterogeneous. Example of a heterogeneous battery of tests: pull-ups on the bar, bending forward (to test flexibility), 1500 m run.
2.7 Ways to improve test reliability
The reliability of tests can be increased to a certain extent by:
a) more stringent standardization of testing,
b) increasing the number of attempts,
c) increasing the number of appraisers (judges, experts) and increasing the consistency of their opinions,
d) increasing the number of equivalent tests,
e) better motivation of the subjects.
3. INFORMATIVE TESTS
3.1 Basic concepts
The informativeness of a test is the degree of accuracy with which it measures the property (quality, ability, characteristic, etc.) that it is used to evaluate. Informativeness is often also called validity (from the English uaNaNu - validity, reality, legality). Let us assume that to determine the level of special strength preparedness of sprinters - runners and swimmers - they want to use the following indicators: 1) carpal dynamometry, 2) plantar flexion strength of the foot, 3) strength of the extensors of the shoulder joint (these muscles bear a large load when swimming crawl) , 4) strength of the neck extensor muscles. Based on these tests, it is proposed to manage the training process, in particular, to find weak links in the motor system and purposefully strengthen them. Are the tests chosen good? Are they informative? Even without conducting special experiments, one can guess that the second test is probably informative for sprinters and runners, the third for swimmers, and the first and fourth, probably, will not show anything interesting for either swimmers or runners (although they may be very useful in other sports, such as wrestling). In different cases, the same tests may have different information content.
The question about the informativeness of the test is divided into 2 specific questions:
What does this test measure?
How exactly does he do this?
For example, is it possible to judge the fitness of long distance runners based on such an indicator as maximum oxygen consumption (MOC), and if so, with what degree of accuracy? In other words, what is the information content of the IPC among stayers? Can this test be used in the control process?
If the test is used to determine (diagnose) the athlete’s condition at the time of examination, then they speak of diagnostic informativeness. If, based on the test results, they want to draw a conclusion about the athlete’s possible future performance, the test must have predictive information. A test can be diagnostically informative, but not prognostically, and vice versa.
The degree of information content can be characterized quantitatively - on the basis of experimental data (the so-called empirical information content) and qualitatively - on the basis of a meaningful analysis of the situation (substantive, or logical, information content).
3.2 Empirical information content (case one - there is a measurable criterion)
The idea of determining empirical information content is that the test results are compared with some criterion. To do this, calculate the correlation coefficient between the criterion and the test (this coefficient is called the informativeness coefficient and is denoted r gk, where I is the first letter in the word “test”, k in the word “criterion”).
The criterion is taken to be an indicator that obviously and indisputably reflects the property that is going to be measured using the test.
It often happens that there is a well-defined criterion with which the proposed test can be compared. For example, when assessing the special preparedness of athletes in sports with objectively measured results, the result itself usually serves as such a criterion: the test whose correlation with the sports result is higher is more informative. In the case of determining prognostic information content, the criterion is the indicator whose forecast must be carried out (for example, if the length of a child’s body is predicted, the criterion is the length of his body in adulthood).
The most common criteria in sports metrology are:
Sports result.
Any quantitative characteristic of a basic sports exercise (for example, stride length in running, push-off force in jumping, success of fighting under the backboard in basketball, serving in tennis or volleyball, percentage of accurate long passes in football).
The results of another test, the information content of which has been proven (this is done if conducting a criterion test is cumbersome and difficult and you can select another test that is equally informative, but simpler. For example, instead of gas exchange, determine the heart rate). This special case, when the criterion is another test, is called competitive information content.
Belonging to a specific group. For example, you can compare members of the national team, masters of sports and first-class athletes; belonging to one of these groups is a criterion. In this case, special types of correlation analysis are used.
The so-called composite criterion, for example the sum of points in the all-around. In this case, all-around types and points tables can be either generally accepted or newly compiled by the experimenter (for how the tables are compiled, see the next chapter). A composite criterion is resorted to when there is no single criterion (for example, if the task is to assess general physical fitness, a player’s skill in sports games, etc., not a single indicator taken by itself can serve as a criterion).
