Task 3. Five preschoolers are presented with a test. The time for solving each task is fixed. Will there be statistically significant differences between the time to solve the first three tasks of the test?

No. of subjects

Reference material

This task is based on the theory of analysis of variance. AT general case, the task of analysis of variance is to identify those factors that have a significant impact on the result of the experiment. Analysis of variance can be used to compare means of several samples if the number of samples is more than two. For this purpose, one-way analysis of variance serves.

In order to solve the tasks set, the following is adopted. If the variances of the obtained values ​​of the optimization parameter in the case of the influence of factors differ from the variances of the results in the absence of the influence of factors, then such a factor is recognized as significant.

As can be seen from the formulation of the problem, methods for testing statistical hypotheses are used here, namely, the problem of testing two empirical variances. Therefore, the analysis of variance is based on the verification of variances by the Fisher criterion. In this task, it is necessary to check whether the differences between the time for solving the first three tasks of the test by each of the six preschoolers are statistically significant.

The null (basic) hypothesis is called H o. The essence of e is reduced to the assumption that the difference between the compared parameters is zero (hence the name of the hypothesis - zero) and that the observed differences are random.

A competing (alternative) hypothesis is called H 1 , which contradicts the null one.

Decision:

Using the method of analysis of variance at a significance level of α = 0.05, we will test the null hypothesis (Hо) about the existence of statistically significant differences between the time of solving the first three tasks of the test in six preschoolers.

Consider the task condition table, in which we find the average time to solve each of the three test tasks

No. of subjects

Factor levels

Time to solve the first task of the test (in sec.).

Time to solve the second task of the test (in sec.).

Time to solve the third task of the test (in sec.).

Group average

Finding the overall average:

In order to take into account the significance of the time differences of each test, the total sample variance is divided into two parts, the first of which is called the factor variance, and the second is the residual

Calculate the total sum of squared deviations of the variant from the total average using the formula

or , where p is the number of time measurements for solving test tasks, q is the number of subjects. To do this, we will make a table of squares option

No. of subjects

Factor levels

Time to solve the first task of the test (in sec.).

Time to solve the second task of the test (in sec.).

Time to solve the third task of the test (in sec.).

Research usually begins with some assumption, requiring verification with the involvement of facts. This assumption - a hypothesis - is formulated in relation to the connection of phenomena or properties in a certain set of objects.

To test such assumptions on the facts, it is necessary to measure the corresponding properties of their carriers. But it is impossible to measure anxiety in all women and men, just as it is impossible to measure aggressiveness in all adolescents. Therefore, when conducting a study, they are limited to only a relatively small group of representatives of the relevant populations of people.

Population- this is the whole set of objects in relation to which a research hypothesis is formulated.

For example, all men; or all women; or all the inhabitants of a city. The general populations in relation to which the researcher is going to draw conclusions based on the results of the study may be smaller in number and more modest, for example, all first-graders of a given school.

Thus, the general population is, although not infinite in number, but, as a rule, a multitude of potential subjects inaccessible for continuous research.

Sample or sample population- this is a group of objects limited in number (in psychology - subjects, respondents), specially selected from the general population to study its properties. Accordingly, the study of the properties of the general population on a sample is called selective research. Almost all psychological studies are selective, and their conclusions apply to general populations.

Thus, after the hypothesis is formulated and the corresponding general populations are determined, the researcher faces the problem of organizing the sample. The sample should be such that the generalization of the conclusions of the sample study is justified - generalization, their distribution to the general population. The main criteria for the validity of the conclusions of the study— these are the representativeness of the sample and the statistical validity of the (empirical) results.

Sample representativeness- in other words, its representativeness is the ability of the sample to represent the studied phenomena quite fully - from the point of view of their variability in the general population.

Of course, only the general population can give a complete picture of the phenomenon under study, in all its range and nuances of variability. Therefore, representativeness is always limited to the extent that the sample is limited. And it is the representativeness of the sample that is the main criterion in determining the boundaries of the generalization of the findings of the study. Nevertheless, there are techniques that allow obtaining a representative sample sufficient for the researcher (These techniques are studied in the course "Experimental Psychology").


The first and main technique is a simple random (randomized) selection. It involves ensuring that each member of the population has an equal chance of being included in the sample. Random selection provides the possibility of getting into the sample of the most diverse representatives of the general population. At the same time, special measures are taken to exclude the appearance of any regularity in the selection. And this allows us to hope that in the end, in the sample, the studied property will be represented, if not in all, then in its maximum possible variety.

