Primitive social statistics originated in Britain and Germany. Almost at the same time, Italy appeared "gambling mathematics", that is, elementary probability theory. It was not until the19th century that primary mathematical statistics were formed because of the law of large numbers and the error theory in probability theory. In other words, the formation of social statistics is two centuries earlier than that of mathematical statistics. Because of the wide application of social statistics in economy and politics, it has been highly valued by successive governments in various countries and has been systematically developed. After the 1940s, due to the development of probability theory, mathematical statistics has developed rapidly. After nearly 400 years of changes, the world has formed two systems: social statistics and mathematical statistics. After more than 30 years' study and research, Professor Wang discovered the connection and difference between social statistics and mathematical statistics. The relationship between them is very similar to the famous relationship between Newtonian mechanics and relativity. Relativistic mechanics is used near the speed of light, but in most cases it is far away from the speed of light. At this time, Newtonian mechanics is accurate and convenient. If relativistic mechanics is applied rigidly, it is a butcher's knife for killing chickens, which is thankless. Social statistics are used to describe variables; Mathematical statistics are used to describe random variables.
We know that variables and random variables are both related and different. When the probability of the variable value is not 1, the variable becomes a random variable; A random variable becomes a variable when its probability is 1.
The relationship between variables and random variables, and the relationship between social statistics and mathematical statistics are clarified. When describing variables in the future, boldly use social statistics; Mathematical statistics will be used when describing random variables. If we must use mathematical statistics to describe variables, it is to kill chickens with a butcher's knife. In recent 70 years, due to the rapid development of mathematical statistics, there is a huge momentum of "swallowing up" social statistics, especially in developed countries represented by the United States, which almost think that statistics is mathematical statistics. In fact, this is a big misunderstanding. Professor Wang's research shows that mathematical statistics can never "eat" social statistics, and in the future, social statistics and mathematical statistics will coexist and complement each other. The debate between social statistics and mathematical statistics can be ended.
Conclusion: The Unity of Social Statistics and Mathematical Statistics scientifically combs the statistics of nearly 400 years, standardizes the development of the whole statistics, and ends the debate between social statistics and mathematical statistics in the past hundred years. Because economy is measured and analyzed by statistics, the unification of social statistics and mathematical statistics will certainly improve the analytical level of economics as a whole.
The great significance of "theoretical unity of social statistics and mathematical statistics"
Wang pointed out that social statistics describe variables, mathematical statistics describe random variables, and variables and random variables are two different and related mathematical concepts, which can be transformed into each other under certain conditions. Professor Wang's exposition of is a great discovery in mathematics. We know that the concept of "variable" was first put forward by the famous mathematician Descartes in17th century, while the concept of "random variable" was first put forward by Soviet scholars after 1930s, with a difference of three centuries. Up to Professor Wang, no second person in the world has put forward the connection, difference and mutual transformation between variables and random variables. We know that the introduction of variables has brought about the emergence and development of a series of major mathematical disciplines such as function theory, equation theory and calculus. The introduction of random variables laid the theoretical foundation of probability theory and mathematical statistics, and promoted their vigorous development. It can be seen that the concepts of variables and random variables are very valuable, so it is not an exaggeration to call the significance of the connection, difference and corresponding transformation between variables and random variables proposed by Professor Wang for the first time in the world great.
Let's return to the theory of "the unity of social statistics and mathematical statistics". Professor Wang pointed out that social statistics describe variables, while mathematical statistics describe random variables. In this way, Professor Wang accurately defined the research scope of social statistics and mathematical statistics, and the relationship that can be transformed into each other under certain conditions, which is the greatest contribution to statistics. It ended the melee situation of dozens or even hundreds of statistics in the past 400 years and put them back on track.
Because variables appear constantly and last forever, social statistics will not die out, but will continue to develop greatly. Of course, mathematical statistics will also develop greatly because of the continuous emergence of random variables. However, the study of random variables is generally more complicated than the study of variables, and until today, the study of mathematical statistics is still at a low level and more complicated to use; In the long run, the study of random variables will eventually turn into the study of variables, which is the same reason that we usually turn the study of complex problems into the study of several simple problems. Because social statistics describe variables, and the scope of variable description is extremely wide, it is by no means what some mathematical statisticians say: social statistics only do simple addition, subtraction, multiplication and division. Theoretically speaking, social statistics should cover the operation of most mathematics disciplines except mathematical statistics. Therefore, the theory of "the unity of social statistics and mathematical statistics" put forward by Professor Wang fundamentally corrects the wrong theory that the statistical community has underestimated social statistics for a long time, and shows the broad prospects of social statistics in theory and application.
The English version of Unity of Social Statistics and Mathematical Statistics was published by China Economic Publishing House on June 20 10, and has been distributed abroad. This book scientifically combs the statistics of nearly 400 years, standardizes the development of the whole statistics, and ends the debate between social statistics and mathematical statistics for more than 100 years. Note: The author of this book, Professor Wang, is a member of the International Statistical Institute and an internationally renowned mathematician. The book "The Unity of Social Statistics and Mathematical Statistics" was published by China Economic Publishing House on June 20 10, and will be distributed all over the world.No.: 342705 Press: China Economic Publishing House. The central problem of statistics is how to explore the real situation of population according to samples. Therefore, how to extract some elements from the population to form samples and what kind of samples can best represent the population directly affect the accuracy of statistics. If the method of extracting elements is to keep the elements in the population unchanged, then the observed values are independent random variables with the same distribution as the population. Such a sample is a simple random sample, which is the best representative of the population. The process of obtaining a simple random sample is called simple random sampling.
Simple random sampling refers to repeating the same random test, that is, each test is conducted under the same set of conditions, so the possibility of what results are obtained from each test is fixed. For a finite population, simple random sampling means extracting one element at a time, putting it back and then extracting it. If it is not put back, the composition of the population will change, so the possibility of various results will change relatively when it is extracted again. As for the infinite population, there is no need to distinguish between "putting it back" and "not putting it back".
In addition to the above principles, on the other hand, whether the specific sample acquisition method can ensure the independence of the observed values is the key to the problem. Therefore, whether a sample is random or not depends on the specific sample acquisition method.
When sampling, we must choose different sampling methods according to different research purposes.
① Simple random sampling method numbers each individual first, and then draws samples from the population by drawing lots. This method is suitable for the research objects with small differences among individuals, small number of individuals to be selected or concentrated distribution of individuals.
② Randomly divide the population into several parts by random sampling, and then randomly select several individuals from each part to form a sample. This sampling method can be more organized, and the distribution of selected individuals in the population is more uniform than that of simple random sampling.
(3) The systematic sampling method first systematically divides the population into several groups, and then randomly determines a starting point from the first group, such as 15 elements in each group, and decides to choose from 13 elements in the first group, so the units selected later are 28, 43, 58, 73, etc.
(4) Stratified sampling method divides the crowd into several levels or types according to the understanding of the characteristics of the crowd, and then randomly selects from each level according to a certain proportion. This method is representative, but if the hierarchy is not correct, a highly representative sample cannot be obtained.