Methods of statistical inference in mathematical statistics. Methods of mathematical statistics (2) - Abstract. Gaussian law - normal distribution law

Topics of class hours, conversations with students, parents on the prevention of crime and neglect among minors.


Class

Crime prevention

Prevention of neglect

1-2 grade

- Conversation “The rights and responsibilities of a child in the family, at school, in society”

Class hour“Responsibilities and daily routine of a schoolchild”

- "Helpline"


- Lesson “Learning to be tolerant”

3rd grade

- Game – training “What is good and what is bad?”

Lesson “My rights”

- "Helpline"


- Event “Class, parents and I are a friendly family together”

4th grade

- Information hour “Know and follow the law”

Lesson “My responsibilities”

- "Helpline"

Conversation “Why are they put on internal school registration?”


- Class hour “My home is my fortress”

5th grade

- Lesson “Steps to adulthood”

Conversation “Respect your elders, protect your younger ones”

Conversation “Problems of aggressive children”

- "Helpline"


- Library hour “So that trouble does not happen”

6th grade

- Conversation “What is the law?”

Class hour "Responsibility of minors before the law"

Lesson “Culture of behavior and communication of minors”

- "Helpline"


- Conversation " Conflict situations in family"

7th grade

- Class hour “Conscience as civic responsibility”

Lesson “Culture of Communication”

Conversation “Adolescents and Conflicts”

Conversation “Why are they put on internal school registration?”


- Conversation “How to live in peace with your parents?”

8th grade

- Class hour “The concept of offenses, forms of legal liability”

Quiz “Know and follow the law”

- "Helpline"


- Essay competition “Our marina is our parents’ home”

9th grade

- Class hour “Me and the Law”

Conversation “How to avoid becoming a victim of crime?”

- "Helpline"


- Students’ stories on the topic: “Family and family values”

Parents

(parent meetings)


- “My child is becoming difficult”

- “Rights, duties and responsibilities of parents”

- « Free time and entertainment for students"

- “Family and school are partners in education”

- “Gaming addiction is a dangerous disease”

- "Helpline"


- "Teenage Suicide"

- “Harmony family relations- the key to a happy family"

- “The lifestyle of parents is an example for children to follow”

- “The Laws of Parental Truth”

- "Helpline"


Teachers

(speeches at pedagogical councils)


- “Organs of the prevention system, their functions”

- “Student’s daily routine”


- “The cause of child suicides”

- “Forms of punishment of children without the use of cruel methods of education”


Appendix 3.

Questionnaire on the prevention of psychoactive substances for students


1) Do your parents know that you smoke?

Yes, they know - they guess - they don’t know


2) Do you have a strong urge to smoke?

Very - almost no pull - not quite


3) What does smoking give you?

Nothing - I find it difficult to answer - it’s easier to communicate with the guys


4) Who gives you money for cigarettes?

I ask for a loan - I earn it myself


5) Have you ever done something unseemly while looking for cigarettes?

Happened - yes, and not rarely - never


6) Do you drink alcohol?

Quite often - only on holidays


7) Who suggested you try?

By choice - relatives - school friends


8) How do you feel after drinking alcohol?

I want to sleep - I want to have fun - I feel nauseous - I feel brave


9) Where do you drink alcohol most often?

On the street - anywhere - at a disco


Appendix 4.

Questionnaire on the prevention of suicidal behavior for students

Express diagnostics of suicidal risk

Please answer the questions below yes or no.
FULL NAME ________________________________________________________________
1. Do you think life can lose value for a person in some situations?

2. Is life sometimes worse than death?

3. In the past I tried to die.

4. Many people love, understand and appreciate me.
5. It is possible to justify the hopelessly ill who chose voluntary death.

6. I don't think I can find myself in a hopeless situation.

7. The meaning of life is not always clear, it can sometimes be lost or found.

8. Do you think that if you find yourself in a situation where you are betrayed by your loved ones and relatives, you can move on with your life?

9. I sometimes think about my voluntary death.

10. In any situation, I will fight for my life, no matter what the cost.
Total points for the key:
Key: 1 point is awarded for answering “yes” to questions 1;2;3;5;7;9 and answering “no” to questions 4;6;8;10. Suicidal risk level Ksr = SR/10.

If the suicide risk coefficient is 0
0,2
0,4
0,6
0,8
Appendix 5.

Event for parents of teenagers on the prevention of substance abuse.

Goal: to determine ways of effective interaction between parents and children for

prevention of drug addictive behavior.

1. Focus parents’ attention on the creation and development favorable conditions for the growth and development of children in the family.

2. Conduct a diagnosis with parents to determine the definition of teenage drug addiction.

3. Give parents addresses for help.

Progress of the lesson.

Presenter's opening remarks:

Hello dear parents! Our lesson today is dedicated to the prevention of addiction to psychoactive substances. We will talk about the role of family in the prevention of drug addictive behavior. What can you, parents, specifically do for your child so that he does not have the desire to use surfactants.

What conditions promote optimal growth and development of children?

Conditions (factors) promoting personality development

How can parents create these conditions?

The work of the groups is posted on the board, read out and discussed.

Parents are invited to play out a role-playing situation.

Situation: daughter comes home late. Mother finds out she has a baby

a suspicious, in her opinion, friend appeared. My daughter spends a lot with him

time and was found to be absent from school.

What are the actions of family members (mom, dad) when having a serious conversation with their daughter? An opportunity is given to play out the tactics of constructing a conversation, the behavior of parents

Discussion:

Have everyone in this family created conditions for favorable development?

personalities?

What would you do in this situation?

What did you like about the actions, what would you do differently?

Pay attention to the need to maintain confidential

relationships, contact with the child, as an important factor in counteracting

abuse of surfactants.

2. Work on filling out the questionnaire “Questionnaire for determining adolescent

drug addiction." Everyone fills out the form individually.

After filling out the form, read the instructions. What can you do if

there are suspicions that the child is using drugs (suspicious smell,

unusual items)

3. Give addresses for help. Committee of Social Security of the Vologda Region.

Address of the institution with postal code 160035 Vologda, st. Zosimovskaya, 65

Head - Korobkina Irina Yurievna. Phone/fax 56-48-88, 56-30-33

Thank you for your cooperation! Goodbye!

Appendix 6.

Parent survey on substance abuse prevention
1. When communicating with a child, do you touch upon the topic of smoking, alcohol, or drugs?

2. How does your child respond to your questions?

3. Do you trust your child in matters related to smoking, alcohol, and drugs?

4. Do you read literature on this problem?

5. If you were offered to listen to a lecture on this problem, would you accept this offer?

6. What questions on this topic would you like answered at the parent meeting?

Appendix 7.

Memo for parents on the prevention of psychoactive substances

Dear fathers and mothers!

In order to avoid problems associated with alcohol and drug use by your children, remember:

1. You should be the closest person to your child, regardless of those difficult situations, which he can get into.

2. If a child is out of your control, do not hush up the problem, go to people and specialists to solve it.

3. If your child smokes or drinks alcohol, you are not immune from the fact that he may start taking drugs.

4. If your child is feeling bad at home, if he lives in a world of quarrels and scandals, then he may find himself in a campaign that will teach him how to escape into the world of happiness and peace with the help of drugs.

5. Observe your child's behavior and health.

6. If your child experiences unexplained nausea, agitation, delirium, or hallucinations, you need to urgently contact a specialist.

7. Try not to brush aside your own child’s questions; be fair and honest in assessing his actions and actions.

8. Remember! If a child smokes, drinks alcohol, or takes drugs, it means that you have made serious mistakes in his upbringing. Don't make them worse!

Appendix 8.

Lesson for 3 classes

“What is good and what is bad?”

Target: formation of value orientation in students, the ability to formulate moral judgments.

Tasks:


  1. Describe the concept of “good”.

  2. Describe the concept of “bad”.

  3. Highlight the main points of good and bad behavior.

  4. Create conditions for consolidating the information received.
Lesson plan:

  1. Greetings. Coverage of the main issues of the lesson.

  2. Main part.

  3. Exercise “What would I do?..”

  4. Reflection.
Progress of the lesson:

  1. Greetings. Warm-up “Dwarfs are giants.”
Instructions “I will speak and show you actions, your task is to look carefully and do everything the other way around, that is, for example, I sit down, and you... that’s right, you must remain standing. So, let's look..."

  1. Main part.
1) For a long time, people have been thinking about the question: “What is good and what is bad?” It is no coincidence that folk wisdom is passed on from generation to generation through proverbs. Look carefully at the screen, there are proverbs written here. Read them (you can have students read them aloud).

Guys, how do you understand these proverbs? (children's statements)

Well done boys! I see that you understand what it means to be a kind person.

Listen to these guys' statements.

1: If you shared it with a friend
You are your candies -
You did well
Everyone will say this.

2: You found out someone else's secret
And he smashed it right away,
It's bad, it's worse
It's even mean!

3: If you filed in front of everyone
Girl's coat
You are a cultured person
World boy!

4: If you are like a wild animal,
You immediately go to fight,
Believe me, you are not worthy
To be called a man!

5: If you warmed up the cat,
You feed the birds in the cold,
It's just beauty
That's the only way it's needed!

6: You blacked out the dog's eye
Threw the cat into a puddle.
Be sure forty times
You are worse than dogs.

7: Respect the people around you
The older ones, the younger ones too,
And then you, my friend,
They will call it good.

Now tell me, is everything right? (children answer). Right!

2) And now I’ll read you another poem, the author of which is Samuil Yakovlevich Marshak, and it’s called “Good Friends,” and after listening to it, you’ll say what good quality or bad, the author showed in this poem.

