Statistics is a branch of applied mathematics, probability theory, mainly through the use of a mathematical model, the observed systematic data collection, quantitative analysis, summary, and thus to infer and predict, provide the basis for the relevant decision-making and reference. It is widely used in various disciplines over, from the physical and social sciences to the humanities, even for business and government decisions on intelligence. Mainly divided into statistical and descriptive statistics inferential statistics. Given a _set_ of data, statistics can be summarized and described the data, the usage referred to as descriptive statistics. In addition, the observer in order to establish a form of data to explain the randomness and uncertainty in mathematical models to infer the study of the steps and the mother, such usage is called inferential statistics. The two uses can be referred to as applied statistics. There is also a discipline called mathematical statistics dedicated to discuss the rationale behind subjects.
Translated by Google
Statistical development process
The earliest statistical statistics stems from the modern English Latin statisticum collegium (Congress) and the Italian statista (national or politicians). German Statistik, first used by Gottfried Achenwall (1749) used, on behalf of the state of knowledge of data analysis, that is, "study the state of the science." In the nineteenth century in a wide range of data and statistical data to explore its meaning, and by John Sinclair introduced to English-speaking world. Statistics is a very ancient science, is generally believed that their scholarly research began in the era of ancient Greece, Aristotle, so far thousand three hundred years of history. It originated in the study of socio-economic problems in the 2000 years of development process, statistically at least through the "city-state's politics" and "political arithmetic" and "statistical analysis of science" three stages of development. The so-called "mathematical statistics" are not statistically independent of the new discipline, rather it is a significant development in the third stage of the formation of all data collection and analysis of a comprehensive new approach term. Mathematical probability theory is the theoretical basis of statistical methods, but it does not belong to the scope of statistics, but of mathematical areas. Statistics of the three stages of the development process The first stage is called "city-state's politics" (Matters of state) stage "City-state's politics" phase began in ancient Greece, Aristotle wrote, "city-state's politics" or "city minutes." He wrote a total of more than ten species for 150 minutes, which includes the city's history, administration, science, art, population, resources and wealth and other social and economic situation of comparison, analysis, features of social science. "City-state political situation" type of continuation of a statistical study of two thousand years, until the mid-seventeenth century was gradually being "political arithmetic" replaced the term, and quickly evolved into "Statistics" (Statistics). Statistics city still retains the (state) this root. The second stage is called "political arithmetic" (Politcal arthmetic) stage And "city-state's politics" stage there is no obvious cut-off point, in essence, the difference is not great. "Political arithmetic" is characterized by statistical methods and mathematical calculations and reasoning methods start with. Analysis of socio-economic approach to issues of greater emphasis on the use of quantitative analysis method. 1690 William Petty published (political arithmetic), a book mark as the beginning of this phase. William Petty with the numbers, weight and scale to the number of social and economic phenomena is an important feature of modern statistics. Thus, William? Petty (political arithmetic) was later scholars of modern statistical evaluation of the source, William? Petty himself is described as the father of modern statistics. Petty figures used in the book are three categories: The first is the phenomenon of socio-economic survey has been conducted and the number of observed experience, because by historical conditions, the book has been through a rigorous survey data from small, according to figures drawn from the experience and more; The second is to use a mathematical method derived from the figures. The projection method can be divided into three types: "(1) datum or a known quantity-based, follow a specific relationship between the projection method; (2) through the use of the number of theoretical reasoning for the projection method; (3) the average as the basis for the projection method "; The third category is to be used in theoretical reasoning and illustrative of the figure. Petty to use numbers and symbols such reasoning as "algebraic algorithms." Petty to use data from the ways of looking at, "political arithmetic" stage has been more obvious to the statistical concept of "data collection and analysis of the science and art" features, statistical analysis of empirical methods and theoretical seamless, even if this method is modern statistics are still inherited. The third stage is called "statistical science" (Science of statistical analysis) stage In the "political arithmetic" stages of a combination of statistical and mathematical development trend of gradually forming a "statistical analysis of science." The late nineteenth century, European universities _set_ up "situation summary" or "political arithmetic" and course name gradually disappeared, replaced by a "statistical science" courses when the "Statistical analysis of science" course content is still the analysis socio-economic problems. "Statistical analysis of science" course there is the beginning stage of development of modern statistics 1908, "students"'s (William Sleey Gos_set_'s pen name Student) published a paper on the t-distribution, which is a landmark in the history of statistics article. It has created a small sample instead of a large sample approach, creating a new era in statistics. Statistically representative of the devaluation of modern Belgian statistician Kuite Lai (Adolphe Quelet), he will be widely used in statistical analysis of science and social sciences, natural sciences and engineering sciences, because he was convinced any statistics can be used to study general scientific research methods. The theoretical basis of modern statistical theory of probability began in research opportunities for gambling problems began about 1477. Opportunities for mathematicians to explain the dominance of the general rule for long-term research, and gradually formed the theoretical framework of probability theory. Further development of probability theory, based on the early nineteenth century, mathematicians have gradually established observation error theory, normal distribution theory and least-squares rule. Thus, modern statistical methods will have a more solid theoretical basis.
