Generally speaking, statistics is to use statistical data to describe, analyze and summarize, or use statistical data to predict the future and infer new statistical data. Descriptive statistics and inferential statistics, respectively. Statistical data is a concept in statistics.
In order to apply statistics to scientific, industrial and social problems, we start with the study of matrices. This may be the people of a country, the crystal in a stone, or the goods produced by a particular factory. A matrix may even consist of the same observation program many times; The matrix composed of such data sets is called time series.
Theoretical Unity of Social Statistics and Mathematical Statistics
According to the authoritative statistical history, from17th century, there have been "political arithmetic" and "national studies", that is, primary social statistics, which 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, social statistics came into being two centuries earlier than 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. It is difficult to distinguish between the two systems because of endless arguments. Professor Wang, a statistician, has discovered the connection and difference between social statistics and mathematical statistics after 30 years of study and research. 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.
Statistician 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.