Boy Misha toils
Misha stutters.
Like others - clean, clear, -
He can't speak.
And asking him is in vain
Repeat what he says.
It's not easy for him
All words starting with "ka"
But the guys don't laugh -
Friendship is great and strong!
- You are Mishutka, don’t get lost!
Take others as an example!
Just gather your courage
And speak more boldly!
Misha said a word
And there’s no other one to be seen...
But my friends are ready
If you need to wait!

Now listen to R. Gamzatov’s poems “Beware of losing friends”

Know, my friend, the price of enmity and friendship,
Do not sin with hasty judgment.
Anger at a friend, perhaps instantaneous,
Don’t rush to pour out yet,
People, I ask you, for God's sake,
Don't be shy about your kindness.
There are not many friends on earth
Beware of losing friends!

What can you say about these lines, because the thread of friendship is easy to break, but more difficult to unite.

(children's statements)

Well done. And now we will look at one small story.

Joint work of school and family in raising children.

About the responsibility of parents for raising children.

Labor education of children in the family.

Teaching children to be thrifty.

Developing children's interest in science and technology.

How to help children with homework.

Fostering a responsible attitude towards learning in students.

Fostering children's independence and perseverance in academic work.

Raising diligence in children in the family.

Methods of instilling conscious discipline in children in the family.

On measures to encourage and punish children in the family.

Cultivating politeness and consideration in children.

Teaching children to be modest.

Cultivating respect for elders.

The importance of daily routine in raising children in a family.

The role of the family in the moral education of children.

Raising children to be honest and truthful.

Developing a sense of collectivism in children.

Fostering friendship and camaraderie in children.

Character education in children.

Developing skills and habits of cultural behavior.

About sex education of children in the family.

Healthy life - necessary condition successful raising of children in the family.

How to guide children's extracurricular reading in the family.

Hardening the child's body.

The role of the family in the development of children's sports.

Aesthetic education of children in the family.

How to develop creative talents in children.
How to develop children's interest and love for work.

Organization of a schoolchild's work corner in the family.

How to help schoolchildren choose a profession.

The state of the modern labor market and educational services.

Rules and mistakes in choosing a profession.

Features of professional self-determination of adolescents with difficulties in social adaptation.

Social and professional orientations of youth.

The situation of youth in the modern labor market.

Demand for professions in the labor market.

Employer requirements for young specialists.

Educational institutions in Kemerovo and the region.

Peculiarities of choosing a profession for children with diseases of internal organs.

Objective conditions for choosing a profession.

Interests, inclinations, abilities and their role in professional self-determination.

Prevention and resolution of conflicts in the family.

Difficult teenager. Who is he?

Prevention of drug and alcohol addiction.

Formation of achievement motivation.

Formation of learning motivation.

Psychophysiological characteristics of adolescence and adolescence.

Psychosexual development of adolescents.

Psychological characteristics of adolescents.

Psychological characteristics of children of different ages.

Sample topics for conversations with parents

Material from IOT Wiki - a project of the network social and pedagogical community "SotsObraz"

You can use these topics for individual conversations, classroom parent meetings, and also conduct electronic blogs on these topics and discuss them with parents.

1. Starting school is an important stage in a child’s life.

2. Fostering respect and love for parents, native land and the history of their people (according to national education).

3. Junior school age and its features.

4. I want and must (for crime prevention).

5. How to identify and develop children's abilities.

6. Creating an atmosphere of emotional security, warmth and love in the family.

7. Play and work in the life of children of primary school age.

8. Education of the child’s character in the family.

9. A regimen for primary schoolchildren as a way to protect health.

10. Law, family, child (moral and legal education of children in the family).

11. Fathers and sons (the role of parents’ personal example in the legal education of junior schoolchildren).

12. New in the system of national education.

13. The use of various types of arts in the aesthetic education of children at school.

14. Family walks in nature as an important factor in the environmental and physical education of children.

15. Preservation of family traditions, family heirlooms.

1. New in the system of national education.

2. The role of the family in the formation of adolescents’ conscious need for the labor system.

4. Organization of summer work and recreation for children in the family.

5. Raising a healthy child in the family. Preservation of the genotype.

6. Family opportunities in developing students’ cognitive independence.

7. The use of family traditions and holidays in patriotic education.

8. The harm of alcohol and smoking.

1. An example of parents in raising children.

2. Features of raising teenagers in the family.

3. Sexual development and methods of sex education.

4. A book in the family. Formation of reading interests in children.

5. Active forms holidays with your family.

6. Methods of vocational guidance for schoolchildren in the family.

7. Features of adolescence and taking them into account in family education.

8. Educational activities senior schoolchild and its leadership in the family.

9. The role of the family in the readiness of the younger generation to work.

10. Instilling a love for the beauty of native nature, works of art, painting, literature and music in the family.

11. Studying the roots of the family line.

12. Establishment of the principles of universal morality in the family.

1. The main directions of education in the family.

2. Psychological and pedagogical self-education of parents, as an important factor in increasing their pedagogical competence.

3. The role of family relationships and traditions in preparing high school students for family life.

Methodological development on the topic:
Sample topics for individual preventive conversations with students enrolled in various types of registration

Individual preventive work with registered children

Preview:

SAMPLE TOPICS FOR INDIVIDUAL PREVENTIVE CONVERSATIONS WITH STUDENTS,

REGISTERED

Topic of conversation, problem, questions for discussion

“School charter, rules of student conduct”

"Your successes and failures"

"Ways to resolve conflict"

"Jokes or hooliganism"

"Responsibility for misconduct"

“Rules of behavior and TB during the autumn holidays”

“Healthy lifestyle - what is it?”

“What is a person?”

"Collective help and sympathy"

"We are for a healthy lifestyle"

"Culture of behavior in in public places»

"Offence and legal responsibility"

“Why do they register with the KDN?”

“Why do they put you in high school?”

“Paralympic sports in our school”

"Administrative and criminal liability"

“Rights and responsibilities of a minor”

"Responsibility for false reports of terrorism"

"The Art of Everyday Communication"

“Relationships with classmates. Rules of conduct at school""

“Purity of spoken language. "Words are weeds"

"Rules of behavior on the street

“Responsibility for damage to school property”

“Culture of greetings and addresses to others”

“Responsibility for violating traffic rules”

"Self confidence"

“Verbal and non-verbal forms of behavior”

“Formula for choosing a profession”

“The consequences of leaving school without permission”

"Professions accessible to people with disabilities"

“Rules of conduct and TB during the winter holidays”

"Rules of conduct in public places"

“Self-control and self-demandingness”

"Safety during the winter holidays"

"My successes and failures"

“Rules of conduct for passengers in public transport”

"Willpower and Character"

"Self-Respect"

“How to avoid injuries in winter”

"Russia is my homeland"

"How I Spent My winter holidays"

"Law of the Krasnodar Territory No. 1539-KZ"

"Firecrackers and Security"

“Be able to say NO”

"Safe driving during icy conditions"

"Computer Friend or Foe"

"The place of a teenager in society"

“How to cope with a bad mood, irritation, resentment”

Quiz: “Who is the smartest person in the world?”

"A culture of speech. Profanity"

“Choose health: Paralympic sports in our school”

"Alcohol and alcohol addiction"

"What is a family for"

“How to choose a profession”

“Conflicts in our lives and ways to overcome them”

"What is politeness"

“Man is the creator of his own destiny”

"Teenager and the Law"

"Teenager and Crime"

"Misdemeanor, Misdemeanor, Crime"

"How to avoid becoming a victim of crime"

“Computer – friend or foe”

“Professions accessible to people with disabilities”

“Time for business, time for fun! »

“About honesty and the ability to keep one’s word”

"Anthem, Coat of Arms, Flag of Russia"

“Life is given for good deeds”

“Types of punishment for minors”

"Crime and Punishment"

“The role of the media in the life of society (the right to receive information)”

"Convention on the Rights of the Child"

"Energy drinks are the new drugs"

"Tender words for mom"

"Pocket Money"

"How to overcome fear of exams"

“Know how to say NO! »

"There is always a choice"

“Life is the main value of a person”

“Types of summer employment for teenagers. Forms of summer recreation and health improvement"

"Me and my street company"

"Responsibilities of a teenager in the family"

“Hard work is worthy of respect”

"Future plans"

On the topic: methodological developments, presentations and notes

This article describes the organization individual work with students enrolled in various types of registration, a coordination plan for working with students, an individual accompanying program is presented.

The regulation on chiefs - mentors of minors who are on various types of registration is created at the school to improve preventive work with students.

I present to your attention a sample card “Individual preventive work” with a registered child or a disadvantaged family, which I use in my work (at the end of each section).

Individual preventive work with parents of registered students.

Plan of individual preventive work with students registered at school.

Based on your personal professional experience I present a technology for organizing individual preventive work with students under in-school supervision.

The material describes technologies for psychological and pedagogical support of minors who have a conflict with the law. while in a children's health camp.

Conversations with parents of minors topics

21 years of experience.

Volgograd 2014

Relevance of the chosen topic:

Modern schools are faced with a number of problems: on the one hand, an increase in delinquency among minors, on the other hand, parents do not pay due attention to their children for various reasons. If earlier teachers considered the process of education in the form of a kind of triangle: school - parents - child, where the school, in close cooperation with parents, since the moral and social guidelines coincided, successfully solved the problem of education, then, unfortunately, today the school often remains in this triangle without the support of the second, parental side.

Over the past five to ten years, there has been a process of lowering the age limit for offenders. Such types of offenses as smoking, using obscene language, causing harm to health, and taking someone else's property have fallen into elementary school. New trends have emerged in the behavior of children and parents: minors leaving home, the risk of suicidal behavior in minors, cruel treatment with children, lack of parental authority in children.