An example of determining the information content of the same test - running speed of 30 m on the move for men - with different criteria is given in Table 4.
The question of choosing a criterion is essentially the most important in determining the real meaning and informativeness of the test. For example, if the task is to determine the information content of such a test as the standing long jump of sprinters, then you can choose different criteria: the result in the 100 m run, step length, the ratio of step length to leg length or to height, etc. Information content the test will change in this case (in the example given, it increased from 0.558 for running speed to 0.781 for the “step length/leg length” ratio).
In sports where it is impossible to objectively measure sportsmanship, they try to get around this difficulty by introducing artificial criteria. For example, in team sports games, experts rank all the players according to their skill in a certain order (i.e., they make lists of the 20, 50, or, say, 100 strongest players). The place occupied by the athlete (as they say, his rank) is considered as a criterion with which the test results are compared in order to determine their informativeness.
The question arises: why use tests if the criterion is known? For example, isn’t it easier to organize control competitions and determine sports results than to determine achievements in control exercises? The use of tests has the following advantages:
a sports result is not always possible or advisable to determine (for example, marathon running competitions cannot be held often; in winter it is usually impossible to register a result in javelin throwing, and in summer in cross-country skiing);
a sports result depends on many reasons (factors), such as the athlete’s strength, endurance, technique, etc. The use of tests makes it possible to determine the strengths and weaknesses of an athlete and evaluate each of these factors separately
3.3 Empirical informativeness (case two - there is no single criterion; factorial informativeness)
It often happens that there is no single criterion with which the results of proposed tests can be compared. Let’s say they want to find the most informative tests to assess the strength readiness of young people. What to prefer: pull-ups on the bar or push-ups, squats with a barbell, barbell rows, or going into a squat from a supine position? What could be the criterion for choosing the right test here?
You can offer subjects a large battery of various strength tests, and then select among them those that give the greatest correlation with the results of the entire complex (after all, you cannot systematically use the entire complex - it is too cumbersome and inconvenient). These tests will be the most informative: they will provide information about the possible results of the subjects for the entire initial set of tests. But the results in a set of tests are not expressed in one number. It is possible, of course, to form some kind of composite criterion (for example, to determine the amount of points scored on some scale). However, another way, based on the ideas of factor analysis, is much more effective.
Factor analysis is one of the methods of multivariate statistics (the word “multidimensional” indicates that many different indicators are studied simultaneously, for example, the results of subjects in many tests). This is a rather complex method, so here it is advisable to limit ourselves to presenting only its main idea.
Factor analysis proceeds from the fact that the result of any test is a consequence of the simultaneous action of a number of directly unobservable (otherwise known as latent) factors. For example, results in running 100, 800 and 5000 m depend on the athlete’s speed, strength, endurance, etc. The significance of these factors for each distance is not equally important. If you choose two tests that are influenced approximately equally by the same factors, then the results in these tests will be highly correlated with each other (say, in running at distances of 800 and 1000 m). If tests have no common factors or they have little influence on the results, the correlation between these tests will be low (for example, the correlation between performance in the 100 m and 5000 m). When a large number of different tests are taken and correlation coefficients between them are calculated, then using factor analysis it is possible to determine how many factors act together on these tests and what is the degree of their contribution to each test. And then it is easy to select tests (or combinations thereof) that most accurately assess the level of individual factors. This is the idea of factorial information content of tests. The following example of a specific experiment shows how this is done.
The task was to find the most informative tests for assessing the general strength readiness of third- and first-class student-athletes involved in different sports. For this purpose, it was examined. (N.V. Averkovich, V.M. Zatsiorsky, 1966) according to 15 tests, 108 people. As a result of factor analysis, three factors were identified: 1) strength of the upper extremities, 2) strength of the lower extremities, 3) strength of the abdominal muscles and hip flexors. The most informative tests among those tested were: for the first factor - push-ups, for the second - a standing long jump, for the third - raising straight legs while hanging and the maximum number of transitions to a squat from a supine position within 1 minute . If we limit ourselves to only one test, then the most informative was the force-flip on the crossbar (the number of repetitions was assessed).
