Significance level - this is the probability that we considered the differences to be significant, but they are actually random.

When we indicate that the differences are significant at the 5% significance level, or when R< 0,05 , then we mean that the probability that they are unreliable is 0.05.

When we indicate that the differences are significant at the 1% significance level, or when R< 0,01 , then we mean that the probability that they are unreliable is 0.01.

If we translate all this into more formalized language, then the significance level is the probability of rejecting the null hypothesis, while it is true.

Error,consisting ofthe onewhat werejectednull hypothesiswhile it is correct, it is called a type 1 error.(See Table 1)

Table 1. Null and alternative hypotheses and possible test conditions.

The probability of such an error is usually denoted as α. In essence, we would have to indicate in parentheses not p < 0.05 or p < 0.01, and α < 0.05 or α < 0,01.

If the probability of error is α , then the probability of a correct decision: 1-α. The smaller α, the greater the probability of a correct decision.

Historically, in psychology it is generally accepted that the lowest level of statistical significance is the 5% level (p≤0.05): sufficient is the 1% level (p≤0.01) and the highest is the 0.1% level ( p≤0.001), therefore, the tables of critical values ​​usually contain the values ​​of the criteria corresponding to the levels statistical significance p≤0.05 and p≤0.01, sometimes p≤0.001. For some criteria, the tables indicate the exact significance level of their different empirical values. For example, for φ*=1.56 p=O.06.

However, until the level of statistical significance reaches p=0.05, we still have no right to reject the null hypothesis. We will adhere to the following rule for rejecting the hypothesis of no differences (Ho) and accepting the hypothesis of statistical significance

differences (H 1).

Rule for rejecting Ho and accepting h1

If the empirical value of the test is equal to or greater than the critical value corresponding to p≤0.05, then H 0 is rejected, but we cannot yet definitely accept H 1 .

If the empirical value of the criterion is equal to the critical value corresponding to p≤0.01 or exceeds it, then H 0 is rejected and H 1 is accepted. : G sign test, Wilcoxon T test and Mann-Whitney U test. Inverse relationships are established for them.

Rice. 4. Example of a “significance axis” for Rosenbaum’s Q criterion.

The critical values ​​of the criterion are designated as Q o, o5 and Q 0.01, the empirical value of the criterion as Q em. It is enclosed in an ellipse.

To the right of the critical value Q 0.01 extends the “zone of significance” - this includes empirical values ​​exceeding Q 0.01 and, therefore, certainly significant.

To the left of the critical value Q 0.05, the “zone of insignificance” extends - this includes empirical Q values ​​that are below Q 0.05 and, therefore, are certainly insignificant.

We see that Q 0,05 =6; Q 0,01 =9; Q em. =8;

The empirical value of the criterion falls in the region between Q 0.05 and Q 0.01. This is a zone of “uncertainty”: we can already reject the hypothesis about the unreliability of differences (H 0), but we cannot yet accept the hypothesis about their reliability (H 1).

In practice, however, the researcher can consider as reliable those differences that do not fall into the zone of insignificance, declaring that they are reliable at p < 0.05, or by indicating the exact level of significance of the obtained empirical criterion value, for example: p=0.02. Using standard tables, which are in all textbooks on mathematical methods, this can be done in relation to the Kruskal-Wallis H criteria, χ 2 r Friedman, Page's L, Fisher's φ* .

The level of statistical significance or critical test values ​​are determined differently when testing directed and non-directed statistical hypotheses.

With a directional statistical hypothesis, a one-tailed test is used, with a non-directional hypothesis, a two-tailed test is used. The two-tailed test is more stringent because it tests differences in both directions, and therefore the empirical value of the test that previously corresponded to the significance level p < 0.05, now corresponds only to the p level < 0,10.

We won't have to decide for ourselves every time whether he uses a one-sided or two-sided criterion. The tables of critical values ​​of the criteria are selected in such a way that directional hypotheses correspond to a one-sided criterion, and non-directional hypotheses correspond to a two-sided criterion, and the given values ​​satisfy the requirements that apply to each of them. The researcher only needs to ensure that his hypotheses coincide in meaning and form with the hypotheses proposed in the description of each of the criteria.

In any scientific and practical situation of an experiment (survey), researchers can study not all people (general population, population), but only a certain sample. For example, even if we are studying a relatively small group of people, such as those suffering from a particular disease, it is still very unlikely that we have the appropriate resources or the need to test every patient. Instead, it is common to test a sample from the population because it is more convenient and less time consuming. If so, how do we know that the results obtained from the sample are representative of the entire group? Or, to use professional terminology, can we be sure that our research correctly describes the entire population, the sample we used?