In connection with the above, at present, in the work on preventing delinquency among minors, the question of the need for preventive work with parents of students has become acute. Gradually, a system of prevention work in general and a system of working with families in a socially dangerous situation was formed. We mean disadvantage towards the child. To talk about a child in a dysfunctional family means to talk about:

  • How does family dysfunction affect a child?
  • How a child can disturb the peace of the family, causing irritation, anger, impatience in parents, turning the family into a dysfunctional one, and the latter, in turn, can further aggravate mental condition child.
  • What should at least general outline what teachers can do to help the child, because it is not his fault that he lives in dysfunctional family conditions.
  • When creating a program of work with parents, we were guided by Federal Law No. 120-FZ “On the fundamentals of the system of prevention, neglect and juvenile delinquency,” which defines the concept “A family in a socially dangerous situation is a family with children in a socially dangerous situation, as well as the same family where parents or other legal representatives of minors do not fulfill their duties for their upbringing, education and (or) maintenance and (or) negatively influence their behavior or treat them cruelly.”

    Fundamental state documents: Law Russian Federation“On Education”, “The Concept of Modernization of Russian Education” restore the status of education as a priority area of ​​activity in the education system, emphasize the exclusive role of the family in solving the problems of education, and indicate the need for an equal, creative, interested union of family and school.

    Since 2011, on the basis of Municipal Educational Institution Secondary School No. 95 of the Krasnooktyabrsky district of the city of Volgograd, a program of parent meetings with disadvantaged families and families in difficult situations has been implemented on the basis of an elementary school. life situation"Family and school." The “Family and School” program is aimed at adjusting the process of raising children in families with special needs and families in difficult life situations.

    Pedagogical interaction between school and family consists of creating favorable conditions for the personal development and growth of children, organizing the active life of a person leading a decent life.

    As a result of the work carried out by the school together with other subjects of prevention, such as the KDN and ZP, the center for socio-psychological services, the PDN OP-2, the State Budgetary Institution Center “Family”, the situation in families has changed in a positive direction.

    Regular patronage, pedagogical control, and continuity on the part of school specialists and other prevention subjects made it possible to consolidate these results and began to successful methods prevention of social maladaptation of the family.

    Since school No. 95 is a school with cadet classes, there are a number of features: 78% of primary school students are boys, children study not only from the microsite, but from all districts of the city with the exception of the Krasnoarmeysky and Kirovsky districts. Children living in the Gorodishchensky district, Krasnaya Sloboda, and the city of Volzhsky study. 30% of families are single-parent families, raised by one of the parents, most often by the mother, 25% are families in which the parents are in a state of divorce, low-income families - 30%, single mothers - 10%, guardianship - 5%, disabled children make up 1%, children from foster families - 1%, children requiring additional pedagogical attention - 9%. Students from other countries who frequently come to school educational institutions are already on various types of accounting.

    Thus, the need arose to systematize technologies for working with families in the community and drawing up a program for working with such families.

    Relevance our program is that the family in modern conditions cannot get out of difficult life situations on his own. She needs outside help. The school can provide such assistance. Preventive work with families is an important component of activities in educational institutions.

    R development of a support system for families who find themselves in special situations and who are on the social border dangerous situation, providing assistance in their successful social rehabilitation and adaptation in modern conditions, psychological and pedagogical support for such families.

  • Implementation integrated approach to the rehabilitation process;
  • Coordination of efforts of prevention subjects to solve family problems and ensure the protection of the rights and legitimate interests of minors;
  • Distribution of responsibility between participants in the implementation of a comprehensive social rehabilitation program;
  • Assessing the effectiveness of the implementation of social rehabilitation programs.
  • Principles for the implementation of the Program

    The principle of complexity involves the interaction of specialists different profiles in the diagnosis, correction and rehabilitation of maladjusted families with children, involves the implementation of a systematic approach to working with families in difficult life situations, and influencing them taking into account various aspects: economic, social, medical, pedagogical and psychological, etc.

    The principle of legality provides for the implementation of laws and other regulatory legal acts corresponding to them in working with dysfunctional families.

    The principle of confidentiality presupposes the inadmissibility of disclosing personal data, as well as other information protected by law, about families in difficult life situations without their consent.

  • Focus on developing the positive potential of the family.
    • relevance and timeliness of providing assistance to a family in difficult life situations;
    • active support from parents (most effective method helping a child means helping his family);
    • reliance on parental responsibility. Using the internal potential of the family. The family itself formulates the goals of the work and determines the deadlines. Specialists do not take on tasks that the family can handle on their own.
    • reliance on positivity in working with families, treating a dysfunctional family as an equal, equal partner.
    • A distinctive feature of the Family and School program is the following:

    • The program includes innovations and original developments implemented by school class teachers.
    • The program is focused on the implementation of not only current, but also long-term expected, predictable social and rehabilitation results
    • The program is built on partnerships with families in difficult life situations, as equal and equal partners.
    • This program can be deepened, expanded, improved by introducing new forms and methods of working with families in difficult life situations, and introducing new technologies for working with families.

      The program is designed for 4 years with five meetings a year with parents of students in grades 1-4. If necessary, meetings are held with parents individually.

    • Reviving the traditions of family education, promoting the formation of values healthy image life;
    • Improving the microclimate in the family;
    • Teaching parents the skills of socially supportive and developmental behavior in the family and in their relationship with the child;
    • Reducing risk factors leading to neglect, delinquency, alcohol and substance abuse among adolescents; risk of leaving the family, suicidal risk;
    • Increasing the level of psychological and pedagogical culture of parents;
    • Increasing the effectiveness of interaction between teachers, students, and parents;
    • Activation of traditional and modern forms working with family in new conditions.
    • Briefly about the implementation of the development:

      Since 2011, on the basis of Municipal Educational Institution Secondary School No. 95 of the Krasnooktyabrsky district of the city of Volgograd, on the basis of an elementary school, a program of parent meetings with disadvantaged families and families who find themselves in difficult life situations “Family and School” has been implemented. The program was approved at a meeting of the Methodological Council of MOU Secondary School No. 95, Minutes No. 1 of August 30, 2013, and put into effect by order of the director of MOU Secondary School No. 95.

      Working methods and techniques:

      Forms of work with families:

      Collective: ( parent thematic meetings, psychodiagnostics (monitoring), joint activities with children: hikes, excursions, holidays, days open doors, parent committee meetings, seminar-workshop, lectures, reports, discussions, conversations; collective creative activities (competitions, holidays, round table), parent conferences, design of a corner with recommendations for parents).

      - general (classroom or parallel) are held 5 times a year - in September and at the end of the quarter;

      Differentiated: (specially invited group of parents);

      Individual: ( correspondence, consultation conversations, open door regime, providing parents with the opportunity to observe their child’s school activities).

      Non-traditional forms of working with parents.

    • Parent readings.
    • Parents' evenings.
    • Business game
    • "Round table"
    • But the main form of work with parents remains parent meetings.

      Types of parent meetings: thematic, organizational, final.

      Forms of parent meetings: lecture, conversation, workshop, club, creative meetings, pedagogical workshop, round table, workshop, debate.

      Stages of working with an assisted family

      Stages

      Events

    • Collecting information about the family and child
    • Message about the family at the Prevention Council
    • Making a decision to accompany the family
    • Highlighting key issues
    • Determining the family's internal potential to achieve positive change
    • Development of an individual family support plan
    • Establishing contact with all family members
    • Establishing trusting relationships with all family members
    • Discussion with family members of an individual family support plan, making adjustments
    • Implementation of an individual family support plan
    • Coordinating the activities of various specialists in providing assistance to the family
    • The mediation activity of the teacher between the family and specialists of other subjects of prevention
    • Motivating family members to receive specialized help
    1. Analysis of changes in the family system, together with the family, the results of correctional activities are summed up and tasks are set further development for family members
    2. The family and class teacher receive final recommendations from specialists
    3. The Prevention Council makes a decision to terminate family accompaniment when there have been incidents in the family. positive changes, the child’s negative behavior is not observed
    4. Support and control of the family throughout the year, the teacher meets with family members at their request, supporting positive changes in family life
    5. Multimedia projector, stereo system, classical music CDs, connection to Internet resources.

      Behavioral reactions of a child that may serve as signs of trouble in the family:

      1. External untidiness;
      2. Decreased academic performance;
      3. Failure to complete training;
      4. Loss of interest in previous hobbies;
      5. A sharp change in your social circle;
      6. The appearance of secrecy in behavior;
      7. Loss of appetite, weight loss, drowsiness;
      8. Irritability, aggressiveness, hot temper, or vice versa passivity, apathy;
      9. Traces of beatings.
      10. The parent meeting should educate parents and not note the mistakes and failures of children in their studies and behavior.
      11. The topic of the meeting should take into account the age characteristics of children.
      12. The meeting should be both theoretical and practical in nature.
      13. The meeting should not engage in discussion and condemnation of the personalities of students.
      14. Parent meetings are especially productive when they are interactive.

        We offer one of the options for planning a parent meeting (meeting).