Translated by Google
Statistical concepts
In order to apply statistics to scientific, industrial and social problems, we start from the parent study. This may be a country's people, a stone in crystal or a plant-specific production of home goods. A mother may even be observed by a number of times the same program components; by this data collection consisting of the mother we call it is called time series. For practical reasons, we choose a sub_set_ of study instead of the mother's mother for a single study, this sub_set_ of the known samples. Experience in the design of a sample of known experimental data collected. Information is the object of statistical analysis, and was used two related purposes: description and inference. Describe the statistical description of the problem: whether the information can be an effective summary, whether in mathematics or a picture show, to be used on behalf of mother nature? Based on mathematical description includes the mean and standard deviation. A summary of the image contains many kinds of tables and charts. Inferential statistics were used to model the data in the data, calculate the probability of it and make inferences for the mother. This inference may be right / wrong answer to the question presented (hypothesis testing), the estimated amount for the number of features (estimated), the forecast for future observations, the relevance of the prediction (correlation), or model of the relationship (regression ). Other modeling techniques include analysis of variance (ANOVA), time series, and data mining. In particular, the concept is relevant to discuss. Data collection for statistical analysis may show two variables (the mother of two types) tend to change together, as if they were connected. For example, income and age at death for human research journals may find that the poor than the rich on average tend to have shorter lives. These two variables are called related. But in fact, we can not directly infer that a causal relationship between two variables; see the relevance of causal inference (logical fallacy). If the sample is representative of the mother, then the inferences made from the sample and conclusions can be extended to the entire population above. The biggest problem is to determine whether the sample is representative of the entire matrix. Provides a number of statistical methods to estimate and correct the sample and data collection process randomness (error), as mentioned above, the experimental design through experience. See experimental design. To understand the randomness or chance must have basic math concepts. Mathematical Statistics (often also called statistical theory) is a branch of applied mathematics that uses probability theory to analyze and validate the theoretical basis of statistics. Any statistical method is valid only when the system or methodology discussed in the parent to meet the basic assumptions. Misuse may lead to statistical inference described surface or face serious error, this error may affect social policy, medical practice and the structure of the bridge program or the reliability of nuclear power. Even if the statistics are correct application of the results for the people who are not specialists may be difficult to state. For example, statistics may be significantly changed by the sample caused by the random variable, but this significance may be related to the public counterintuitive. People need some statistical skills (or suspected) to face daily life in the statistical data obtained through the reference information.