To answer this question, it is necessary to determine the statistical significance of the test results. Statistical significance (Significant level, abbreviated Sig.), or /7-significance level (p-level) - is the probability that a given result correctly represents the population from which the study was sampled. Note that this is only probability- it is impossible to say with absolute certainty that a given study correctly describes the entire population. IN best case scenario Based on the level of significance, one can only conclude that this is very likely. Thus, the next question inevitably arises: what level of significance must be before a given result can be considered a correct characterization of the population?

For example, at what probability value are you willing to say that such chances are enough to take a risk? What if the odds are 10 out of 100 or 50 out of 100? What if this probability is higher? What about odds like 90 out of 100, 95 out of 100, or 98 out of 100? For a situation involving risk, this choice is quite problematic, because it depends on the personal characteristics of the person.

In psychology, it is traditionally believed that a 95 or more chance out of 100 means that the probability of the results being correct is high enough for them to be generalizable to the entire population. This figure was established in the process of scientific and practical activity - there is no law according to which it should be chosen as a guideline (and indeed, in other sciences sometimes other values ​​of the significance level are chosen).

In psychology, this probability is operated in a somewhat unusual way. Instead of the probability that the sample represents the population, the probability that the sample doesn't represent population. In other words, it is the probability that the observed relationship or differences are random and not a property of the population. So, instead of saying there is a 95 in 100 chance that the results of a study are correct, psychologists say that there is a 5 in 100 chance that the results are wrong (just as a 40 in 100 chance that the results are correct means a 60 in 100 chance in favor of their incorrectness). The probability value is sometimes expressed as a percentage, but more often it is written as a decimal fraction. For example, 10 chances out of 100 are expressed as a decimal fraction of 0.1; 5 out of 100 is written as 0.05; 1 out of 100 - 0.01. With this form of recording, the limit value is 0.05. For a result to be considered correct, its significance level must be below this number (remember, this is the probability that the result wrong describes the population). To get the terminology out of the way, let's add that the “probability of the result being incorrect” (which is more correctly called significance level) usually denoted Latin letter R. Descriptions of experimental results usually include a summary statement such as “the results were significant at the confidence level (R(p) less than 0.05 (i.e. less than 5%).

Thus, the significance level ( R) indicates the likelihood that the results Not represent the population. Traditionally in psychology, it is believed that the results reliably reflect big picture, if value R less than 0.05 (i.e. 5%). However, this is only a probabilistic statement, and not at all an unconditional guarantee. In some cases this conclusion may not be correct. In fact, we can calculate how often this might happen if we look at the magnitude of the significance level. At a significance level of 0.05, 5 out of 100 times the results are likely to be incorrect. 11a at first glance it seems that this is not very common, but if you think about it, then 5 chances out of 100 is the same as 1 out of 20. In other words, in one out of every 20 cases the result will be incorrect. Such odds do not seem particularly favorable, and researchers should beware of committing errors of the first kind. This is the name for the error that occurs when researchers think they have discovered real results, but in fact there are none. The opposite error, which consists in researchers believing that they have not found a result when in fact there is one, is called errors of the second type.

These errors arise because the possibility that the statistical analysis performed cannot be ruled out. The probability of error depends on the level of statistical significance of the results. We have already noted that for a result to be considered correct, the significance level must be below 0.05. Of course, some results are more low level, and it is not uncommon to find results as low as 0.001 (a value of 0.001 indicates that the results have a 1 in 1000 chance of being wrong). How less value p, the stronger our confidence in the correctness of the results.

In table 7.2 shows the traditional interpretation of significance levels about the possibility of statistical inference and the rationale for the decision about the presence of a relationship (differences).

Table 7.2

Traditional interpretation of significance levels used in psychology

Based on the experience of practical research, it is recommended: in order to avoid errors of the first and second types as much as possible, when drawing important conclusions, decisions should be made about the presence of differences (connections), focusing on the level R n sign.

Statistical test(Statistical Test - it is a tool for determining the level of statistical significance. This is a decisive rule that ensures that a true hypothesis is accepted and a false hypothesis is rejected with high probability.

Statistical criteria also denote the method for calculating a certain number and the number itself. All criteria are used with one main goal: define significance level the data they analyze (i.e., the likelihood that the data reflects a true effect that correctly represents the population from which the sample is drawn).