        Meeting plan

      15. Report (short speech about the main problems, views on this issue).
      16. Formulation of the problem.
      17. Work in groups (solution and search for a solution to the problem.).
      18. Performances from groups.
      19. Summarizing what has been said. Solution.
      20. Distribution of recommendations and memos on this topic.
      21. It is possible to introduce other stages, for example, acting out and subsequent analysis of pedagogical situations.
      22. Conclusion: This form of parent meetings has the following advantages:

      23. Participation of all parents.
      24. There is an exchange of experience and knowledge within the group and between groups.
      25. Specific methods and techniques of education are mastered in practice.
      26. Each parent receives methodological recommendations and assistance.
      27. The individual characteristics of parents are taken into account, a differentiated approach is carried out
      28. When working with parents from disadvantaged families, the class teacher must:

      29. Identification of dysfunctional families as a means of preventing social orphanhood (knowledge of the child’s living conditions, availability of a material examination report).
      30. Improving the pedagogical culture of all categories of parents:
      31. Organization of pedagogical education. The conviction of parents that family upbringing is not morality, lectures or physical punishment, but the entire lifestyle of parents (primarily healthy), the way of thinking and actions of the parents themselves, constant communication with children from a position of humanity.
      32. Involving parents as active educators (family holidays at school, extracurricular extracurricular activities, participation in school management).
      33. To avoid violence, cruelty, and aggressive behavior towards their children, formulate a legal culture for parents.
      34. Conducting control and correctional work with parents (questionnaires, testing, analysis of the level of education, training of children, individual conversations, etc.).
      35. Take into account the peculiarities of upbringing in each individual family, based on positive experience, increase the priority of family and family traditions in all subjects educational activities: children, parents, teachers.
      36. Eliminate parents' feelings of guilt for their inadequacy (a separate plan for working with problem groups of parents).
      37. Memo for class teachers when interacting with disadvantaged families.

      38. Never take educational actions in a bad mood.
      39. Clearly and clearly define for yourself what you want from your family, what the family thinks about this, try to convince them that your goals are, first of all, their goals.
      40. Don't be definitive ready-made recipes and recommendations. Do not lecture your parents, but show possible ways to overcome difficulties, analyze the right and wrong decisions leading to the goal.
      41. The class teacher is obliged to encourage the successes of a problem child, to notice even the most insignificant successes.
      42. If there are errors or incorrect actions, point them out. Evaluate and pause to allow the family to process what they have heard.
      43. Let the family know that you sympathize with them and believe in them, despite the missteps of their parents.
      44. Parent meeting program “Family and School”

        Topic of the meeting, questions for discussion

        1 class

        “Family and school – together we can do a lot”

        Psychologist. Deputy Director for VR.

        “Happy is he who is happy at home.”

        Round table with game elements; workshop “Family traditions...Is this important?”

        What does it mean to love your child (debate).

        Round table “The cry of a child’s soul: Parents are getting divorced. "

        Psychologist. Deputy according to VR.

        "Child safety every day"

        Understand yourself and your child"

        Discussion “Why is my child becoming difficult?”

        Conference of fathers “The role of the father in raising his son”

        “There is no sweeter friend than your own mother”

        Free time and family leisure. Organizational and activity game.

        Psychologist. Deputy according to BP

        Dispute

        "Education by non-violence in the family." Round table.

        Thematic meeting “Dad, Mom, Me - a healthy family”

        Dispute: “Alcohol in the family.”

        Emotional well-being of children in the family .

        4th grade

        “It’s not easy to be a human being,”

        or how to raise children

        moral qualities by example."

        Deputy Director for VR.

        Carrot or stick? (about rewards and punishments and their impact on children).

        Taking into account the physiological and psychological characteristics of children of this age in their upbringing.

        "Children's aggression: its causes and prevention."

        Causes of teenage suicide. The role of adults in helping adolescents in crisis situations.

        Labor participation of the child in family life. His role in development

        performance and personal qualities.

        “Family and school - together we can do a lot” (meeting - game). To determine, together with parents, the basic principles of building interaction with first-graders, uniting the efforts of family and school in the upbringing and development of children, determining the level of contact between parents and children, and communication in the family.

        “Happy is he who is happy at home” Parental education. How to make school your second home. Difficulties in adaptation of first-graders to school.

        Round table with game elements; workshop “Family traditions...Is this important?” Create the prerequisites for the formation of those present’ attitude towards family as one of the main life values. "Exchange" family traditions with subsequent use of the latter in comprehensive development and raising children; show the important role of values ​​in every family; create a situation of success for every family; unity of parents and children.

        What does it mean to love your child (debate). Help parents analyze their parental behavior, focus on the positive aspects of raising a child, forms of showing love for a child, consider the positive and negative sides educational influence of parents on the child, derive a formula for successfully fulfilling the role of parents, convince parents of the need for generous manifestations of their unconditional parental love.

        Round table with parents “The cry of a child’s soul: Parents are getting divorced. » Divorce of parents is a serious stressful situation for any child, stages and periods of divorce, experiences of adults, experiences of children, how to behave: if you do not live with a child, if you have entered into a new marriage, the new partner of a divorced parent should adhere to a certain line of behavior.

        "Child safety every day" We learn to live in the world of people. Lessons on ethical behavior for children and parents during the summer. Rules of behavior in public places (about patience and tolerance, restraint, self-respect and politeness in the world of adults and children). Results of the first year of communication. Organization of summer holidays for children.

        2nd grade

        “Problems of education. Understand yourself and your child" Improving the pedagogical culture of parents, replenishing their arsenal of knowledge on the specific issue of raising a child in the family; development of collective decisions and uniform requirements for raising children, integration of the efforts of families and teachers in activities to develop the child’s personality; promoting the experience of successful family education, preventing incorrect actions towards families on the part of parents; planning the work of joint activities of teachers, students and parents.

        Discussion “Why is my child becoming difficult?” A difficult child is a child who finds it difficult, a difficult child through the eyes of adults, why a child becomes difficult, the reasons for children’s uncontrollability, what a child takes revenge for.

        First school grades. Recommendations for parents. Standards for assessing the learning outcomes and development of students, the causes of difficulties in the educational process of younger schoolchildren; replenishment of parents’ knowledge on the specific upbringing of a child in the family and school.

        Conference of fathers “The role of the father in raising his son” To update the problem of raising a son in a family. To give fathers the opportunity to realize that paternal happiness is the highest value; outline ways, means and techniques for raising boys in the family; involve fathers in a collective discussion of difficult pedagogical situations; give recommendations to fathers on how to build relationships with children based on mutual understanding; direct the efforts of fathers to joint activities in the life of a class team.

        “There is no sweeter friend than your own mother” (holiday meeting). The role of the mother in raising a child. Introduce the conditions for successful family education; to give mothers the opportunity to realize that maternal happiness is the highest value; involve mothers in collective role-playing of situations; mother's love for a child is not for something, but simply for the fact that the child exists.

        Free time and family leisure. Organizational and activity game. To actualize the problem of children's leisure in the upcoming summer period; encourage parents and children to spend leisure time together; disassemble and play some types of useful time spent together. Results of the year. Organization of summer holidays for children.

        3rd grade

        “The role of the family and the role of school in raising a child.” Dispute. The family can act as both a positive and negative factor in education. Parable “Good family” (Appendix 13).

        Inform parents of the need to:

    • - creating confidence in the child that he is loved and cared for;
    • - treating a child at any age lovingly and attentively;
    • - constant psychological contact with the child;
    • - interest in everything that happens in the child’s life.

    "Education by non-violence in the family." Round table. Introduce parents to various types domestic violence:

  • - On the part of the husband in relation to his wife;
  • - On the part of the wife in relation to her husband;
  • - On the part of parents in relation to children;
  • - On the part of older children in relation to younger ones.
  • Develop the ability to separate the concepts of “persistence” and “aggression”. Questions for discussion round table. (Appendix 14). Recommendations for parents. (Appendix 15) Viewing and discussion of the social video “Don’t destroy children’s dreams” on youtube.com›watch?v=b_gUXaZfVZw

    Thematic meeting “Dad, Mom, Me – a healthy family.” Make parents aware of the importance of understanding that a healthy lifestyle is important for schoolchildren. Identify the main components of a healthy lifestyle for a schoolchild: development and adherence to a daily routine; proper nutrition; exercise stress; workplace organization; maintaining personal and public hygiene; Test for parents “Can your lifestyle be called healthy.” (Appendix 16).

    Dispute: “Alcohol in the family.” Make parents aware of how the characteristics of the family environment affect the upbringing of children, which in turn can influence the onset of alcohol abuse. Consideration of such questions as: Alcoholism is familial in nature if a woman suffers from it. What is it like for children to live in a family of alcoholics? What life scenario will a child carry into adulthood, observing drunken parents? Medical and social aspects of the influence of alcoholism on children. Types of behavior characteristic of children of alcoholics. (Appendix 18).

    Seminar-workshop “Difficult dialogue with studies, or how to help your child study.” Expand the knowledge of parents about the forms and methods of solving problems that arise with children. Develop a joint action program to stimulate cognitive activity students. Identify problems of interaction with the child to overcome learning difficulties. Discussion on the question “Why do we want our child to study well?” Exchange of views on the question “Why are our children losing interest in learning?” Organization of homework for schoolchildren. Atmosphere homework. Teaching children to be independent. (Appendix 19).

    Emotional well-being of children in the family. Promoting the experience of successful family upbringing, preventing incorrect actions towards their son or daughter on the part of parents. Introduce parents to the concepts of “competence”, “affect”, “stress”. Contribute to the development of communication competence. Help parents understand their own emotional state, express their feelings and recognize the feelings of their children. Discuss techniques that allow a child to reduce the impact of a stressful situation on the body and help overcome emotional difficulties. Memo to parents from the child. (Appendix 17). Results of the year. Organization of summer holidays for children.