The second way to ensure representativeness is stratified random selection, or selection according to the properties of the general population. It involves a preliminary determination of those qualities that may affect the variability of the property being studied (this may be gender, income level or education, etc.). Then the percentage ratio of the number of groups (strata) differing in these qualities in the general population is determined and an identical percentage ratio of the corresponding groups in the sample is provided. Further, in each subgroup of the sample, the subjects are selected according to the principle of simple random selection.

Statistical validity, or statistical significance, the results of the study are determined using the methods of statistical inference.

Are we insured against making mistakes when making decisions, with certain conclusions from the results of the study? Of course not. After all, our decisions are based on the results of a study of a sample population, as well as on the level of our psychological knowledge. We are not completely immune from mistakes. In statistics, such errors are considered acceptable if they occur no more than in one case out of 1000 (error probability α = 0.001 or the associated value of the confidence probability of the correct conclusion p = 0.999); in one case out of 100 (error probability α = 0.01 or the associated value of the confidence probability of the correct conclusion p = 0.99) or in five cases out of 100 (error probability α = 0.05 or the associated value of the confidence probability of the correct output p=0.95). It is at the last two levels that it is customary to make decisions in psychology.

Sometimes, speaking of statistical significance, the concept of "significance level" (denoted as α) is used. The numerical values ​​of p and α complement each other up to 1,000 - a complete set of events: either we did correct conclusion or we are wrong. These levels are not calculated, they are set. The level of significance can be understood as a kind of "red" line, the intersection of which will allow us to speak of this event as non-random. In every competent scientific report or publication, the conclusions drawn must be accompanied by an indication of the p or α values ​​at which the conclusions are made.

Methods of statistical inference are discussed in detail in the course "Mathematical Statistics". For now, we only note that they impose certain requirements on the number, or sample size.

Unfortunately, there are no strict recommendations on the preliminary determination of the required sample size. Moreover, the researcher usually receives an answer to the question about the necessary and sufficient number of it too late - only after analyzing the data of the already surveyed sample. However, the most general recommendations can be formulated:

1. The largest sample size is needed when developing a diagnostic technique - from 200 to 1000-2500 people.

2. If it is necessary to compare 2 samples, their total number must be at least 50 people; the number of compared samples should be approximately the same.

3. If the relationship between any properties is being studied, then the sample size should be at least 30-35 people.

4. The more variability of the studied property, the larger should be the sample size. Therefore, variability can be reduced by increasing the homogeneity of the sample, for example, by sex, age, etc. This, of course, reduces the possibility of generalizing conclusions.

Dependent and independent samples. A typical research situation is when a property of interest to the researcher is studied on two or more samples for the purpose of their further comparison. These samples may be in different proportions, depending on the procedure for their organization. Independent samples are characterized by the fact that the probability of selection of any subject of one sample does not depend on the selection of any of the subjects of another sample. Against, dependent samples are characterized by the fact that each subject of one sample is matched by a certain criterion with a subject from another sample.

In the general case, dependent samples involve a pairwise selection of subjects in the compared samples, and independent samples - an independent selection of subjects.

It should be noted that the cases of “partially dependent” (or “partially independent”) samples are not allowed: this violates their representativeness in an unpredictable way.

In conclusion, we note that two paradigms of psychological research can be distinguished.

So-called R-methodology involves the study of the variability of a certain property (psychological) under the influence of some influence, factor or other property. The sample is a set of subjects.

Another approach Q-methodology, involves the study of the variability of the subject (single) under the influence of various stimuli (conditions, situations, etc.). It corresponds to the situation when the sample is a set of stimuli.

When justifying a statistical inference, one should decide where is the line between accepting and rejecting the null hypothesis? Due to the presence of random influences in the experiment, this boundary cannot be drawn absolutely exactly. It is based on the concept significance level. Significance level is the probability of incorrectly rejecting the null hypothesis. Or, in other words, significance level - is the probability of a Type I error in decision making. To denote this probability, as a rule, they use either the Greek letter α, or latin letter R. In what follows, we will use the letter R.

Historically, in the applied sciences that use statistics, and in particular in psychology, it is believed that the lowest level of statistical significance is the level p = 0.05; sufficient - level R= 0.01 and top level p = 0.001. Therefore, in the statistical tables that are given in the appendix to textbooks on statistics, tabular values ​​\u200b\u200bare usually given for the levels p = 0,05, p = 0.01 and R= 0.001. Sometimes tabular values ​​are given for levels R - 0.025 and p = 0,005.

