2. Population: A set of variables of all observation units are homogeneous according to the research purpose.
3. Variation: the difference between the observed values (variable values) of things of the same nature.
4. Sampling research: Randomly select some representative samples from the people under study for research, infer the people with sample indicators, and finally achieve the purpose of understanding the people. This method of inferring population parameters with sample indicators is called sampling research.
5. Statistical description: using statistical charts or calculating statistical indicators to express a certain phenomenon or characteristic of a specific group.
6. Statistical inference: The method of estimating or inferring the overall characteristics according to the characteristics of sample data is called statistical inference, and the commonly used methods include parameter estimation and hypothesis testing.
7. Probability: refers to the measure of the probability of an event, which is represented by the symbol P. ..
8. Medical reference value range: Reference value range is also called normal value range. In medicine, an index contains the numerical range of most people, which is often called the reference range of the index.
9. Normal distribution law: In practical work, it is often necessary to know the percentage of an area on the horizontal axis under the normal curve to the total area, so as to estimate the percentage of observed cases in the interval to the total cases, or the frequency or probability that the variable value falls within the interval.
10, comparability: it means that the non-therapeutic factors affecting the research results are as similar or similar as possible among the treatment groups.
1 1. Dynamic series: it is a series of statistical indicators arranged in time sequence, including absolute number, relative number or average number, to explain the changes and development trends of things in time.
12. Sampling error: when several samples with the same sample content are randomly selected from the same population, the differences between sample indicators and the differences between sample indicators and the overall indicators.
13, standard error: indicates the degree of change between sample means.
14. Ratio sampling error: the difference between the mean values of the same population in the sampling process is called mean sampling error, and the difference between ratios is called ratio sampling error.
15. Parameter estimation: refers to the estimation of the overall indicators (called parameters) by using sample indicators (called statistics).
16, confidence interval: the value range of the overall parameters is usually called the confidence interval or confidence interval of the parameters, that is, the interval contains the overall parameters with a certain probability (such as 95% or 99%).
17, type I error: H0 that can be established by actual lying is rejected. This kind of "discarding truth" error is called type I error.
18, the second kind of error: accepting H0 can't be established when actually lying. This kind of "keeping false" error is called the second kind of error.
19, inspection efficiency: 1-b is called inspection efficiency and guarantee. It means: when there are differences between two populations, the ability to find out the differences between the two populations according to the prescribed test level A.
20. Four-grid data: Data with two sampling rates is also called four-grid data. In the four-grid data, the actual frequency of appearance and the actual frequency of absence of two samples are basic data, and other data can be calculated from these four basic data.
2 1, contingency table data: the same sample data is summarized into a two-way cross-arranged statistical table according to its two unordered variables (row variable and column variable). Row variables can be divided into R categories, and column variables can be divided into C categories, which are called R*C contingency tables.
22. Parameter test: it is a hypothesis test, which requires that the sample comes from a known population distribution type (such as normal distribution), and based on this assumption, the population parameters (such as population mean) are statistically inferred.
23. nonparametric test: it is a hypothesis test that does not depend on the type of population distribution and does not make statistical inference on population parameters (such as population mean).
24. Rank: the serial number in the usual sense. In fact, the observed values are arranged in order from small to large, and the variable values themselves are replaced by serial numbers.
25. Linear correlation coefficient: it is a statistical index to explain the degree and direction of correlation between two variables with linear relationship. The correlation coefficient has no unit, and its value range is-1 < = R < = 1. The greater the absolute value of r, the closer the relationship between the two variables.
26. Complete negative correlation: This is a very special negative correlation. As can be seen from the scatter diagram, the scattered points composed of x and y are completely distributed on a straight line. As x increases, y decreases correspondingly, and the calculated correlation coefficient r=- 1.
27. Positive correlation: It means that there is a positive correlation direction between two variables in a linear relationship, that is, when X increases, Y has a corresponding increasing trend, and the calculated correlation coefficient R is positive.
28. Rank correlation: it is a nonparametric statistical method for correlation analysis of rank data, also known as rank correlation.
29. Evaluation: It is a process of judging the observation results with certain standards and giving the results certain meaning and value.
30. Comprehensive evaluation: refers to that people choose corresponding evaluation forms according to different evaluation purposes, and then select multiple factors or indicators, and through a certain mathematical model, transform multiple evaluation factors or indicators into information that can reflect the overall characteristics of the evaluation object.