    “It’s not easy to be a human being,” or how to raise children moral qualities by example." Create conditions for understanding the importance of moral education in the family. To promote the formation of a culture of communication between parents and children, the ability of parents to see negative points in raising your own children. Methods and conditions for the moral education of a child in the family. View and discuss the social video “The Parable of Good and Evil” on youtube.com›watch?v=b_gUXaZfVZw

    Carrot or stick? (About rewards and punishments. Their influence on children). Expanding parents' understanding of the influence of rewards and punishments and the variety of methods of influence for behavior correction. Consider the reasons for disobedience. Rewards are effective if...Ways to get a child to change their behavior in the right direction. Punishments are effective when... Watch the social video “Don’t destroy children’s dreams” youtube.comwatch?v=b_gUXaZfVZw

    Taking into account the physiological and psychological characteristics of children of this age in their upbringing. Consideration of the features of physical and psychological development younger age and their influence on the process of training and education. The origin of major changes in a child’s life due to physiological transformations. Changes in the emotional sphere of the child. Provide assistance to parents in overcoming difficulties in communicating with their children and teenagers.

    "Children's aggression: its causes and prevention." To form parents’ knowledge about the problem of adolescent aggressiveness, skills and abilities on how to help cope with an aggressive state, and teach them how to deal with their anger. Determine the causes of aggression and give recommendations. Portrait of an aggressive child. (Appendix 20)

    Causes of child suicide. The role of adults in helping adolescents in crisis situations. Together with parents, identify possible causes. Signs and nature of child and adolescent suicide. Provide an opportunity to reflect and evaluate the relationship with your child. Psychological meaning of suicide. Signs of suicidal behavior. Advice for parents. (Appendix 21).

    Labor participation of the child in family life. His role in development performance and personal qualities. Determining the goals and objectives of labor education in the family. Work assignments for a child in the family. Work and its importance in the life of a child. The importance of the example of family and school in developing a child’s work skills. The child’s labor efforts and their assessment in the family and school. Results of the year. Organization of summer holidays for children.

    Criteria for assessing the achievement of planned results:

    Evaluating the effectiveness of the Family and School program.

    The basis for the creation of the program was the many years of work of the teaching staff with disadvantaged families. This program is initial stage preventive work with parents who are in social security and difficult life situations.

    In addition to theoretical classes, the program includes practical developments in parent meetings.

    Criteria for assessing the effectiveness of working with parents

    The degree of achievement of positive program results is recorded by the following parameters:

  • Increasing the erudition of parents in the field of family education, their readiness to cooperate with teachers.
  • Formation of an atmosphere of creative cooperation in parent groups.
  • Parents' satisfaction with the quality and quantity of forms of interaction with the school.
  • Growing parental competence, enriching the parental fund with forms of interaction with the child, increasing the depth and intensity of communication with the child.
  • Correction of family relationships, creation of positive conditions for raising a child in the vast majority of families.
  • The implementation of the “Family and School” program on the basis of an elementary school brought positive result. In the 2011-2012 academic year in primary school 3 families were identified and registered within the school; in the 2012-2013 academic year - 2 families. 4 families were removed from the in-school register; not a single family was transferred to the KDN and ZP, as they coped with the forces of in-school prevention.

    Classroom parent meetings were held 5 times a year, their topics related to the problems of education in families in difficult life situations. Attendance at parent meetings is as follows.

    * this work is not a scientific work, is not a final qualifying work and is the result of processing, structuring and formatting the collected information intended for use as a source of material for self-study educational works.

      Introduction.

      References.

    Methods of mathematical statistics

      Introduction.

      Basic concepts of mathematical statistics.

      Statistical processing of the results of psychological and pedagogical research.

      References.

    Methods of mathematical statistics

      Introduction.

      Basic concepts of mathematical statistics.

      Statistical processing of the results of psychological and pedagogical research.

      References.

        Introduction.

    The application of mathematics to other sciences makes sense only in unity with a deep theory of a specific phenomenon. It is important to remember this so as not to fall into a simple game of formulas, which has no real content behind it.

    Academician Yu.A. Metropolitan

    Theoretical research methods in psychology and pedagogy make it possible to reveal the qualitative characteristics of the phenomena being studied. These characteristics will be more complete and deeper if the accumulated empirical material is subjected to quantitative processing. However, the problem of quantitative measurements within the framework of psychological and pedagogical research is very complex. This complexity lies primarily in the subjective-causal diversity of pedagogical activity and its results, in the very object of measurement, which is in a state of continuous movement and change. At the same time, the introduction of quantitative indicators into research today is a necessary and obligatory component of obtaining objective data on the results of teaching work. As a rule, these data can be obtained both by direct or indirect measurement of various components of the pedagogical process, and by quantitative assessment of the corresponding parameters of an adequately constructed mathematical model. For this purpose, methods of mathematical statistics are used when studying problems of psychology and pedagogy. With their help, various tasks are solved: processing factual material, obtaining new, additional data, justifying the scientific organization of research, and others.

    2. Basic concepts of mathematical statistics

    An extremely important role in the analysis of many psychological and pedagogical phenomena is played by average values, which represent a generalized characteristic of a qualitatively homogeneous population according to a certain quantitative criterion. It is impossible, for example, to calculate the average specialty or the average nationality of university students, since these are qualitatively heterogeneous phenomena. But it is possible and necessary to determine on average the numerical characteristics of their academic performance (average score), the effectiveness of methodological systems and techniques, etc.

    In psychological and pedagogical research, various types of averages are usually used: arithmetic mean, geometric mean, median, mode and others. The most common are the arithmetic mean, median and mode.

    The arithmetic mean is used in cases where there is a directly proportional relationship between the defining property and this attribute (for example, when the performance of a training group improves, the performance of each of its members improves).

    The arithmetic mean is the quotient of dividing the sum of quantities by their number and is calculated using the formula:

    where X is the arithmetic mean; X1, X2, X3 ... Xn - results of individual observations (techniques, actions),

    n - number of observations (techniques, actions),

    The sum of the results of all observations (techniques, actions).

    Median (Me) is a measure of average position that characterizes the value of a characteristic on an ordered (based on increasing or decreasing) scale, which corresponds to the middle of the population under study. The median can be determined for ordinal and quantitative characteristics. The location of this value is determined by the formula: Median location = (n + 1) / 2

    For example. According to the results of the study, it was found that:

    – 5 people from those participating in the experiment are studying “excellently”;

    – 18 people study “good”;

    – “satisfactory” – 22 people;

    – “unsatisfactory” – 6 people.

    Since a total of N = 54 people took part in the experiment, the middle of the sample is equal to one person. From this it is concluded that more than half of the students study below the “good” rating, that is, the median is more “satisfactory”, but less than “good” (see figure).

    Mode (Mo) is the most common typical value of a characteristic among other values. It corresponds to the class with the maximum frequency. This class is called modal value.

    For example.

    If the survey question: “indicate the degree of proficiency foreign language”, the answers were distributed:

    1 – fluent – ​​25

    2 – I speak sufficiently for communication – 54

    3 – I speak, but have difficulty communicating – 253

    4 – I understand with difficulty – 173

    5 – I don’t know – 28

    Obviously, the most typical meaning here is “I own it, but have difficulty communicating,” which will be modal. Thus, the mode is – 253.

    When using mathematical methods in psychological and pedagogical research, great importance is given to the calculation of dispersion and standard deviations.

    Dispersion is equal to the average square of deviations of the value of the options from the mean value. It acts as one of the characteristics of individual results of the scatter of values ​​of the variable under study (for example, student grades) around the average value. Calculation of dispersion is carried out by determining: deviation from the average value; the square of the specified deviation; the sum of squared deviations and the average value of the squared deviation (see Table 6.1).

    The variance value is used in various statistical calculations, but is not directly observable. The value directly related to the content of the observed variable is the standard deviation.

    Table 6.1

    Variance Calculation Example

    Meaning

    indicator

    Deviation

    from average

    deviations

    2 – 3 = – 1

    The standard deviation confirms the typicality and indicativeness of the arithmetic mean and reflects the measure of fluctuation in the numerical values ​​of the characteristics from which the average value is derived. It is equal to the square root of the variance and is determined by the formula:

    where: – mean square. If the number of observations (actions) is small—less than 100—in the value of the formula you should put not “N”, but “N – 1”.

    The arithmetic mean and the mean square are the main characteristics of the results obtained during the study. They allow you to summarize data, compare them, and establish the advantages of one psychological and pedagogical system (program) over another.

    The root mean square (standard) deviation is widely used as a measure of dispersion for various characteristics.

    When assessing the results of a study, it is important to determine the dispersion of a random variable around the mean value. This dispersion is described using Gauss's law (the law of the normal probability distribution of a random variable). The essence of the law is that when measuring a certain characteristic in a given set of elements, there are always deviations in both directions from the norm due to many uncontrollable reasons, and the greater the deviations, the less often they occur.

    Further processing of the data may reveal: coefficient of variation (stability) the phenomenon under study, which is the percentage ratio of the standard deviation to the arithmetic mean; measure of obliquity, showing in which direction the majority of deviations are directed; measure of coolness, which shows the degree of accumulation of random variable values ​​around the average, etc. All these statistical data help to more fully identify the signs of the phenomena being studied.

    Measures of relationships between variables. Relationships (dependencies) between two or more variables in statistics are called correlation. It is assessed using the value of the correlation coefficient, which is a measure of the degree and magnitude of this relationship.

    There are many correlation coefficients. Let's consider only some of them, which take into account the presence of a linear relationship between variables. Their choice depends on the scales of measurement of the variables, the relationship between which needs to be assessed. The Pearson and Spearman coefficients are most often used in psychology and pedagogy.

    Let's look at calculating the values ​​of correlation coefficients using specific examples.