3.4 Empirical informatics in practical work
When using empirical informativeness indicators in practice, it should be borne in mind that they are valid only in relation to those subjects and the conditions for which they are calculated. A test that is informative in a group of beginners may turn out to be completely uninformative if you try to use it in a group of masters of sports.
The information content of the test is not the same in different groups. In particular, in groups that are more homogeneous in composition, the test is usually less informative. If the information content of a test in any group is determined, and then the strongest of it are included in the national team, then the information content of the same test in the national team will be significantly lower. The reasons for this are clear from Fig. 5: selection reduces the overall variance of results in the group and reduces the magnitude of the correlation coefficient. For example, if we determine the information content of such a test as the MPC of 400 m swimmers who have sharply different results (say, from 3.55 to 6.30), then the information content coefficient will be very high (Y 4th>0.90); if we carry out the same measurements in a group of swimmers with results of 3.55 to 4.30, g No. in absolute value will not exceed 0.4--0.6; if we determine the same indicator among the strongest swimmers in the world (3.53>, 5=4.00), the coefficient of information content in general ""may be equal to zero: with the help of this test alone it will be impossible to distinguish between swimmers swimming, say, 3.55 and 3.59: and those and others have MIC values. will be high and approximately the same.
Informativeness coefficients very much depend on the reliability of the test and criterion. A test with low reliability is always not very informative, so it makes no sense to check low-reliability tests for information content. Insufficient reliability of the criterion also leads to a decrease in informativeness coefficients. However, in this case, it would be wrong to neglect the test as uninformative - after all, the upper limit of the possible correlation of a test is not ±1, but its reliability index. Therefore, it is necessary to compare the information content coefficient with this index. The actual information content (adjusted for the unreliability of the criterion) is calculated using the formula:
Thus, in one of the works, the rank of an athlete in water polo (rank was considered as a criterion of skill) was established based on the assessments of 4 experts. Reliability (consistency) of the criterion, determined using the intraclass correlation coefficient, was 0.64. The information coefficient was 0.56. The actual coefficient of information content (adjusted for the unreliability of the criterion) is equal to:
Closely related to the informativeness and reliability of the test is the concept of its discriminative ability, which is understood as the minimal difference between subjects that is diagnosed using the test (this concept is similar in meaning to the concept of the sensitivity of the device). The discriminative ability of the test depends on:
Interindividual variation in results. For example, a test such as “maximum number of repeated throws of a basketball against a wall from a distance of 4 m within 10 seconds” is good for beginners, but unsuitable for skilled basketball players, since they all show approximately the same result and become indistinguishable . In many cases, interrater variation (interclass variation) can be increased by increasing the difficulty of the test. For example, if you give athletes of different qualifications a functional test that is easy for them (say, 20 squats or working on a bicycle ergometer with a power of 200 kgm/min), then the magnitude of physiological changes in everyone will be approximately the same and it will be impossible to assess the degree of readiness. If you offer them a difficult task, then the differences between the athletes will become large, and based on the test results it will be possible to judge the preparedness of the athletes.
Reliability (i.e., the relationship between inter- and intra-individual variation) of the test and criterion. If the results of the same subject in the standing long jump vary, say,
In cases ±10 cm, then, although the length of the jump can be determined with an accuracy of ±1 cm, it is impossible to distinguish with confidence the subjects whose “true” results are 315 and 316 cm.
There is no fixed value for the information content of a test, after which the test can be considered suitable. Much depends on the specific situation: the desired accuracy of the forecast, the need to obtain at least some additional information about the athlete, etc. In practice, tests are used for diagnostics, the information content of which is not less than 0.3 For a forecast, as a rule, a higher information content is needed - at least 0.6.
The information content of a battery of tests is naturally higher than the information content of one test. It often happens that the information content of one individual test is too low to use this test. The information content of a battery of tests may be quite sufficient.