Some tests can only be used for normally distributed data (and if the trait is measured on an interval scale) - these tests are usually called parametric. Using other criteria, you can analyze data with almost any distribution law - they are called nonparametric.

Parametric criteria are criteria that include distribution parameters in the calculation formula, i.e. means and variances (Student's t-test, Fisher's F-test, etc.).

Nonparametric criteria are criteria that do not include distribution parameters in the formula for calculating distribution parameters and are based on operating with frequencies or ranks (criterion Q Rosenbaum criterion U Manna - Whitney

For example, when we say that the significance of the differences was determined by the Student's t-test, we mean that the Student's t-test method was used to calculate the empirical value, which is then compared with the tabulated (critical) value.

By the ratio of the empirical (calculated by us) and critical values ​​of the criterion (tabular) we can judge whether our hypothesis is confirmed or refuted. In most cases, in order for us to recognize the differences as significant, it is necessary that the empirical value of the criterion exceeds the critical value, although there are criteria (for example, the Mann-Whitney test or the sign test) in which we must adhere to the opposite rule.

In some cases, the calculation formula for the criterion includes the number of observations in the sample under study, denoted as P. Using a special table, we determine what level of statistical significance of differences a given empirical value corresponds to. In most cases, the same empirical value of the criterion may be significant or insignificant depending on the number of observations in the sample under study ( P ) or from the so-called number of degrees of freedom , which is denoted as v (g>) or how df (Sometimes d).

Knowing P or the number of degrees of freedom, using special tables (the main ones are given in Appendix 5) we can determine the critical values ​​of the criterion and compare the obtained empirical value with them. This is usually written like this: “when n = 22 critical values ​​of the criterion are t St = 2.07" or "at v (d) = 2 critical values ​​of the Student’s test are = 4.30”, etc.

Typically, preference is still given to parametric criteria, and we adhere to this position. They are considered to be more reliable and can provide more information and deeper analysis. As for the complexity of mathematical calculations, when using computer programs this difficulty disappears (but some others appear, however, quite surmountable).

• In this textbook we do not consider in detail the problem of statistical
• hypotheses (null - R0 and alternative - Hj) and statistical decisions made, since psychology students study this separately in the discipline “Mathematical methods in psychology”. In addition, it should be noted that when preparing a research report (coursework or thesis, publications) statistical hypotheses and statistical solutions, as a rule, are not given. Usually, when describing the results, they indicate the criterion, provide the necessary descriptive statistics (means, sigma, correlation coefficients, etc.), empirical values ​​of the criteria, degrees of freedom, and necessarily the p-level of significance. Then a meaningful conclusion is formulated regarding the hypothesis being tested, indicating (usually in the form of an inequality) the level of significance achieved or not achieved.

Before collecting and studying data, experimental psychologists typically decide how the data will be analyzed statistically. Often the researcher sets the level of significance, defined as a statistical value, higher than ( or lower) which contains values ​​that allow us to consider the influence of factors non-random. Researchers usually represent this level in the form of a probabilistic expression.

In many psychological experiments it can be expressed as " level 0.05" or " level 0.01" This means that random results will only occur with frequency 0.05 (1 of the times) or 0.01 (1 in 100 times). Results of statistical data analysis that satisfy a pre-established criterion ( be it 0.05, 0.01 or even 0.001), are referred to below as statistically significant.

It should be noted that the result may not be statistically significant, but still be of some interest. Often, especially in preliminary studies or experiments involving a small number of subjects or with a limited number of observations, the results may not reach the level of statistical significance, but suggest that in further studies, with more precise control and with a larger number of observations, they will become more reliable . At the same time, the experimenter must be very careful in his desire to purposefully change the experimental conditions in order to achieve desired result at any cost.

In another example of a 2x2 plan Ji used two types of subjects and two types of tasks to study the influence of specialized knowledge on the memorization of information.

In his study Ji studied memorizing numbers and chess pieces ( variable A) children in chairs RECARO Young Sport and adults ( variable B), that is, according to the 2x2 plan. The children were 10 years old and good at chess, while the adults were new to the game. In the first task, you had to remember the location of the pieces on the board, as it might be during a normal game, and restore it after the pieces were removed. Another part of this task required memorizing a standard series of numbers, as is usually done when determining IQ.