    Example 1. Let two compared variables X (marital status) and Y (exclusion from university) be measured on a dichotomous scale (a special case of the name scale). To determine the relationship, we use the Pearson coefficient.

    In cases where there is no need to count the frequency of occurrence of different values ​​of the variables X and Y, it is convenient to calculate the correlation coefficient using a contingency table (see Tables 6.2, 6.3, 6.4), showing the number of joint occurrences of pairs of values ​​for two variables (features) . A – the number of cases when the variable X has a value equal to zero, and at the same time the variable Y has a value equal to one; B is the number of cases when variables X and Y simultaneously have values ​​equal to one; C – the number of cases when variables X and Y have simultaneously values ​​equal to zero; D – the number of cases when the variable X has a value equal to one, and, at the same time, the variable Y has a value equal to zero.

    Table 6.2

    General contingency table

    Sign X

    In general, the formula for the Pearson correlation coefficient for dichotomous data has the form

    Table 6.3

    Example of data on a dichotomous scale

    Let’s substitute into the formula the data from the contingency table (see Table 6.4) corresponding to the example under consideration:

    Thus, the Pearson correlation coefficient for the selected example is 0.32, that is, the relationship between the marital status of students and the facts of exclusion from the university is insignificant.

    Example 2: If both variables are measured on order scales, then Spearman's rank correlation coefficient (Rs) is used as a measure of association. It is calculated by the formula

    where Rs is the Spearman rank correlation coefficient; Di – difference in ranks of compared objects; N – number of compared objects.

    The value of the Spearman coefficient varies from –1 to + 1. In the first case, there is an unambiguous but oppositely directed relationship between the analyzed variables (as the values ​​of one increase, the values ​​of the other decrease). In the second, as the values ​​of one variable increase, the value of the second variable increases proportionally. If the value of Rs is equal to zero or has a value close to it, then there is no significant relationship between the variables.

    As an example of calculating the Spearman coefficient, we use the data from Table 6.5.

    Table 6.5

    Data and intermediate results of calculating the coefficient value

    rank correlation Rs

    Qualities

    Ranks assigned by an expert

    Rank difference

    Squared difference of ranks

    –1
    –1
    –1

    Sum of squared rank differences Di = 22

    Let's substitute the example data into the formula for the Smearman coefficient:

    The calculation results allow us to assert that there is a fairly pronounced relationship between the variables under consideration.

    Statistical testing of a scientific hypothesis. The proof of the statistical significance of an experimental effect differs significantly from the proof in mathematics and formal logic, where the conclusions are more universal in nature: statistical evidence is not so strict and final - they always allow the risk of making mistakes in conclusions and therefore statistical methods do not definitively prove the legitimacy of a particular conclusion, but show the degree of plausibility of accepting a particular hypothesis.

    A pedagogical hypothesis (scientific assumption about the advantage of a particular method, etc.) in the process of statistical analysis is translated into the language of statistical science and reformulated anew in at least two statistical hypotheses. The first (main) is called null hypothesis(H 0), in which the researcher talks about his initial position. He (a priori) seems to declare that the new method (presumed by him, his colleagues or opponents) does not have any advantages, and therefore from the very beginning the researcher is psychologically ready to take an honest scientific position: the differences between the new and old methods are declared equal to zero. In another, alternative hypothesis(H 1) an assumption is made about the advantage of the new method. Sometimes several alternative hypotheses are put forward with appropriate notations.

    For example, the hypothesis about the advantage of the old method (H 2). Alternative hypotheses are accepted if and only if the null hypothesis is rejected. This happens in cases where the differences, say, in the arithmetic means of the experimental and control groups are so significant (statistically significant) that the risk of error in rejecting the null hypothesis and accepting the alternative does not exceed one in three accepted significance levels statistical output:

    – first level – 5% (in scientific texts sometimes they write p = 5% or a? 0.05, if presented in fractions), where the risk of error in the conclusion is allowed in five cases out of a hundred theoretically possible similar experiments with a strictly random selection of subjects for each experiment;

    – second level – 1%, i.e., accordingly, the risk of making a mistake is allowed only in one case out of a hundred (a? 0.01, with the same requirements);

    – third level – 0.1%, i.e. the risk of making a mistake is allowed only in one case out of a thousand (a? 0.001). The last level of significance places very high demands on substantiating the reliability of experimental results and is therefore rarely used.

    When comparing the arithmetic means of experimental and control groups, it is important not only to determine which mean is larger, but also how much larger. The smaller the difference between them, the more acceptable the null hypothesis about the absence of statistically significant (significant) differences will be. In contrast to thinking at the level of ordinary consciousness, which tends to perceive the difference in averages obtained as a result of experience as a fact and a basis for a conclusion, a teacher-researcher familiar with the logic of statistical inference will not rush in such cases. He will most likely make an assumption about the randomness of the differences, put forward a null hypothesis about the absence of significant differences in the results of the experimental and control groups, and only after refuting the null hypothesis will he accept an alternative one.

    Thus, the question of differences within scientific thinking is transferred to another plane. The point is not only in the differences (they almost always exist), but in the magnitude of these differences and hence - in determining the difference and the limit after which we can say: yes, the differences are not random, they are statistically significant, which means that the subjects of these two groups belong after the experiment is no longer to one (as before), but to two different general populations and that the level of preparedness of students potentially belonging to these populations will differ significantly. In order to show the boundaries of these differences, so-called estimates of general parameters.

    Let's look at a specific example (see Table 6.6) of how, using mathematical statistics, you can refute or confirm the null hypothesis.

    Let’s say it is necessary to determine whether the effectiveness of students’ group activities depends on the level of development of interpersonal relationships in the study group. The null hypothesis is the assumption that such a dependence does not exist, and the alternative hypothesis is that the dependence exists. For these purposes, the results of the effectiveness of activities in two groups are compared, one of which in this case acts as an experimental group, and the second as a control group. To determine whether the difference between the average performance indicators in the first and second groups is significant (significant), it is necessary to calculate the statistical significance of this difference. To do this, you can use Student's t-test. It is calculated by the formula:

    where X 1 and X 2 are the arithmetic mean of the variables in groups 1 and 2; M 1 and M 2 are the values ​​of average errors, which are calculated using the formula:

    where is the root mean square, calculated using formula (2).

    Let's determine the errors for the first row (experimental group) and the second row (control group):

    We find the value of t - criterion using the formula:

    Having calculated the t-criterion value, it is required to use a special table to determine the level of statistical significance of the differences between the average performance indicators in the experimental and control groups. The higher the t-criterion value, the higher the significance of the differences.

    To do this, we compare the calculated t with the tabulated t. The table value is selected taking into account the selected confidence level (p = 0.05 or p = 0.01), as well as depending on the number of degrees of freedom, which is found by the formula:

    where U is the number of degrees of freedom; N 1 and N 2 – the number of measurements in the first and second rows. In our example, U = 7 + 7 –2 = 12.

    Table 6.6

    Data and intermediate results of calculating the significance of statistical

    Differences in mean values

    Experimental group

    Control group

    The importance of operational efficiency

    For the t-criterion table, we find that the value of t table. = 3.055 for the one percent level (p

    However, the teacher-researcher should remember that the existence of statistical significance of the difference in average values ​​is an important, but not the only argument in favor of the presence or absence of a relationship (dependence) between phenomena or variables. Therefore, it is necessary to involve other arguments for quantitative or substantive justification of a possible connection.

    Multivariate methods of data analysis. Analysis of the relationship between a large number of variables is carried out using multivariate statistical processing methods. The purpose of using such methods is to make hidden patterns visible and to highlight the most significant relationships between variables. Examples of such multivariate statistical methods are:

      - factor analysis;

      – cluster analysis;

      – analysis of variance;

      - regression analysis;

      – latent structural analysis;

      – multidimensional scaling and others.

    Factor analysis is to identify and interpret factors. A factor is a generalized variable that allows you to collapse part of the information, i.e., present it in an easily understandable form. For example, the factor theory of personality identifies a number of generalized characteristics of behavior, which in this case are called personality traits.

    Cluster analysis allows you to identify the leading feature and the hierarchy of feature relationships.

    Analysis of variance– a statistical method used to study one or more simultaneously operating and independent variables for the variability of an observed characteristic. Its peculiarity is that the observed feature can only be quantitative, while at the same time the explanatory features can be both quantitative and qualitative.

    Regression analysis allows us to identify the quantitative (numerical) dependence of the average value of changes in the resulting characteristic (explained) on changes in one or more characteristics (explanatory variables). As a rule, this type of analysis is used when it is necessary to find out how much the average value of one characteristic changes when another characteristic changes by one unit.

    Latent structure analysis represents a set of analytical and statistical procedures for identifying hidden variables (signs), as well as the internal structure of connections between them. It makes it possible to study the manifestations of complex relationships between directly unobservable characteristics of socio-psychological and pedagogical phenomena. Latent analysis can be the basis for modeling these relationships.

    Multidimensional scaling provides a visual assessment of the similarities or differences between certain objects described by a large number of different variables. These differences are represented as distances between the objects being assessed in multidimensional space.

    3. Statistical processing of the results of psychological and pedagogical

    research

    In any study, it is always important to ensure the scale and representativeness of the objects of study. To solve this issue, they usually resort to mathematical methods of calculating the minimum size of objects to be studied (groups of respondents), so that objective conclusions can be drawn on this basis.

    Based on the degree of completeness of coverage of primary units, statistics divides research into continuous, when all units of the phenomenon being studied are studied, and selective, when only a part of the population of interest, taken according to some characteristic, is studied. The researcher does not always have the opportunity to study the entire set of phenomena, although this should constantly be strived for (there is not enough time, funds, necessary conditions, etc.); on the other hand, often a complete study is simply not required, since the conclusions will be quite accurate after studying a certain part of the primary units.