3 1, pecking order method: in order to compare the advantages and disadvantages of a few things or schemes, after selecting various evaluation indexes, the objects or schemes to be evaluated are arranged according to the measured values of each evaluation index, and the serial number (grade) is given a corresponding score, that is, the pecking order, and then the evaluation indexes are combined to calculate the total pecking order of the evaluation objects respectively, and the pecking order is evaluated according to the total pecking order size.
32.Topsis:Topsis method is often used in multi-objective decision analysis of limited schemes in system engineering, in addition, it can also be used in benefit evaluation, health decision-making, health management and many other fields.
33. The root cause of death: According to WHO, the root cause of death refers to: "(a) diseases or injuries that cause a series of pathological events that directly lead to death, or (b) accidents or violent situations that lead to fatal injuries."
34. Demand for health services: refers to the demand that people should actually accept various health services (such as preventive health care, treatment and rehabilitation, etc.) because diseases affect health and cause obstacles to normal human activities.
35. Health service survey and statistics is one of the main contents of health statistics. Investigation and Statistics of Health Services This paper expounds the characteristics, research methods and matters needing attention of health service research from the perspective of design, collection, collation and analysis of health service data, so as to make health service research more scientific.
36. Health service survey: refers to the social survey on the current situation of health services, health risk factors of the population, the demand and utilization of health services of the population, and the distribution and utilization of health service resources.
37. Statistical tables: Listing statistical indicators in tabular form is a common means of statistical description of data.
38. Statistical chart: Various geometric figures (such as points, lines, planes or solids) are used to represent the size, fluctuation, distribution and relationship of data, and it is also a common means to describe data statistically.
39. Sampling error of the average: Statistically, the difference between the averages of the same population generated in the sampling process is called the sampling error of the average.
Statistical overview
Statistics is a branch of applied mathematics, which mainly uses probability theory to establish mathematical models, collect data from observation systems, make quantitative analysis and summary, and then infer and predict, providing basis and reference for relevant decisions. It is widely used in various disciplines, from physics, social sciences to humanities, and even in industrial and commercial and government information decision-making.
Statistics are mainly divided into descriptive statistics and inferential statistics. Given a set of data, statistics can summarize and describe these data. This usage is called descriptive statistics. In addition, the observer establishes a mathematical model in the form of data to explain its randomness and uncertainty, thus inferring the steps and matrices in the research. This usage is called inferential statistic. Both of these usages can be called applied statistics. In addition, there is a subject called mathematical statistics, which is devoted to discussing the theoretical basis behind this subject.
[Edit this paragraph] The development of statistics
English statistics of statistics originated from modern Latin statisticum collegium (Congress) and Italian statista (country or politician). German Statistik, first used by Gottfried Achenwall( 1749), stands for the knowledge of analyzing national data, that is, "studying national science". /kloc-in the 20th century, statistics explored its significance in a wide range of data and materials, and was introduced to the English-speaking world by John Sinclair.
Statistics is a very old science. It is generally believed that its theoretical research began in Aristotle's time in ancient Greece and has a history of more than 2300 years. It originated from the study of social and economic problems. In the development process of more than 2,000 years, statistics has experienced at least three stages of development: city-state politics, political arithmetic and statistical analysis science. The so-called "mathematical statistics" is not a new discipline independent of statistics, to be exact, it is the general name of all the new methods of collecting and analyzing data formed by statistics in the third development stage. Probability theory is the theoretical basis of mathematical statistics, but it belongs to mathematics rather than statistics.
Three stages of statistical development
The first stage is called "national affairs".
The stage of "polis politics" began when Aristotle in ancient Greece wrote "polis politics" or "polis minutes". He wrote 150 kinds of minutes, including a comparative analysis of the social and economic conditions of each city-state, such as history, administration, science, art, population, resources and wealth, which has the characteristics of social science. The statistical study of "city-state politics" lasted for one or two thousand years, and it was not until the middle of the seventeenth century that it was gradually replaced by the word "political arithmetic" and soon evolved into "statistics". Statistics still retains the word "country".
The second stage is called "political art" stage.
There is no obvious dividing point with the stage of "city-state politics", and there is little difference in essence.
Political Arithmetic is characterized by the combination of statistical methods with mathematical calculation and reasoning methods. The way to analyze social and economic problems pays more attention to the application of quantitative analysis methods.
1690, william petty published a book (political arithmetic) as the beginning of this stage.