The information content of a test cannot always be determined using an experiment and mathematical processing of its results. For example, if the task is to develop tickets for exams or topics for dissertations (this is also a type of testing), it is necessary to select questions that are the most informative, by which you can most accurately assess the knowledge of graduates and their preparedness for practical work. So far, in such cases, they rely only on a logical, meaningful analysis of the situation.
Sometimes it happens that the information content of a test is clear without any experiments, especially when the test is simply part of the actions that an athlete performs in competitions. Experiments are hardly needed to prove the informativeness of such indicators as the time it takes to perform turns in swimming, the speed in the last steps of the run-up in the long jump, the percentage of free throws in basketball, the quality of the serve in tennis or volleyball.
However, not all such tests are equally informative. For example, a throw-in in football, although an element of the game, can hardly be considered one of the most important indicators of the skill of football players. If there are many such tests and you need to select the most informative ones, you cannot do without mathematical methods of test theory.
The content analysis of the information content of the test and its experimental and mathematical justification should complement each other. None of these approaches taken on their own is sufficient. In particular, if as a result of an experiment a high coefficient of information content of a test is determined, it is necessary to check whether this is not a consequence of the so-called false correlation. It is known that false correlations appear when the results of both correlated characteristics are influenced by some third indicator, which in itself does not represent
interest. For example, among high school students one can find a significant correlation between the result in the 100 m run and knowledge of geometry, since they, compared to elementary school students, on average will show higher performance in both running and knowledge of geometry. The third, extraneous feature that caused the emergence of a correlation was the age of the subjects. Of course, the researcher who did not notice this and recommended the geometry exam as a test for 100 m runners would make a mistake. In order to avoid making such mistakes, it is necessary to analyze the cause-and-effect relationships that caused the correlation between the criterion and the test. It is useful, in particular, to imagine what would happen if the test scores improved. Will this lead to an increase in criterion results? In the example above, this means: if the student knows geometry better, will he be faster in the 100 m race? The obvious negative answer leads to a natural conclusion: knowledge of geometry cannot serve as a test for sprinters. The correlation found is false. Of course, real-life situations are much more complex than this deliberately stupid example.
A special case of meaningful informativeness of tests is informativeness by definition. In this case, they simply agree on what meaning should be put into this or that word (term). For example, they say: “a standing high jump is characterized by jumping ability.” It would be more accurate to say this: “let’s agree to call jumping ability what is measured by the result of jumping up from a place.” Such mutual agreement is necessary, since it prevents unnecessary misunderstandings (after all, someone may understand by jumping ability the results in a ten-fold jump on one leg, and consider a standing high jump, say, a test of “explosive” leg strength).
56.0 Standardization of tests
Standardization of physical fitness tests to assess human aerobic performance is achieved by adhering to the following principles.
The testing methodology must allow for direct measurements or indirect calculation of the body's maximum oxygen consumption (aerobic capacity), since this physiological indicator of human physical fitness is the most important. It will be designated by the symbol gpax1ggsht U 0g and expressed in milliliters per kilogram of the subject’s weight per minute (ml/kg-min.).
In general, the test methodology should be the same for both laboratory and field measurements, however:
1. In laboratory conditions (in stationary and mobile laboratories), a person’s aerobic performance can be directly determined using fairly complex equipment and a large number of measurements.
2. In the field, aerobic performance is assessed indirectly based on a limited number of physiological measurements.
The test methodology should allow comparison of their results.
Testing should be carried out in one day and preferably without interruptions. This will make it possible to expediently distribute time, equipment, and effort during initial and re-testing.
The testing methodology must be flexible enough to allow testing of groups of people with different physical abilities, different ages, genders, different activity levels, etc.
57.0. Equipment selection
All of the above principles of physiological testing can be observed, first of all, subject to the correct selection of the following technical means:
treadmill,
bicycle ergometer,
stepergometer,
necessary auxiliary equipment that can be used in any type of test.