Translated by Google
Statistical Methods
1) measurement scale There are four statistical measurement scale or four kinds of measurement methods. These four measurements (nominal, order, off_set_, geometric) with a statistical process, ranging from practical. Geometric scale (Ratio measurements) have zero value and is equal to the distance between data is defined, equidistant scale (Interval measurements) is equal to the distance between data is defined, but its non-zero value is not absolute but define their own (such as intelligence or temperature measurements). (Ordinal measurements) the significance of the order of scale are not reflected in its value but in the order above. Nominal scale (Nominal measurements) the measured value is not a significant amount. 2) statistical techniques Here are some well-known statistical test methods and procedures for validation of experimental data Fisher least significant difference method (Fisher's Least Significant Difference test) Student t test (Student's t-test) Mann - Whitney U test (Mann-Whitney U) Regression analysis (regression analysis) Correlation (correlation) Pearson product-moment correlation coefficient (Pearson product-moment correlation coefficient) Spitzer Man's rank correlation coefficient (Spearman's rank correlation coefficient) Chi-square distribution (chi-square)
Translated by Google
Statistical history of the school
A 18-19th century - the creation and development of statistics Germany Sile Zi once said: "Statistics is a dynamic history, history is static statistics." Visible creation and development of statistics and production development, social progress are closely connected. (1) the creation of statistical period The seeds produced in the European statistics. Mid-17th century to the mid-18th century is the creation of statistical period. In this period, the statistical theory of the initial formation of a certain academic factions, mainly the national power school and school of political arithmetic. 1, the national power school National school, also known account of the potential school, in the 17th century Germany. The school mainly because the text describes the significant matters of state, so that accounts of school. The main representative of the Waldorf Haier Mankang orders and Aachen. Sport in Germany that the first university to Helms Tete "national trend study" in the title should have taught the knowledge of political activists. Aachen University of Göttingen Waldorf opened the "State" course, the main book is "The trend in modern European country Compendium" book about the "one country, or significant issues in most countries," mainly used the method of comparative analysis understanding of national organizations, territory, population, resources, wealth and national conditions and strength, compared the national strength, the strength of the German monarchy services. In the foreign language because of "national power" and "statistics" meaning the same, later officially named "Statistics." The school during the comparative analysis of national power, the emphasis on interpretation of the nature of things, rather than on comparing the number and amount of calculation, but for the statistical development has laid a foundation of economic theory. But with the capitalist market economy, the calculation of the amount of things and analysis has become increasingly important, then the school has undergone division, differentiation, school and more school for the chart. 2, school of political arithmetic School of political arithmetic in the 19th century Britain, the founder of William Petty (1623-1687), his masterpiece was completed in 1676 his "political arithmetic," a book. Here the "political" refers to political economy, "arithmetic" refers to statistical methods. In this book, he used actual data, the use of numbers, weights and scales and other statistical methods to Britain, France and the Netherlands national conditions and strength, made a comparative analysis of the number of systems, so as to formation and development of statistical methodology laid basis. Therefore, Marx said: "Wei Lianpei first - the father of political economy, to some extent also the founder of statistics." Another school of political arithmetic representative is Yue Hange Bronte (1620-1674). Church in London in 1604 he published the weekly "death Bulletin" for the research data, published in 1662, "bulletin on the death of the natural and political observations" on the. The book analyzes the 60-year resident of London causes of death and population changes in the relationship, first proposed by a large number of observations, can be found in newborn sex ratio is stable and the proportion of population in different laws of cause of death; and for the first time developed a "life table ", and an analysis of mortality and life expectancy, causing widespread concern. His research clearly shows the statistics as the important role of state management tools. (2) The period of development statistics 18th century to the 19th century is the period of development statistics. During this period, various schools of the academic point of view has been formed, and the formation of two major schools of thought, that school of mathematical statistics and social statistics school. 1, School of Mathematical Statistics 2, school of social statistics Socio-economic development requires more statistical methods statistics; social science itself constantly to the segmentation and quantification of the development also requires statistical survey to provide more effective collation, analysis of data method. Therefore, the school is also increasing emphasis on social statistics methodology of the study, there has been substantial methodological transformation from the trend. However, the school continues to stress the social statistics study of the statistical nature of things must be premised on material things and understand the importance of this same school of mathematical statistics, excluding the measurement of the nature of qualitative methodology is essentially different. Second, the 20th century - the rapid development of statistical Since the early 20th century, the rapid development of science and technology, society has undergone tremendous changes, statistics entered a rapid development period. Summed up in the following areas. 