    The theoretical basis of the sampling method of research is the theory of probability and the law large numbers. In order for the study to have a sufficient number of facts and observations, a table of sufficiently large numbers is used. In this case, the researcher is required to establish the magnitude of the probability and the magnitude of the permissible error. Let, for example, the permissible error in the conclusions that should be drawn as a result of observations, in comparison with theoretical assumptions, should not exceed 0.05 in both positive and negative directions (in other words, we can be mistaken by no more than 5 cases out of 100). Then, using the table of sufficiently large numbers (see Table 6.7), we find that the correct conclusion can be made in 9 cases out of 10 when the number of observations is at least 270, in 99 cases out of 100 when there are at least 663 observations, etc. d. This means that as the accuracy and probability with which we expect to draw conclusions increases, the number of required observations increases. However, in psychological and pedagogical research it should not be excessively large. 300–500 observations are often quite sufficient for solid conclusions.

    This method of determining the sample size is the simplest. Mathematical statistics also has more complex methods for calculating the required sample populations, which are covered in detail in the specialized literature.

    However, compliance with the mass requirements does not yet ensure the reliability of the conclusions. They will be reliable when the units chosen for observation (conversations, experiments, etc.) are sufficiently representative for the class of phenomena being studied.

    Table 6.7

    A short table of sufficiently large numbers

    Magnitude

    probabilities

    Acceptable

    The representativeness of observation units is ensured primarily by their random selection using tables of random numbers. Let's say we need to identify 20 study groups to conduct a mass experiment from the available 200. To do this, a list of all groups is compiled, which is numbered. Then 20 numbers are written out from the random number table, starting from a certain number, at a certain interval. These 20 random numbers, according to the numbers, determine the groups that the researcher needs. A random selection of objects from the general (general) population gives grounds to assert that the results obtained from studying a sample population of units will not differ sharply from those that would exist in the case of studying the entire population of units.

    In the practice of psychological and pedagogical research, not only simple random selections are used, but also more complex selection methods: stratified random selection, multi-stage selection, etc.

    Mathematical and statistical research methods are also means of obtaining new factual material. For this purpose, template techniques are used that increase the informative capacity of the questionnaire question and scaling, which makes it possible to more accurately assess the actions of both the researcher and the subjects.

    The scales arose out of the need to objectively and accurately diagnose and measure the intensity of certain psychological and pedagogical phenomena. Scaling makes it possible to organize phenomena, quantify each of them, and determine the lowest and highest levels of the phenomenon under study.

    Thus, when studying the cognitive interests of listeners, their boundaries can be established: very strong interest - very weak interest. Between these boundaries, introduce a series of steps creating a scale of cognitive interests: very great interest (1); great interest (2); medium (3); weak (4); very weak (5).

    In psychological and pedagogical research, scales of different types are used, for example,

    a) Three-dimensional scale

    Very active……..…………..10

    Active…………………………5

    Passive………………………...0

    b) Multidimensional scale

    Very active…………………..8

    Medium active………………….6

    Not too active…………...4

    Passive………………………..2

    Completely passive…………...0

    c) Two-sided scale.

    Very interested……………..10

    Interested enough………...5

    Indifferent……………………….0

    Not interested…………………..5

    No interest at all………10

    Numerical rating scales give each item a specific numerical designation. Thus, when analyzing students’ attitudes to study, their persistence in work, willingness to cooperate, etc. you can create a numerical scale based on the following indicators: 1 – unsatisfactory; 2 – weak; 3 – average; 4 – above average, 5 – much above average. In this case, the scale takes on the following form (see Table 6.8):

    Table 6.8

    If the number scale is bipolar, a bipolar ordering with a zero value at the center is used:

    Discipline Indiscipline

    Pronounced 5 4 3 2 1 0 1 2 3 4 5 Not pronounced

    Rating scales can be depicted graphically. In this case, they express the categories in a visual form. Moreover, each division (step) of the scale is characterized verbally.

    The methods under consideration play a large role in the analysis and synthesis of the data obtained. They make it possible to establish various relationships, correlations between facts, and identify trends in the development of psychological and pedagogical phenomena. Thus, the theory of groupings of mathematical statistics helps to determine which facts from the collected empirical material are comparable, on what basis they should be correctly grouped, and what degree of reliability they will have. All this allows you to avoid arbitrary manipulation of facts and determine a program for processing them. Depending on the goals and objectives, three types of groupings are usually used: typological, variational and analytical.

    Typological grouping is used when it is necessary to divide the received factual material into qualitatively homogeneous units (distribution of the number of violations of discipline between different categories of students, breakdown of indicators of their performance of physical exercises by year of study, etc.).

    If it is necessary to group the material according to the value of any changing (varying) attribute - breakdown of groups of students by level of performance, percentage of assignments completed, similar violations of the established order, etc. – applies variation grouping, which makes it possible to consistently judge the structure of the phenomenon being studied.

    Analytical view of grouping helps to establish the relationship between the phenomena being studied (the dependence of the degree of students’ preparation on various teaching methods, the quality of tasks performed on temperament, abilities, etc.), their interdependence and interdependence in exact terms.

    The importance of the researcher's work in grouping the collected data is demonstrated by the fact that errors in this work devalue the most comprehensive and meaningful information.

    Currently, the mathematical foundations of grouping, typology, and classification have received the most profound development in sociology. Modern approaches and methods of typology and classification in sociological research can be successfully applied in psychology and pedagogy.

    During the study, methods of final data synthesis are used. One of them is the technique of compiling and studying tables.

    When compiling a summary of data regarding one statistical value, a distribution series (variation series) of the value of this value is formed. An example of such a series (see Table 6.9) is a summary of data regarding the chest circumference of 500 individuals.

    Table 6.9

    Summary of data simultaneously for two or more statistical quantities involves the compilation of a distribution table that reveals the distribution of the values ​​of one static quantity in accordance with the values ​​​​taken by other quantities.

    As an illustration, Table 6.10 is provided, compiled on the basis of statistical data regarding the chest circumference and weight of these people.

    Table 6.10

    Chest circumference in cm

    The distribution table gives an idea of ​​the relationship and connection that exists between the two values, namely: with low weight, the frequencies are located in the upper left quarter of the table, which indicates the predominance of individuals with a small chest circumference. As the weight increases to the average value, the frequency distribution moves to the center of the plate. This indicates that people who are closer to average weight have chest circumferences that are also close to average. With a further increase in weight, the frequencies begin to occupy the lower right quarter of the plate. This indicates that a person who weighs above average also has a chest circumference that is above average.

    It follows from the table that the established connection is not strict (functional), but probabilistic, when with changes in the values ​​of one quantity, another changes as a trend, without a strict unambiguous dependence. Similar connections and dependencies are often found in psychology and pedagogy. Currently, they are usually expressed using correlation and regression analysis.

    Variation series and tables give an idea of ​​the statics of a phenomenon, while dynamics can be shown by development series, where the first line contains successive stages or time intervals, and the second - the values ​​of the statistical value being studied at these stages. This way, increases, decreases, or periodic changes in the phenomenon being studied are revealed, and its trends and patterns are revealed.

    Tables can be filled with absolute values, or summary figures (average, relative). The results of statistical work - in addition to tables, are often depicted graphically in the form of diagrams, figures, etc. The main methods of graphically representing statistical quantities are: the method of points, the method of straight lines and the method of rectangles. They are simple and accessible to every researcher. The technique of using them is drawing coordinate axes, establishing a scale, and writing out the designations of segments (points) on the horizontal and vertical axes.

    Diagrams depicting series of distributions of values ​​of one statistical quantity allow one to draw distribution curves.

    The graphical representation of two (or more) statistical quantities makes it possible to form a certain curved surface, called the distribution surface. The series of developments in graphic execution form development curves.

    A graphical representation of statistical material allows you to penetrate deeper into the meaning of digital quantities, to grasp their interdependencies and features of the phenomenon being studied, which are difficult to notice in the table. The researcher is freed from the work that he would have to do to understand the abundance of numbers.

    Tables and graphs are important, but only the first steps in the study of statistical quantities. The main method is analytical, operating with mathematical formulas, with the help of which the so-called “generalizing indicators” are derived, that is, absolute values ​​​​brought into a comparable form (relative and average values, balances and indices). Yes, with the help relative values(percent) are determined quality features analyzed populations (for example, the ratio of excellent students to the total number of students; the number of errors when working on complex equipment caused by mental instability of students to the total number of errors, etc.). That is, the relationships are revealed: parts to the whole (specific gravity), components to the sum (structure of the totality), one part of the totality to its other part; characterizing the dynamics of any changes over time, etc.

    As you can see, even the most general understanding of the methods of statistical calculus suggests that these methods have great capabilities in the analysis and processing of empirical material. Of course, the mathematical apparatus can dispassionately process everything that a researcher puts into it, both reliable data and subjective speculation. That is why perfect mastery of the mathematical apparatus for processing accumulated empirical material in conjunction with a thorough knowledge of the qualitative characteristics of the phenomenon under study is necessary for every researcher. Only in this case is it possible to select high-quality, objective factual material, its qualified processing and obtain reliable final data.

    This is a brief description of the most commonly used methods for studying problems in psychology and pedagogy. It should be emphasized that none of the methods considered, taken on their own, can claim universality or a complete guarantee of the objectivity of the data obtained. Thus, elements of subjectivity in the answers obtained by surveying respondents are obvious. The results of observations, as a rule, are not free from the subjective assessments of the researcher himself. Data taken from various documentation simultaneously requires verification of the accuracy of this documentation (especially personal documents, second-hand documents, etc.).