The values ​​0.05, 0.01 and 0.001 are the so-called standard levels of statistical significance. In the statistical analysis of experimental data, the psychologist, depending on the objectives and hypotheses of the study, must choose the required level of significance. As you can see, here is the largest value, or bottom line the level of statistical significance is 0.05 - this means that five errors are allowed in a sample of one hundred elements (cases, subjects) or one error out of twenty elements (cases, subjects). It is believed that neither six, nor seven, nor large quantity times out of a hundred we can't be wrong. The cost of such mistakes would be too high.

Note that in modern statistical software packages on computers, not standard significance levels are used, but levels calculated directly in the process of working with the corresponding statistical method. These levels, denoted by the letter R, may have different numeric expression in the range from 0 to 1, for example, p = 0,7, R= 0.23 or R= 0.012. It is clear that in the first two cases the significance levels obtained are too high and it is impossible to say that the result is significant. At the same time, in the latter case, the results are significant at the level of 12 thousandths. This is a valid level.

The rule for accepting a statistical conclusion is as follows: on the basis of the experimental data obtained, the psychologist calculates the so-called empirical statistics, or empirical value, using the statistical method chosen by him. It is convenient to denote this value as H emp . Then empirical statistics H emp compared with two critical values, which correspond to the 5% and 1% significance levels for the selected statistical method and which are denoted as H kr . Quantities H kr are found for a given statistical method according to the corresponding tables given in the appendix to any textbook on statistics. These quantities, as a rule, are always different and, for convenience, they can be further referred to as H cr1 and H kr2 . Critical values ​​found from the tables H cr1 and H kr2 It is convenient to represent in the following standard notation:

We emphasize, however, that we have used the notation H emp and H kr as an abbreviation of the word "number". In all statistical methods, their symbolic designations of all these quantities are accepted: both the empirical value calculated by the corresponding statistical method, and the critical quantities found from the corresponding tables. For example, when calculating Spearman's rank correlation coefficient from the table of critical values ​​of this coefficient, the following values ​​of critical values ​​were found, which for this method are denoted by the Greek letter ρ ("ro"). So for p = 0.05 value found according to the table ρ kr 1 = 0.61 and for p = 0.01 value ρ kr 2 = 0,76.

In the standard notation adopted below, it looks like this:

Now we need to compare our empirical value with the two critical values ​​found in the tables. This is best done by placing all three numbers on the so-called "significance axis". The “significance axis” is a straight line, at the left end of which is 0, although it, as a rule, is not marked on this straight line itself, and the number series increases from left to right. In fact, this is the usual school x-axis OH Cartesian coordinate system. However, the peculiarity of this axis is that three sections, “zones”, are distinguished on it. One extreme zone is called the zone of insignificance, the second extreme zone is called the zone of significance, and the intermediate zone is called the zone of uncertainty. The boundaries of all three zones are H cr1 for p = 0.05 and H kr2 for p = 0.01, as shown in the figure.

Depending on the decision rule (inference rule) prescribed in this statistical method, two options are possible.

Option 1: The alternative hypothesis is accepted if H emp ≥H kr .

Or the second option: the alternative hypothesis is accepted if H emp ≤H kr .

Counted H emp according to some statistical method, it must necessarily fall into one of the three zones.

If the empirical value falls into the zone of insignificance, then the hypothesis H 0 about the absence of differences is accepted.

If a H emp fell into the zone of significance, the alternative hypothesis H 1 is accepted about there are differences, and the hypothesis H 0 is rejected.

If a H emp falls into the zone of uncertainty, the researcher faces a dilemma. So, depending on the importance of the problem being solved, he can consider the obtained statistical estimate reliable at the level of 5%, and thus accept the hypothesis H 1, rejecting the hypothesis H 0 , or - unreliable at the level of 1%, thus accepting the hypothesis H 0 . We emphasize, however, that this is exactly the case when a psychologist can make mistakes of the first or second kind. As discussed above, in these circumstances it is best to increase the sample size.

We also emphasize that the value H emp can exactly match either H cr1 or H kr2 . In the first case, we can assume that the estimate is reliable exactly at the level of 5% and accept the hypothesis H 1 , or, conversely, accept the hypothesis H 0 . In the second case, as a rule, the alternative hypothesis H 1 about the presence of differences is accepted, and the hypothesis H 0 is rejected.