It turns out that specialized knowledge, such as knowing how to play chess, makes it easier to remember information relevant to this area, but does not have much effect on remembering numbers. Adults who are not too experienced in wisdom the oldest game, remember fewer figures, but are more successful in memorizing numbers.

In the text of the report Ji gives statistical analysis, which mathematically confirms the presented results.

The 2x2 design is the simplest of all factorial designs. Increasing the number of factors or levels individual factors significantly complicates these plans.

Statistical reliability is essential in the FCC's calculation practice. It was noted earlier that from the same population multiple samples can be selected:

If they are selected correctly, then their average indicators and the indicators of the general population differ slightly from each other in the magnitude of the representativeness error, taking into account the accepted reliability;

If they are selected from different populations, the difference between them turns out to be significant. Statistics is all about comparing samples;

If they differ insignificantly, unprincipally, insignificantly, i.e., they actually belong to the same general population, the difference between them is called statistically unreliable.

Statistically reliable A sample difference is a sample that differs significantly and fundamentally, that is, it belongs to different general populations.

At the FCC, assessing the statistical significance of sample differences means solving a set practical problems. For example, the introduction of new teaching methods, programs, sets of exercises, tests, control exercises is associated with their experimental testing, which should show that the test group is fundamentally different from the control group. Therefore, special statistical methods, called statistical significance criteria, allowing to detect the presence or absence of a statistically significant difference between samples.

All criteria are divided into two groups: parametric and non-parametric. Parametric criteria require the presence of a normal distribution law, i.e. This means the mandatory determination of the main indicators of the normal law - the arithmetic mean and the standard deviation s. Parametric criteria are the most accurate and correct. Nonparametric tests are based on rank (ordinal) differences between sample elements.

Here are the main criteria for statistical significance used in the FCC practice: Student's test and Fisher's test.

Student's t test named after the English scientist K. Gosset (Student - pseudonym), who discovered this method. Student's t test is parametric and is used for comparison absolute indicators samples. Samples may vary in size.

Student's t test is defined like this.

1. Find the Student t test using the following formula:

where are the arithmetic averages of the compared samples; t 1, t 2 - errors of representativeness identified based on the indicators of the compared samples.

2. Practice at the FCC has shown that for sports work it is enough to accept the reliability of the account P = 0.95.

For counting reliability: P = 0.95 (a = 0.05), with the number of degrees of freedom

k = n 1 + n 2 - 2 using the table in Appendix 4 we find the value of the limit value of the criterion ( t gr).

3. Based on the properties of the normal distribution law, the Student’s criterion compares t and t gr.

We draw conclusions:

if t t gr, then the difference between the compared samples is statistically significant;

if t t gr, then the difference is statistically insignificant.

For researchers in the field of FCS, assessing statistical significance is the first step in solving a specific problem: whether the samples being compared are fundamentally or non-fundamentally different from each other. The next step is to evaluate this difference from a pedagogical point of view, which is determined by the conditions of the task.

Let's consider the application of the Student test using a specific example.

Example 2.14. A group of 18 subjects was assessed for heart rate (bpm) before x i and after y i warm-up.

Assess the effectiveness of the warm-up based on heart rate. Initial data and calculations are presented in table. 2.30 and 2.31.

Table 2.30

Processing heart rate indicators before warming up

The errors for both groups coincided, since the sample sizes are equal (the same group is studied at different conditions), and the standard deviations were s x = s y = 3 beats/min. Let's move on to defining the Student's test:

We set the reliability of the account: P = 0.95.

Number of degrees of freedom k 1 = n 1 + n 2 - 2 = 18 + 18-2 = 34. From the table in Appendix 4 we find t gr= 2,02.

Statistical inference. Since t = 11.62, and the boundary t gr = 2.02, then 11.62 > 2.02, i.e. t > t gr, therefore the difference between the samples is statistically significant.

Pedagogical conclusion. It was found that in terms of heart rate the difference between the state of the group before and after warm-up is statistically significant, i.e. significant, fundamental. So, based on the heart rate indicator, we can conclude that the warm-up is effective.

Fisher criterion is parametric. It is used when comparing sample dispersion rates. This usually means a comparison in terms of stability of sports performance or stability of functional and technical indicators in practice physical culture and sports. Samples can be of different sizes.

The Fisher criterion is defined in the following sequence.

1. Find the Fisher criterion F using the formula

where , are the variances of the compared samples.

The conditions of the Fisher criterion stipulate that in the numerator of the formula F there is a large dispersion, i.e. the number F is always greater than one.