William petty's method of quantifying social and economic phenomena with numbers, weights and scales is an important feature of modern statistics. William. Pei Di (political arithmetic) was evaluated by later scholars as the source of modern statistics, William? Pei Di himself was also evaluated as the father of modern statistics.
Pei Di used three types of characters in his book:
The first category is the figures obtained from statistical investigation and empirical observation of social and economic phenomena. Due to the limitation of historical conditions, there are few data in the book after strict statistical investigation, and many figures are based on experience.
The second category is the number calculated by some mathematical method. There are three calculation methods:
"(1) A calculation method based on a known number or quantity and following a specific relationship;
(2) the method of calculation by theoretical reasoning of numbers;
(3) Calculation method based on average value ";
The third category is illustrative numbers used for theoretical reasoning. Pego called this reasoning using numbers and symbols "algebraic algorithm". Judging from the methods used by the cooperators, the statistics in the stage of "political arithmetic" has clearly embodied the characteristics of "science and art of collecting and analyzing data", and the statistical empirical method is integrated with the theoretical analysis method, which is still inherited even by modern statistics.
The third stage is called "statistical analysis science".
The trend of combining statistics and mathematics in the stage of "political arithmetic" has gradually developed into "statistical analysis science".
/kloc-At the end of 0/9th century, the names of courses offered by European universities such as "Outline of National Conditions" or "Political Arithmetic" gradually disappeared and were replaced by "Statistical Analysis Science", which was still about analyzing and studying social and economic problems.
The emergence of the course "Statistical Analysis Science" is the beginning of the development stage of modern statistics. 1908, Student (alias William Sleey Gosset) published a paper on T distribution, which is an epoch-making article in the history of statistical development. It pioneered the method of replacing large samples with small samples and initiated a new era of statistics.
Belgian statistician Adolf Quelley is the first representative of modern statistics. He widely applied statistical analysis science to social science, natural science and engineering technology science, because he was convinced that statistics could be used as a general research method to study any science.
Probability theory, the theoretical basis of modern statistics, began to study the timing of gambling, probably from 1477. Mathematicians have conducted long-term research to explain the general laws governing opportunities, and gradually formed the theoretical framework of probability theory. On the basis of further development of probability theory, mathematicians gradually established observation error theory, normal distribution theory and least square method by the early 19th century. Therefore, modern statistical methods have a solid theoretical foundation.
[Edit this paragraph] Historical school statistics
I.18-19th century-establishment and development of statistics
German Schlitz once said: "Statistics is dynamic history, and history is static statistics." It can be seen that the emergence and development of statistics are closely related to the development of production and social progress.
Statistics during the period of the founding of the People's Republic of China (1)
The germination of statistics originated in Europe. /kloc-from the middle of 0/7th century to the middle of 0/8th century, statistics was founded. During this period, statistical theory initially formed certain academic factions, mainly including national trend school and political arithmetic school.
1, National Potential School
The national trend school, also known as the narrative school, was born in Germany in the17th century. Because this school mainly describes the major issues of the country in words, it is called the narrative school. Its main representatives are Hailmann Kang Ling and Ahenwall. Kang Ling was the first person to teach the knowledge that political activists should have at Tete University in Helms. Ahenwall opened a course of "National Studies" at the University of G? ttingen. His main work is "Outline of Ethnic Studies in Modern European Countries", which is about "the salient issues of a country or most countries". He mainly used the method of comparative analysis to study and understand the country's organization, territory, population, resources, wealth and national strength, and compared the strength of various countries to serve the German monarchy. Because "national conditions" and "statistics" have the same meaning in foreign languages, they were officially named "statistics" later. In the comparative analysis of national conditions, this school emphasizes the explanation of the essence of things, but does not pay attention to quantitative comparison and quantitative calculation, but it lays the economic theoretical foundation for the development of statistics. However, with the development of capitalist market economy, the calculation and analysis of things become more and more important. Later, this school was divided into the chart school and the comparison school.
2. Political Arithmetic School
/kloc-in the middle of the 0/9th century, a school of political arithmetic appeared in Britain. Its founder is william petty (1623- 1687), and his masterpiece is Political Arithmetic, which was completed in 1676. "Politics" here refers to political economy, and "arithmetic" refers to statistical methods. In this book, he made a systematic and quantitative comparative analysis of the national conditions and national strength of Britain, France and the Netherlands by using the statistical methods of number, weight and scale, which laid a methodological foundation for the formation and development of statistics. Therefore, Marx said: "william petty, the father of political economy, is also the founder of statistics to some extent."