RELIABILITY STATISTICAL

- English credibility/validity, statistical; German Validitat, statistische. Consistency, objectivity, and lack of ambiguity in a statistical test or in C.L. set of measurements. D. s. can be tested by repeating the same test (or questionnaire) on the same subject to see if the same results are obtained; or comparison various parts tests that are supposed to measure the same object.

Antinazi. Encyclopedia of Sociology, 2009

See what "STATISTICAL RELIABILITY" is in other dictionaries:

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    RELIABILITY OF DIFFERENCE (similarity)- analytical and statistical procedure for establishing the level of significance of differences or similarities between samples according to the studied indicators (variables) ... Modern educational process: basic concepts and terms

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    REPORTING, STATISTICAL- a form of state statistical observation, in which the relevant authorities receive from enterprises (organizations and institutions) the information they need in the form of legally prescribed reporting documents (statistical reports) for ... Big Economic Dictionary

    The science that studies the methods of systematic observation of mass phenomena social life human, compiling their numerical descriptions and scientific processing of these descriptions. Thus, theoretical statistics is a science ... ... encyclopedic Dictionary F. Brockhaus and I.A. Efron

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  • Research in mathematics and mathematics in research: Methodical collection on research activities of students, Borzenko V.I.. The collection presents methodological developments applicable in the organization research activities students. The first part of the collection is devoted to the application of the research approach in…

Statistical validity is of significant importance in the settlement practice of the FCC. It was noted earlier that many samples can be selected from the same population:

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

If they are chosen from different general populations, the difference between them turns out to be significant. Comparison of samples is commonly considered in statistics;

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

statistically significant a sample difference is a sample that differs significantly and fundamentally, i.e., belongs to different general populations.

In the FCC, assessing the statistical significance of sample differences means solving many practical problems. For example, the introduction of new teaching methods, programs, sets of exercises, tests, control exercises is associated with their experimental verification, which should show that the test group is fundamentally different from the control group. Therefore, special statistical methods are used, called statistical significance criteria, 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 provide for the mandatory presence of a normal distribution law, i.e. this refers to 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 criteria are based on rank (ordinal) differences between the elements of the samples.

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

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

Student's criterion is defined like this.

1. We find Student's criterion t according to the following formula:


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

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

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

k \u003d n 1 + p 2 - 2 according to the table in Appendix 4, we find the value of the boundary value of the criterion ( t gr).

3. Based on the properties of the normal distribution law, 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 not statistically significant.

For researchers in the field of FCC, the assessment of statistical significance is the first step in solving a specific problem: whether the compared samples differ fundamentally or not. The next step is to evaluate this difference from a pedagogical point of view, which is determined by the condition of the problem.

Consider the application of the Student's criterion on a specific example.

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

Evaluate the effectiveness of the warm-up in terms of heart rate. The initial data and calculations are presented in table. 2.30 and 2.31.

Table 2.30

Processing heart rate data before warm-up


The errors for both groups coincided, since the sample sizes are equal (the same group is studied under different conditions), and the standard deviations were s x = s y = 3 bpm. Let's move on to the definition of Student's criterion:

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

The number of degrees of freedom k 1 \u003d n 1 + p 2 - 2 \u003d 18 + 18-2 \u003d 34. According to the table in Appendix 4, we find t gr= 2,02.

Statistical inference. Since t \u003d 11.62, and the boundary t gr \u003d 2.02, then 11.62\u003e 2.02, i.e. t > t gr, so 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 the warm-up is statistically significant, i.e. significant, important. So, according to the heart rate indicator, we can conclude that the warm-up is effective.

Fisher's criterion is parametric. It is used when comparing the scatter rates of samples. This, as a rule, means a comparison in terms of the stability of sports work or the stability of functional and technical indicators in practice. physical education and sports. Samples can be of different sizes.

The Fisher criterion is defined in the following sequence.

1. Find the Fisher Criterion F by the formula


where , are the variances of the compared samples.

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

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

According to the table of Appendix 4, we find the boundary value of the criterion F gr.

Comparison of criteria F and F gr allows us to draw the following 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 take a concrete example.

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

Are repulsion rates the same?