We set the calculation reliability: P = 0.95 - and determine the number of degrees of freedom for both samples: k 1 = n 1 - 1, k 2 = n 2 - 1.

Using the table in Appendix 4, we find the limit value of criterion F gr.

Comparison of F and F criteria gr allows us to formulate conclusions:

if F > F gr, then the difference between the samples is statistically significant;

if F< F гр, то различие между выборками статически недо­стоверно.

Let's give a specific example.

Example 2.15. Let's analyze two groups of handball players: x i (n 1= 16 people) and y i (p 2 = 18 people). These groups of athletes were studied for the take-off time (s) when throwing the ball into the goal.

Are the repulsion indicators of the same type?

Initial data and basic calculations are presented in table. 2.32 and 2.33.

Table 2.32

Processing of repulsion indicators of the first group of handball players

Let us define the Fisher criterion:

According to the data presented in the table of Appendix 6, we find Fgr: Fgr = 2.4

Let us pay attention to the fact that the table in Appendix 6 lists the numbers of degrees of freedom of both greater and lesser dispersion when approaching large numbers gets rougher. Thus, the number of degrees of freedom of the larger dispersion follows in this order: 8, 9, 10, 11, 12, 14, 16, 20, 24, etc., and the smaller one - 28, 29, 30, 40, 50, etc. d.

This is explained by the fact that as the sample size increases, the differences in the F-test decrease and it is possible to use tabular values ​​that are close to the original data. So, in example 2.15 =17 is absent and we can take the value closest to it k = 16, from which we obtain Fgr = 2.4.

Statistical inference. Since Fisher's test F= 2.5 > F= 2.4, the samples are statistically distinguishable.

Pedagogical conclusion. The values ​​of the take-off time (s) when throwing the ball into the goal for handball players of both groups differ significantly. These groups should be considered different.

Further research should reveal the reason for this difference.

Example 2.20.(on the statistical reliability of the sample ). Has the football player's qualifications improved if the time (s) from giving the signal to kicking the ball at the beginning of the training was x i , and at the end y i .

Initial data and basic calculations are given in table. 2.40 and 2.41.

Table 2.40

Processing time indicators from giving a signal to hitting the ball at the beginning of training

Let us determine the difference between groups of indicators using the Student’s criterion:

With reliability P = 0.95 and degrees of freedom k = n 1 + n 2 - 2 = 22 + 22 - 2 = 42, using the table in Appendix 4 we find t gr= 2.02. Since t = 8.3 > t gr= 2.02 - the difference is statistically significant.

Let us determine the difference between groups of indicators using Fisher’s criterion:

According to the table in Appendix 2, with reliability P = 0.95 and degrees of freedom k = 22-1 = 21, the value F gr = 21. Since F = 1.53< F гр = = 2,1, различие в рассеивании исходных данных статистически недостоверно.

Statistical inference. According to the arithmetic average, the difference between groups of indicators is statistically significant. In terms of dispersion (dispersion), the difference between groups of indicators is statistically unreliable.

Pedagogical conclusion. The football player's qualifications have improved significantly, but attention should be paid to the stability of his testimony.

Preparing for work

Before conducting this laboratory work in the discipline “Sports Metrology” all students in the study group must form work teams of 3-4 students each, to jointly complete the work assignment of all laboratory work.

In preparation for work read the relevant sections of the recommended literature (see section 6 of the data methodological instructions) and lecture notes. Study sections 1 and 2 for this laboratory work, as well as the work assignment for it (section 4).

Prepare a report form on standard sheets of A4 size writing paper and fill it with the materials necessary for the work.

The report must contain :

Title page indicating the department (UC and TR), study group, last name, first name, patronymic of the student, number and title of laboratory work, date of its completion, as well as last name, academic degree, academic title and position of the teacher accepting the job;

Goal of the work;

Formulas with numerical values ​​explaining intermediate and final results computing;

Tables of measured and calculated values;

Required by assignment graphic material;

Brief conclusions based on the results of each stage of the work assignment and in general on the work performed.

All graphs and tables are drawn carefully using drawing tools. Conditional graphic and letter designations must comply with GOST standards. It is allowed to prepare a report using computer technology.

Work assignment

Before carrying out all measurements, each member of the team must study the rules of use sports game Darts given in Appendix 7, which are necessary for carrying out the following stages of research.