1, from the account of the development of statistics to inferential statistics. Account of statistics is collected by a large number of data processing order, summarize, through icons, lists and figures, such as the preparation of frequency distribution table, draw a histogram, the calculation of the number of features, etc., for data analysis and description. And inferential statistics, it is in the collection, sorting on the basis of the observed sample data, inferences about the overall. The feature is based on observations with a random sample of data and problem conditions and assumptions (model), and made the unknown, the probability expressed in the form of inference. Western countries are currently under scientific statistical methods, is the main means of statistical inference. 2, by the social and economic statistics to a multi-branch development. In the 20th century, the main statistical area population statistics, vital statistics, social statistics and economic statistics. With the social, economic and scientific and technological development, and today, the scope of statistics has covered all areas of social life, almost everything, a general methodology of science. It is widely used to study all aspects of society and nature, and has developed into many branches of science. 3, statistical forecasting and decision science. Traditional statistics are already occurred and are occurring things statistical, statistical information and data. Since the 1930s, especially since World War II, due to economic, social, and military aspects of the objective needs of statistical forecasting and statistical decision science has made significant progress, the statistics out of the traditional areas have been given new the meaning and mission. 4, information theory, cybernetics, systems theory and statistics of the mutual penetration and integration, further development of statistical science and maturing. Information theory, cybernetics, systems theory in a number of basic concepts, basic, basic methods, have in common, all three from different angles, side proposed to solve common problems and principles. Three of the creation and development, completely changed the world picture of science and scientists way of thinking, but also the statistics of science and statistics draw nutrition, broaden horizons and enrich the content, the emergence of new trends. 5, computing technology and a range of new technologies and new methods continue to be developed in the field of statistics and applications. In recent decades, computer technology continues to develop, so that statistical data collection, processing, analysis, storage, transmission, printing and other processes become increasingly modernized, improved statistical performance. Development of computer technology, expanding the traditional and advanced applications of statistical techniques, statistical science and statistics to promote a revolutionary change. Today, computer science has become an integral part of statistical science. With the development of science and technology, statistics, depth and breadth of the theory and practice are also evolving. 6. Statistics in modern management and social life becomes more and more important. With the social, economic and scientific and technological development, statistics in the modern state administration and business management position, the position in social life, more and more important. People's daily lives and life are inseparable from all social statistics. British statistician Haas Bartlett said: "The application of statistical methods is so prevalent in our lives and habits, the statistical impact is so great that no matter how the importance of statistics can not be overstated." And even some science of our time have also called "statistical era." Obviously, the 20th century, the development of statistical science and its future, has been given great significance.
Translated by Google
Statistics Status
In today's rapid development of science and technology, statistics and integration of related disciplines to absorb a wide range of new theories, and constantly develop new technologies and new ways to deepen and enrich the traditional areas of statistical theory and methods, and develop new fields. Today's statistics already show a strong vitality. In China, the socialist market economic system gradually established, practice development needs of the more significant proposed a new and higher requirements. With the growth of China's socialist market economy and constant improvement of the statistical potential function will be fuller and perfect opening. Second, a combination of qualitative and quantitative methods for the statistical analysis of comprehensive and integrated approach for the development of new ideas. A combination of qualitative and quantitative comprehensive integrated approach is Qian Xuesen in 1990's. The essence of this approach to scientific theories, experience, knowledge and expertise to judge by combining the empirical assumptions, empirical data and information and then model the exact nature of its testing, calculation and after repeated quantitative comparison, the final form conclusions . It is an effective means of studying complex systems, but also in the course of the study the problem everywhere permeated with statistical thinking, statistical analysis methods for the development of a new way of thinking. Statistics derived from the application, development and growth in the application process. With the economic and social development, convergence between the various disciplines of development and the rapid development of computer technology, statistical applications, statistical theory and analysis methods will continue to develop in all areas to show its vitality and important role.