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's 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 in the table of Appendix 6 the enumeration of the numbers of degrees of freedom of both greater and lesser dispersion becomes coarser when approaching large numbers. So, the number of degrees of freedom of a larger dispersion follows in this order: 8, 9, 10, 11, 12, 14, 16, 20, 24, etc., and of a smaller one - 28, 29, 30, 40, 50, etc. d.

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

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

pedagogical conclusion. The values ​​of the repulsion time (s) when throwing the ball into the goal of the handball players of both groups differ significantly. These groups should be considered as different.

Further research should show what is the reason for this difference.

Example 2.20.(on the statistical significance of the sample ). Has the footballer's qualification increased 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 it was i .

The initial data and basic calculations are given in table. 2.40 and 2.41.

Table 2.40

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


Let's determine the difference between groups of indicators according to Student's criterion:

With reliability P \u003d 0.95 and degrees of freedom k \u003d n 1 + n 2 - 2 \u003d 22 + 22 - 2 \u003d 42, according to 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's determine the difference between the groups of indicators according to the Fisher criterion:


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

Statistical inference. According to the arithmetic mean, the difference between the groups of indicators is statistically significant. In terms of dispersion (dispersion), the difference between the groups of indicators is not statistically significant.

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

Preparation for work

Before this laboratory work in the discipline "Sports metrology" to all students study group it is necessary to form working teams of 3-4 students in 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 these guidelines) and lecture notes. Study sections 1 and 2 for this lab, as well as the work task for it (section 4).

Prepare a report form on standard sheets of A4 writing paper and put in it the materials necessary for work.

The report must contain :

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

Objective;

Formulas with numerical values ​​that explain the intermediate and final results of calculations;

Tables of measured and calculated values;

Required graphic material for the assignment;

Brief conclusions according to the results of each of the stages of the work task and in general on the work performed.

All graphs and tables are drawn accurately using drawing tools. Conditional graphic and alphabetic designations must comply with GOSTs. It is allowed to draw up a report using computer (computer) technology.

Work task

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

I - th stage of research"Research of the results of hitting the target of the sports game Darts by each member of the brigade for compliance with the normal distribution law according to the criterion χ 2 Pearson and the three sigma test"

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

2. Results of measurements (tests) x i(in points) arrange in the form of a variational series and enter in table 4.1 (columns , perform all the necessary calculations, fill in the necessary tables and draw the appropriate conclusions on the correspondence of the obtained empirical distribution to the normal distribution law, by analogy with similar calculations, tables and conclusions of example 2.12, given in section 2 of this guideline on pages 7-10.

Table 4.1

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

No. p / p rounded
…
…
Total

II - th stage of research

"Estimation of the average indicators of the general population of hits on the target of the sports game Darts of all students of the educational group based on the results of measurements of members of one brigade"

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

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

Table 4.2

Processing indicators of speed and coordination of actions

brigade members

No. p / p
…
…
Total

Table 4.2 under should be understood , matched average score (see the results of calculations according to table 4.1) members of your team , obtained at the first stage of research. It should be noted that, usually, in table 4.2 there is a calculated average value of the measurement results obtained by one member of the team at the first stage of the research , since the probability that the results of measurements by different members of the team will coincide is very small. Then, usually values in a column tables 4.2 for each of the rows - are 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 in 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 borne in mind when calculating the error of representativeness "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 - th stage of research

Evaluation of the effectiveness of the warm-up in terms of "Speed ​​and coordination of actions" by each member of the team using the Student's criterion

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 the research of this laboratory work, by each member of the team in terms of "Speed ​​and coordination of actions", using the Student's criterion - a parametric criterion of statistical reliability of the empirical distribution law to the normal distribution law .

… Total

2. dispersion and North Kazakhstan , the results of measurements of the indicator "Speed ​​and coordination of actions" based on the results of the 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 the warm-up,

… Total

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

6. Perform all the 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 borne in mind when calculating the error of representativeness "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 of the general population N ( is unknown.

IV - th stage of research

Evaluation of the uniformity (stability) of the indicators "Speed ​​and coordination of actions" of two members of the team using the Fisher criterion

Assess the uniformity (stability) of the indicators "Speed ​​and coordination of actions" of two members of the team using the Fisher criterion, according to the measurement results obtained at the third stage of the research of this laboratory work.

To do this, do the following.

Using the data of tables 4.3 and 4.4, the results of calculating dispersions for these tables, obtained at the third stage of the 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 - th stage of research

Evaluation of the groups of indicators "Speed ​​and coordination of actions" of one member of the team before and after the warm-up