Stage I of research“Study of the results of hitting the target of the sport game Darts by each member of the team for compliance normal law distributions according to criterion χ 2 Pearson and criterion of three sigma"

1. measure (test) your (personal) speed and coordination of actions, by throwing darts 30-40 times at a circular target in the sports game Darts.

2. Results of measurements (tests) x i(with glasses) arrange in the form variation series and enter into table 4.1 (columns , do all necessary calculations, fill out the necessary tables and draw appropriate conclusions regarding the compliance of the received empirical distribution the normal distribution law, by analogy with similar calculations, tables and conclusions of example 2.12, given in section 2 of these guidelines on pages 7 -10.

Table 4.1

Correspondence of the speed and coordination of the subjects’ actions to the normal distribution law

No.										rounded
…
…
Total

II – stage of research

“Assessment of the average indicators of the general population of hits on the target of the sport game Darts of all students of the study group based on the results of measurements of members of one team”

Assess the average indicators of speed and coordination of actions of all students in the study group (according to the list of the study group in the class magazine) based on the results of hitting the target of the Darts sport game of all team members, obtained at the first stage of research of this laboratory work.

1. Document the results of measurements of speed and coordination of actions when throwing darts at a circular target in the sports game Darts of all members of your team (2 - 4 people), who represent a sample of measurement results from the general population (measurement results of all students in a study group - for example, 15 people), entering them in the second and third columns Table 4.2.

Table 4.2

Processing indicators of speed and coordination of actions

brigade members

No.
…
…
Total

In table 4.2 under should be understood , matched average score (see calculation results in Table 4.1) members of your team ( , obtained at the first stage of research. It should be noted that, usually, Table 4.2 contains the calculated average value of the measurement results obtained by one member of the team at the first stage of research , since the likelihood that the measurement results of different team members will coincide is very small. Then, as a rule, the values in the column Table 4.2 for each row - equal to 1, A in the line “Total " columns " ", is written the number of members of your team.

2. Perform all the necessary calculations to fill out table 4.2, as well as other calculations and conclusions similar to the calculations and conclusions of example 2.13 given in the 2nd section of this methodological development on pages 13-14. It should be kept in mind when calculating the representativeness error "m" it is necessary to use formula 2.4 given on page 13 of this methodological development, since the sample is small (n, and the number of elements of the general population N is known, and is equal to the number of students in the study group, according to the list of the journal of the study group.

III – stage of research

Evaluation of the effectiveness of the warm-up according to the indicator “Speed ​​and coordination of actions” by each team member using the Student’s t-test

To evaluate the effectiveness of the warm-up for throwing darts at the target of the sports game "Darts", performed at the first stage of research of this laboratory work, by each member of the team according to the indicator "Speed ​​and coordination of actions", using the Student's criterion - a parametric criterion for the statistical reliability of the empirical distribution law to the normal distribution law .

… Total

2. variances and RMS , results of measurements of the indicator “Speed ​​and coordination of actions” based on the results of warm-up, given in table 4.3, (see similar calculations given immediately after table 2.30 of example 2.14 on page 16 of this methodological development).

3. Each member of the work team measure (test) your (personal) speed and coordination of actions after warming up,

… Total

5. Perform average calculations variances and RMS ,results of measurements of the indicator “Speed ​​and coordination of actions” after warm-up, given in table 4.4, write down the overall measurement result based on the warm-up results (see similar calculations given immediately after table 2.31 of example 2.14 on page 17 of this methodological development).

6. Perform all necessary calculations and conclusions similar to the calculations and conclusions of example 2.14 given in the 2nd section of this methodological development on pages 16-17. It should be kept in mind when calculating the representativeness error "m" it is necessary to use formula 2.1 given on page 12 of this methodological development, since the sample is n and the number of elements in the population N ( is unknown.

IV – stage of research

Assessment of the uniformity (stability) of the indicators “Speedness and coordination of actions” of two team members using the Fisher criterion

Assess the uniformity (stability) of the indicators “Speedness and coordination of actions” of two team members using the Fisher criterion, based on the measurement results obtained at the third stage of research in this laboratory work.

To do this you need to do the following.

Using the data from tables 4.3 and 4.4, the results of calculating variances from these tables obtained at the third stage of research, as well as the methodology for calculating and applying the Fisher criterion for assessing the uniformity (stability) of sports indicators, given in example 2.15 on pages 18-19 of this methodological development, draw appropriate statistical and pedagogical conclusions.

V – stage of research

Assessment of groups of indicators “Speedness and coordination of actions” of one team member before and after warm-up