Another representative of the school of political arithmetic is john grant (1620- 1674). Based on the weekly Death Bulletin published by the Church of London in 1604, he published his work Natural and Political Observations in the Death Bulletin in 1662. The book analyzes the causes of death of London residents in the past 60 years and the relationship between population changes. For the first time, it is found that the sex ratio of newborns is stable through a large number of observations, and different proportions of causes of death are demographic laws. And compiled a "life table" for the first time, and analyzed the mortality rate and life expectancy, which attracted widespread attention. His research clearly shows the important role of statistics as a national management tool.
(2) the development period of statistics
The development period of statistics is from the end of 18 to the end of 19. During this period, various schools of academic views were formed, and two main schools were formed, namely, mathematical statistics school and social statistics school.
1, School of Mathematical Statistics
18th century, due to the maturity of probability theory, it laid the foundation for the development of statistics. /kloc-in the middle of the 0/9th century, probability theory was introduced into statistics, forming a school of mathematics. Its founder is Belgian Lambert Adolphe Jacques Quetelet (1796- 1874), and his main works are: On Man, Probabilistic Letters, Social System and Social Physics. He advocated studying social phenomena by studying natural science, and formally introduced classical probability theory into statistics, which made statistics enter a new stage of development. Due to historical limitations, kettler confused natural phenomena and essential differences in his research, and made some mechanical and vulgar explanations on social problems such as crime and morality with the viewpoint and method of studying natural phenomena. However, he introduced probability theory into statistics, which made statistics take a step forward on the accurate road on the basis of the "arithmetic" method established by "political arithmetic" and laid the foundation for the formation and development of mathematical statistics.
2. School of Social Statistics
The school of social statistics came into being in the second half of19th century. Its founder is German economist and statistician Knies (182 1- 1889), and its main representatives are Engel (182 1- 1896) and Meyer. They integrated the viewpoints of the National Trend School and the Political Arithmetic School, and developed along kettler's "Basic Theory of Statistics". However, they thought that statistics was a social science and a substantive science to study the causes and laws of social phenomena, which was contrary to the general methods of the Mathematical Statistics School. The school of social statistics believes that statistics is the research object rather than an individual phenomenon. Because of the complexity and integrity of social phenomena, it is necessary to observe and analyze them as a whole and study their internal relations in order to reveal the internal laws of the phenomena. This is a remarkable feature of the "substantive science" of the social statistics school.
The development of social economy requires statistics to provide more statistical methods; Social science itself is constantly developing into subdivision and quantification, which also requires statistics to provide more effective methods for investigating, sorting out and analyzing data. Therefore, the school of social statistics pays more and more attention to the research of methodology, and there is a trend of changing from substantive methodology. However, the school of social statistics still emphasizes that the quality of things must be the premise and importance of understanding things, which is essentially different from the methodological nature of the school of mathematical statistics.
Second, the 20th century-the rapid development of statistics
Since the 20th century, with the rapid development of science and technology, great changes have taken place in society, and statistics has entered a period of rapid development. To sum up, there are the following aspects.
1, from descriptive statistics to inferred statistics. Descriptive statistics is to process and summarize a large number of collected data, and analyze and describe the data through charts, lists and graphs, such as compiling frequency distribution tables, drawing histograms and calculating various feature numbers. Inference statistics, on the basis of collecting and sorting out the observed sample data, infer the relevant population. It is characterized by the inference of unknown things in the form of probability according to the conditions and assumptions (models) of random observation of sample data and problems. At present, the scientific statistical methods referred to by western countries mainly refer to inferential statistics.
2. From socio-economic statistics to multidisciplinary development. Before the 20th century, the fields of statistics were mainly demographic statistics, vital statistics, social statistics and economic statistics. With the development of society, economy and science and technology, today, the category of statistics has covered all fields of social life, almost all-encompassing, and has become a general methodological science. It is widely used to study all aspects of society and nature, and has developed into a science with many branches.
3. The development of statistical forecasting and decision science. Traditional statistics is to count what has happened and what is happening, and provide statistical information and data. Since the 1930s, especially since the Second World War, due to the objective needs of economy, society and military affairs, the science of statistical prediction and statistical decision-making has made great progress, which has made statistics go out of the traditional field and been endowed with new significance and mission.