57.1. The treadmill can be used in a wide variety of studies. However, this device is the most expensive. Even the smallest version is too bulky to be widely used in the field. The treadmill should allow speeds from 3 to (at least) 8 km/h (2-5 mph) and inclines from 0 to 30%. The inclination of a treadmill is defined as the percentage of vertical rise to the horizontal distance traveled."
Distance and vertical elevation must be expressed in meters, speed in meters per second (m/sec) or kilometers per hour (km/h).
57.2. Bicycle ergometer. This device is easy to use both in laboratory and field conditions. It is quite versatile; it can be used to perform work of varying intensity - from minimal to maximum level.
The bicycle ergometer has a mechanical or electrical braking system. The electric braking system can be powered either from an external source or from a generator located on the ergometer.
Adjustable mechanical resistance is expressed in kilogram meters per minute (kgm/min) and in watts. Kilometers per minute are converted to watts using the formula:
1 watt = 6 kgm/min. 2
The bicycle ergometer must have a movably fixed seat so that the height of its position can be adjusted for each individual person. When testing, the seat is installed in such a way that the person sitting on it can reach the lower pedal with an almost fully straightened leg. On average, the distance between the seat and the pedal in the maximum lowered position should be 109% of the length of the test subject's leg.
There are various designs of bicycle ergometer. However, the type of ergometer does not affect the results of the experiment if the specified resistance in watts or kilograms per minute exactly corresponds to the total external load.
Stepergometer. This is a relatively inexpensive device with adjustable step heights from 0 to 50 cm. Like a bicycle ergometer, it can be easily used both in the laboratory and in the field.
Comparison of three testing options. Each of these instruments has its own advantages and disadvantages (depending on whether it is used in laboratories or in the field). Usually, when working on a treadmill, the value of max1ggsht U07 is slightly larger than when working on a bicycle ergometer; in turn, the readings on the bicycle ergometer exceed the readings on the stepergometer.
The level of energy expenditure of subjects at rest or performing a task to overcome gravity is directly proportional to their weight. Therefore, exercises on the treadmill and stepergometer create for all subjects the same relative workload of lifting (their body. - Ed.) to a given height: at a given speed and inclination of the treadmill, frequency of steps and heights of steps on the stepergometer, the height of the body will be lifted - is the same (but the work performed is different. - Ed.). On the other hand, a bicycle ergometer at a fixed value of a given load requires almost the same energy expenditure, regardless of the gender and age of the subject.
58.0, General Notes on Test Procedures
To apply tests to large groups of people, simple and time-efficient testing methods are needed. However, for a more detailed study of the physiological characteristics of the subject, more in-depth and labor-intensive tests are needed. To get more value from tests and use them more flexibly, it is necessary to find the optimal compromise between these two requirements.
58.1. Work intensity. Testing must begin with small loads that the weakest of the test subjects can handle. Assessment of the adaptive capabilities of the cardiovascular and respiratory systems should be carried out during work with gradually increasing loads. Functional limits must therefore be established with sufficient precision. Practical considerations suggest taking the baseline metabolic rate (i.e., resting metabolic rate) as a unit of measurement for the amount of energy required to perform a given activity. The initial load and its subsequent stages are expressed in Meta, multiples of the metabolic rate of a person in a state of complete rest. The physiological indicators underlying Meta are the amount of oxygen (in milliliters per minute) consumed by a person at rest, or its caloric equivalent (in kilocalories per minute).
To monitor loads in Met units or equivalent oxygen consumption values directly during testing, complex electronic computing equipment is required, which is currently still relatively inaccessible. Therefore, when determining the amount of oxygen required by the body to perform loads of a certain type and intensity, it is practically convenient to use empirical formulas. The predicted (based on empirical formulas. - Ed.) values of oxygen consumption when working on a treadmill - by speed and inclination, during a step test - by height and frequency of steps are in good agreement with the results of direct measurements and can be used as the physiological equivalent of physical effort, with which all physiological indicators obtained during testing are correlated.