    Therefore, every researcher should strive, on the one hand, to improve the technique of using any specific method, and on the other, to the complex, mutually controlling use of different methods to study the same problem. Mastery of the entire system of methods makes it possible to develop a rational research methodology, clearly organize and conduct it, and obtain significant theoretical and practical results.

      References.

      Shevandrin N.I. Social psychology in education: Textbook. Part 1. Conceptual and applied foundations of social psychology. – M.: VLADOS, 1995.

    2. Davydov V.P. Fundamentals of methodology, methods and technology of pedagogical research: Scientific and methodological manual. – M.: FSB Academy, 1997.

    Let's look at some concepts and basic approaches to classifications errors. According to the method of calculation, errors can be divided into absolute and relative.

    Absolute error equal to the difference in the average measurement of the quantity X and the true value of this quantity:

    In some cases, if necessary, calculate the errors of single determinations:

    Note that the measured quantity in chemical analysis can be either the content of a component or an analytical signal. Depending on whether the analysis result overestimates or underestimates the error, the errors may be positive And negative.

    Relative error can be expressed as fractions or percentages and usually has no sign:

    or

    Errors can be classified according to their sources. Since there are extremely many sources of errors, their classification cannot be unambiguous.

    Most often, errors are classified according to the nature of the reasons that cause them. In this case, the errors are divided by more systematicallyskiy and random, misses (or gross errors) are also highlighted.

    TO systematic refer to errors that are caused by a permanent cause, are constant in all measurements or change according to a constantly operating law, and can be identified and eliminated.

    Random errors, the causes of which are unknown, can be estimated by methods of mathematical statistics.

    Miss - this is an error that sharply distorts the result of the analysis and is usually easily detected, usually caused by the negligence or incompetence of the analyst. In Fig. 1.1 presents a diagram explaining the concepts of systematic errors and errors. Straight 1 corresponds to the ideal case when there are no systematic or random errors in all N definitions. Lines 2 and 3 are also idealized examples of chemical analysis. In one case (line 2) there are completely no random errors, but all N definitions have a constant negative systematic error Δx; in another case (line 3) There is absolutely no systematic error. The line reflects the real situation 4: There are both random and systematic errors.

    Rice. 4.2.1 Systematic and random errors in chemical analysis.

    The division of errors into systematic and random is to a certain extent arbitrary.

    Systematic errors in one sample of results may turn into random errors when considering a larger number of data. For example, a systematic error caused by incorrect instrument readings turns into a random error when measuring an analytical signal on different instruments in different laboratories.

    Reproducibility characterizes the degree of closeness of individual definitions to each other, the dispersion of individual results relative to the average (Fig. 1.2).

    Rice. 4.2..2. Reproducibility and accuracy of chemical analysis

    In some cases Along with the term “reproducibility” the term is used "convergence". In this case, by convergence we mean the dispersion of the results of parallel determinations, and by reproducibility - the dispersion of results obtained by different methods, in different laboratories, at different times, etc.

    Right - this is the quality of chemical analysis, reflecting the closeness to zero systematic error. Correctness characterizes the deviation of the obtained analysis result from the true value of the measured value (see Fig. 1.2).

    Population - a hypothetical set of all conceivable results from -∞ to +∞;

    Analysis of experimental data shows that large errors are observed less often than small ones. It is also noted that with an increase in the number of observations, the same errors different sign meet the same often. These and other properties of random errors are described by a normal distribution or Gauss equation, which describes the probability density
    .

    Where X-value of a random variable;

    μ – general average (expected value- constant parameter);

    Expected value- for a continuous random variable represents the limit to which the mean tends with an unlimited increase in the sample. Thus, the mathematical expectation is the average value for the entire population as a whole, sometimes called general average.

    σ 2 -dispersion (constant parameter) - characterizes the dispersion of a random variable relative to its mathematical expectation;

    σ – standard deviation.

    Dispersion– characterizes the dispersion of a random variable relative to its mathematical expectation.

    Sample population (sample)- the real number (n) of results that the researcher has, n = 3 ÷ 10.

    Normal distribution law unacceptable to handle a small number of changes in the sample population (typically 3–10) – even if the population as a whole is normally distributed. For small samples, use the normal distribution instead Student distribution (t– distribution), which connects three main characteristics of the sample population -

    Width of the confidence interval;

    Its corresponding probability;

    Sample size.

    Before processing data using mathematical statistics methods, it is necessary to identify misses(gross errors) and exclude them from the results considered. One of the simplest is the method of identifying errors using the Q - criterion with the number of measurements n< 10:

    Where R = X Max - X min– range of variation; X 1 – suspiciously prominent value; x 2 – the result of a single determination, closest in value to X 1 .

    The obtained value is compared with the critical value Q crit at a confidence level of P = 0.95. If Q > Q crit, the roll is a miss and is discarded.

    Main characteristics of the sample population. To sample from n results are calculated average,:

    And dispersion, characterizing the dispersion of results relative to the average:

    Dispersion cannot be used explicitly to quantitatively characterize the dispersion of results, since its dimension does not coincide with the dimension of the analysis result. To characterize scattering, use standard deviation,S.

    This value is also called the mean square (or square) deviation or the root mean square error of an individual result.

    ABOUTrelative standard deviation or the coefficient of variation (V) is calculated from the relation

    Dispersion of the arithmetic mean calculate:

    and standard deviation of the mean

    It should be noted that all quantities - dispersion, standard deviation and relative standard deviation, as well as the dispersion of the arithmetic mean and the standard deviation of the arithmetic mean - characterize the reproducibility of the results of chemical analysis.

    Used when processing small (n<20) выборок из нормально распределенной генеральной совокупности t – распределение (т.е. распределение нормированной случайной величины) характеризуется соотношением

    Wheret p , f Student's t distribution for the number of degrees of freedom f= n-1 and confidence probability P=0.95(or significance level p=0.05).

    The t-distribution values ​​are given in the tables; they are calculated from them for a sample in n results, the value of the confidence interval of the measured value for a given confidence probability according to the formula

    Confidence interval characterizes both the reproducibility of the results of chemical analysis and, if the true value of x is known, their correctness.

    Example of test work No. 2

    Exercise

    At A Analysis of air for nitrogen content by chromatographic method for two series of experiments obtained the following results:

    Solution:

    We check the series for the presence of gross errors using the Q-criterion. Why do we arrange the results in descending order (from minimum to maximum or vice versa):

    First episode:

    77,90<77,92<77,95<77,99<78,05<78,07<78,08<78,10

    We check the extreme results of the series (whether they contain a gross error).

    We compare the obtained value with the table one (Table 2 of the appendix). For n=8, p=0.95 Q tab =0.55.

    Because Q tab >Q 1 calculation, the leftmost digit is not a “miss”.

    Checking the rightmost digit

    Q calc

    The rightmost number is also not erroneous.

    We have results of the second row Yes, in ascending order:

    78,02<78,08<78,13<78,14<78,16<78,20<78,23<78,26.

    We check the extreme results of the experiments to see if they are erroneous.

    Q (n=8, p=0.95)=0.55. Table value.

    The leftmost value is not an error.

    The rightmost digit (whether it is erroneous).

    Those. 0.125<0,55

    The number on the far right is not a "miss".

    We subject the experimental results to statistical processing.

      We calculate the weighted average of the results:

    - for the first row of results.

    - for the second row of results.

      Dispersion relative to the mean:

    - for the first row.

    - for the second row.

      Standard deviation:

    - for the first row.

    - for the second row.

      Standard deviation of the arithmetic mean:

    For small (n<20) выборках из нормально распределенной генеральной совокупности следует использовать t – распределение, т.е. распределение Стьюдента при числе степени свободы f=n-1 и доверительной вероятности p=0,95.

    Using t-distribution tables, the value of the confidence interval of the measured value for a given confidence probability is determined for a sample of n-results. This interval can be calculated:

    WITH equalize variances And average results two sample populations.

    Comparison of two variances is carried out using the F-distribution (Fisher distribution). If we have two sample populations with variances S 2 1 and S 2 2 and degrees of freedom numbers f 1 =n 1 -1 and f 2 =n 2 -1, respectively, then we calculate the value of F:

    F=S 2 1 / S 2 2

    Moreover the numerator always contains the larger of the two compared sample variances. The obtained result is compared with the table value. If F 0 > F crit (at p = 0.95; n 1, n 2), then the discrepancy between the variances is significant and the sample populations under consideration differ in reproducibility.

    If the discrepancy between the variances is insignificant, it is possible to compare the means x 1 and x 2 of two sample populations, i.e. find out whether there is a statistically significant difference between the test results. To solve the problem, t-distribution is used. The weighted average of the two variances is preliminarily calculated:

    And the weighted average standard deviation

    and then – the t value:

    Meaning t exp compared with t Crete with the number of degrees of freedom f=f 1 +f 2 =(n 1 +n 2 -2) and sample confidence probability p=0.95. If at the same time t exp > t Crete,then the discrepancy between the averages And significant and the sample does not belong to the same population. If t exp< t крит, расхождение между средними незначимо, т.е. выборки принадлежат одной и той же генеральной совокупности, и, следовательно, данные обеих серий можно объединить и рассматривать их как одну выборочную совокупность из n 1 +n 2 результатов.

    Test task No. 2

    Analysis of air for the content of component X by chromatographic method for two series gave the following results (Table 1).

    3. Do the results of both samples belong to the same general population? Check using Student's t test (p = 0.95; n = 8).

    Table-4.2.1- Initial data for control task No. 2

    Option No.

    Component