Translated by Google
Areas of learning
Some subjects use a large number of applied statistics, as well as their own has become a separate discipline. Statistical branches are: Statistics History Statistical Theory Survey analysis theory Statistics Accounting Theory Statistical monitoring theory Statistical Prediction Theory Statistics logic Statistics Law Descriptive Statistics Statistical inference Economic Statistics Macroeconomic Statistics Micro-economic statistics Management Statistics Science and Technology Statistics Rural Economic Survey Social Statistics Education Statistics Culture and Sports Statistics Health Statistics Judicial Statistics Social Welfare and Social Security Statistics Statistical quality of life Demographics Environmental and Ecological Statistics Statistics of natural resources Environment Statistics Ecological balance statistics International Statistics International Standard Statistical Classification International accounting system and methodology of system International Comparison Statistics Other Biostatistics Business Statistics Engineering Statistics Psychological Statistics Chemometrics File Statistics Socio-economic statistics Hydrological statistics Mathematical statistics Statistical linguistics Statistical physics Chemometrics Extension of academic Some scientific statistical methods widely used so that they have their own statistical terms, these disciplines include: Agricultural Sciences Biostatistics Business Statistics Data mining (application of statistical and graphical access to knowledge from the information) Economic Statistics Motor statistics Statistical physics Demographics Psychological Statistics Education Statistics Social statistics (including all the social sciences) Statistical analysis of the literature Chemical and process analysis (analysis of all relevant chemical information and chemical sciences) Sports statistics, especially baseball and hockey Statistics for business and industry is a basic key. He used to understand variability and measurement systems, process control, for information to draw conclusions, and complete data-oriented decision-making. Statistics in these areas play an important role.
Translated by Google
Economic 百科
Statistics is the statistical theory is% 26ldquo; data collection and analysis of the science and art% 26rdquo;. A _set_ of statistical data collection and processing by the method of composition, these methods of statistical data from the study, which aims to explore the amount of data within the law, in order to achieve scientific understanding of objective things.
Translated by Google
Encyclopedia
Statistics Statistics This relationship, then make the same storage time and the effects of temperature. This test method is not only a waste of time and financial resources, but also easily lead to Wrong conclusions, because there are two factors likely between Interaction, that is, when the temperature changes when the influence of storage time May change in the way is not obvious. Even if one believes it Accurately the impact of storage time extrapolated to other temperatures. However, if If trials are well designed, without additional cost to do this, So there are still many do not support the use of extrapolation in the test method is intended See. As an example of the use of design, we consider a very simple One who used the so-called randomized block design. Suppose a factory main Considered purchasing a machine, the machine can have three sources of X, Y or Z. To compare the performance of the machine, for each source machine, he the Try buy one and use the factory workers of a number of operations, say five Two workers A, B, C, D and E for the proposed test. This is A two-factor test, in which the machine performance is the theme, but two factors Is both man and machine. In the evaluation of the machine, the workers are not actually feeling Xing Interesting factors, but of course test required. If the use of 15 workers (5 individual arrangements for each machine). This would be a mistake. Because of differences in the ability of workers, there is a machine May be due to luck to be assigned to some good workers but that it is Good. We have the same environment as close as possible under the machine For comparison, when each worker is to arrange each machine operation Device, so the machine can block (workers) more, although the block of Can vary considerably between, but within a single block is uniform. Data by a worker on each machine in each (in Within a specified time) measurement of the products obtained, these Data to fill in the following table, where it is essential that A worker in order to work on three machines should be random (eg For example, child-like way with throwing the decision), this can make some Design did not take into account secondary factors will not cause biased results with Sex. However, such learning is an important factor in operating the machine, then Test must be three factors, then need more complex designs. ┌ ─ ─ ─ ┬ ─ ─ ┐ │ total hoot, │ workers yz │ ├ ─ ─ ─ ┼ ─ ─ ┤ │ A │ │ │ B │ │ │ C │ │ │ D │ │ │ E │ │ └ ─ ─ ─ ┴ ─ ─ ┘ Figure 8 randomized trial data in the form In the resulting test data, the effect is mixed and the machine Together, but through the proper design of the experiment, there Called analysis of variance is calculated to distinguish between them, which A method of the total variance can be divided into several parts: the variance caused by the machine, Human-induced variance and the variance caused by the interaction; if test Experience is repeated, the test can generate corresponding error variance. That way, people will be able to estimate the main effects of individual machines, the main effects were And individual interaction effect should be. Include more factors in the test Experience, people can (depending on the choice of experimental design) high-end estimate Interaction, for example, a main effect factors and the other two factors Of
Translated by Google
English Expression
n.: statistics, [sing v] science of collecting, classifying and analysing such information
contaminate