58.2. Duration of tests. The desire to shorten the testing process should not be to the detriment of the goals and objectives of the test. Tests that are too short will not produce sufficiently distinguishable results and their discriminative capabilities will be small; tests that are too long activate thermoregulatory mechanisms to a greater extent, which interferes with the establishment of maximum aerobic performance. In the recommended testing procedure, each load level is maintained for 2 minutes. The average test time is from 10 to 16 minutes.
58.3. Indications for stopping the test. Testing should be stopped unless:
pulse pressure drops steadily despite increased workload;
systolic blood pressure exceeds 240--250 mmHg. Art.;
diastolic blood pressure rises above 125 mm Hg. Art.;
symptoms of malaise appear, such as increasing chest pain, severe shortness of breath, intermittent claudication;
clinical signs of anoxia appear: pallor or cyanosis of the face, dizziness, psychotic phenomena, lack of response to irritation;
Electrocardiogram readings indicate paroxysmal superventricular or ventricular arrhythmia, the appearance of ventricular extrasystolic complexes that occur before the end of the T wave, conduction disturbances, except for mild L V blockade, a decrease in /?--5G horizontal or descending type by more than 0.3 mV . .;";, -
58.4. Precautionary measures.
Health of the subject. Before being examined, the subject must undergo a medical examination and receive a certificate stating that he is healthy. It is highly advisable to do an electrocardiogram (at least one chest lead). For men over 40 years of age, an electrocardiogram is mandatory. Regularly repeated blood pressure measurements should be an integral part of the entire testing procedure. At the end of testing, subjects should be informed about measures to prevent dangerous accumulation of blood in the lower extremities.
Contraindications. The subject is not allowed to take tests in the following cases:
lack of permission from a doctor to take part in tests with maximum loads;
oral temperature exceeds 37.5°C;
heart rate after a long rest is above 100 beats/min;
obvious decline in cardiac activity;
a case of myocardial infarction or myocarditis in the last 3 months; symptoms and electrocardiogram readings indicating the presence of these diseases; signs of angina pectoris;
infectious diseases, including colds.
Menstruation is not a contraindication to participation in the tests. However, in some cases it is advisable to change the schedule of their holding.
B. STANDARD TESTS
59.0. Description of the main methodology for conducting standard
In all three types of exercise, and regardless of whether the test is performed at a maximal or submaximal load, the basic testing procedure is the same.
The subject comes to the laboratory in light sportswear and soft shoes. Within 2 hours. Before starting the test, he should not eat, drink coffee, or smoke.
Rest. The test is preceded by a rest period that lasts 15 minutes. During this time, while the physiological measuring instruments are being installed, the subject sits comfortably in a chair.
Accommodation period. The very first testing of any subject, like all repeated tests, will give fairly reliable results if the main test is preceded by a short period of exercise with a low load - a period of accommodation. It lasts 3 minutes. and serves the following purposes:
familiarize the subject with the equipment and type of work that he must perform;
preliminary study of the physiological response of the subject to a load of approximately 4 Meta, which corresponds to a heart rate of approximately 100 beats/min;
speed up the body’s adaptation to the actual test itself.
Rest. The accommodation period is followed by a short (2 min.) rest period; the subject sits comfortably in a chair while the experimenter makes the necessary technical preparations.
Test. At the beginning of the test, a load equal to the load of the accommodation period is set, and the subject performs the exercises without interruption until the test is completed. Every 2 min. work load increases by 1 Meter.
Testing stops when one of the following conditions occurs:
the subject is unable to continue performing the task;
there are signs of physiological decompensation (see 58.3);
data obtained at the last stage of the load allow the extrapolation of maximum aerobic performance based on sequential physiological measurements (performed during testing. - Editor's note).
59.5. Measurements. Maximum oxygen consumption in milliliters per kilogram per minute is measured directly or calculated. Methods for determining oxygen consumption are very diverse, as are the additional techniques used to analyze the physiological capabilities of each individual. This will be discussed in more detail later.
59.6. Recovery. At the end of the experiment, physiological observation continues for at least 3 minutes. The subject again rests in a chair, slightly raising his legs.