4. The mutual penetration and combination of information theory, cybernetics, system theory and statistics has further developed and improved statistical science. Information theory, cybernetics and system theory are similar in many basic concepts, ideas and methods, and they put forward methods and principles to solve the same problem from different angles and sides. The establishment and development of the "Three Theories" have completely changed the scientific picture of the world and the way of thinking of scientists, and also enabled statistical science and statistical work to draw nutrition from it, broaden their horizons, enrich their contents and have a new development trend.
5. Computing technology and a series of new technologies and methods have been continuously developed and applied in the field of statistics. In recent decades, the continuous development of computer technology has modernized the collection, processing, analysis, storage, transmission and printing of statistical data, and improved the efficiency of statistical work. The development of computer technology has increasingly expanded the application fields of traditional and advanced statistical techniques, which has revolutionized statistical science and work. Nowadays, computer science has become an inseparable part of statistical science. With the development of science and technology, the depth and breadth of statistical theory and practice are also developing.
6. Statistics play an increasingly important role in modern management and social life. With the development of society, economy and science and technology, statistics play an increasingly important role in modern state management, enterprise management and social life. People's daily life and all social life are inseparable from statistics. British statistician Haslet said: "The application of statistical methods is so common that statistics have such a great influence on our lives and habits that the importance of statistics cannot be overemphasized." Some sciences even call our age "the statistical age". Obviously, the development of statistical science in the 20th century and its future are endowed with epoch-making significance.
[Edit this paragraph] Statistical status quo
With the rapid development of science and technology, statistics widely absorbs and integrates new theories of related disciplines, constantly develops and applies new technologies and methods, deepens and enriches the theories and methods in the traditional statistical field, and expands new fields. Today's statistics show great vitality. In China, the gradual establishment of the socialist market economic system and the needs of realistic development put forward new, more and higher requirements for statistical work. With the development and continuous improvement of China's socialist market economy, the potential role of statistics will be fully and comprehensively brought into play.
First, the understanding of systematicness and system complexity has added new ideas for the future development of statistics. Due to the rapid development of the breadth and depth of social practice and the high development of science and technology, people have a more comprehensive and in-depth understanding of the systematicness and complexity of the objective world. With the rise of the trend of scientific integration, the research tentacles of statistics extend to new fields, and the research on statistical methods of exploratory data arises at the historic moment. The research field has expanded to complex and objective phenomena. 2 1 century, the focus of statistical research will shift from deterministic and stochastic phenomena to the study of complex phenomena. Such as fuzzy phenomenon, mutation phenomenon and chaos phenomenon. It can be said that the study of complex phenomena has opened up a new research field for statistics.
Secondly, the comprehensive integration method combining qualitative and quantitative methods will provide new ideas for the development of statistical analysis methods. The comprehensive integration method combining qualitative and quantitative methods was put forward by Professor Qian Xuesen in 1990. The essence of this method is to combine scientific theory, empirical knowledge and expert judgment, put forward empirical hypothesis, then test its effectiveness with empirical data, materials and models, and finally form a conclusion after quantitative calculation and repeated comparison. It is an effective means to study complex systems, and statistical ideas are permeated everywhere in the process of problem research, which provides a new idea for the development of statistical analysis methods.
Third, the infiltration of statistical science and other sciences will open up new fields for the application of statistics. The development of modern science shows a trend of integration, and various disciplines are constantly integrated, forming an interconnected and unified whole. Because things are interrelated, the infiltration and transfer of research methods between disciplines has become the general trend of modern scientific development. The new progress made in many disciplines provides brand-new development opportunities for the development of other disciplines. The emergence of new frontier disciplines such as fuzzy theory and catastrophe theory provides new scientific methods and ideas for the further development of statistics. Introducing some cutting-edge scientific achievements into statistics and making statistics interact with them will become the development trend of statistics in the future. Statistics will also have an exciting prospect. Today, some pioneers have begun to introduce methods and theories such as cybernetics, information theory, system theory, graph theory, chaos theory and fuzzy theory into statistics. The penetration of these new theories and methods will have a far-reaching impact on the development of statistics.
Statistics comes from application and develops in application. With the development of economy and society, the integration of various disciplines and the rapid development of computer technology, the application field of statistics, statistical theory and analysis methods will continue to develop, showing its vitality and important role in various fields.
[Edit this paragraph] Branch discipline
Some disciplines use applied statistics so much that they have become independent disciplines.