Note. The described testing technique provides comparable physiological data obtained with the same sequence of increasing load on a treadmill, bicycle ergometer and stepergometer. Below, the testing methodology is described separately for each of the three devices.
60.0. Treadmill test
Equipment. Treadmill and necessary auxiliary equipment.
Description. The basic testing procedures described in 59.0 are carefully followed.
The speed of the treadmill with the subject walking on it is 80 m/min (4.8 km/h, or 3 mph). At this speed, the energy required to move horizontally is approximately 3 Meta; Each 2.5% increase in slope adds one unit of initial metabolic rate, i.e. 1 Met, to energy expenditure. At the end of the first 2 min. the inclination of the treadmill quickly increases to 5%, at the end of the next 2 minutes - to 7.5%, then to 10%, 12.5%, etc. The complete scheme is given in table. 1.
Similar documents
Conducting control tests using control exercises or tests to determine readiness for physical exercise. The problem of test standardization. External and internal validity of tests. Maintaining a control examination protocol.
abstract, added 11/12/2009
Characteristics of motor abilities and methods for developing flexibility, endurance, agility, strength and speed. Testing the motor abilities of schoolchildren in physical education lessons. Application of motor tests in practical activities.
thesis, added 02/25/2011
Assessing the dynamics of changes in anthropometric data in schoolchildren systematically involved in athletics and schoolchildren who do not participate in sports sections. Development of tests to determine general physical fitness; analysis of results.
thesis, added 07/07/2015
The main directions of using tests, their classification. Tests for selection in wrestling. Methods for assessing sports achievements. Testing a wrestler's special endurance. The relationship between test indicators and the technical skill of freestyle wrestlers.
thesis, added 03/03/2012
Assessing a swimmer’s special endurance using control exercises. Adaptability of the basic reactions of physiological systems in an aquatic environment. Development of principles for assessing medical and biological indicators used when testing a swimmer.
article, added 08/03/2009
Consideration of healthy energy as the fundamental basis of health. Familiarization with the features of gymnastic exercises according to the qigong system. Selection of a set of exercises for home exercises. Drawing up tests to draw conclusions on the work done.
thesis, added 07/07/2015
Sports metrology is the study of physical quantities in physical education and sports. Basics of measurement, theory of tests, assessments and norms. Methods for obtaining information on quantitative assessment of the quality of indicators; qualimetry. Elements of mathematical statistics.
presentation, added 02/12/2012
The essence and importance of control in physical education and its types. Testing and evaluation of motor skills acquired in physical education lessons. Testing the level of physical fitness. Monitoring the functional state of students.
course work, added 06/06/2014
Calculation of absolute and relative measurement errors. Converting test results into scores using regressive and proportional scales. Ranking of test results. Changes in group placements compared to previous assessments.
test, added 02/11/2013
Motor activity mode. The role of factors determining the physical performance of football players at different stages of long-term training. Types of ergogenic aids. Methodology for conducting tests to determine the level of physical performance.
- What does individuality mean?
- What does a person’s individuality depend on?
- Issues of formation of a cluster education system in the Russian Federation
- Unified State Exam tests in literature What is included in the Unified State Examination in literature
- How to pay transport tax for legal entities
- Card for individual accounting of the amounts of accrued payments and other remunerations and the amounts of accrued insurance premiums Card for insurance premiums per year
- Error when filling in Contour
- Desk audit: developments
- Conditions for performing the stern experiment
- System status and processes
- Alexey Sergeevich Obukhov development of student research activities
- Oriental and African studies
- Yelets State University named after
- What does it show and how to calculate the internal rate of return?
- Yaroslav Samoilov is a relationship specialist with no professional education. Do you want to save your relationship?
- Perm Pharmaceutical Academy: reviews, faculties
- Trader Dmitry Cheremushkin
- Main economic issues
- Creative competition: we enter the Faculty of Journalism of St. Petersburg State University Bachelor's training programs
- Management of a modern school using the example of creating an educational cluster