Ma Yinchu, a famous contemporary economist and educator in China, once said: "Scholars can't learn without statistics, industrialists can't practice without statistics, and politicians can't be in power without statistics."
Statistics is a way to understand the real existence. As big as a country, as small as a company or even an individual, it will be used. Whoever can get accurate statistical information can grasp the real present and provide basis for subsequent decision-making. However, it is not easy to count the number of students. Numbers, formulas, functions and curves are too difficult for most people, and I don't know what help I can get from learning statistics.
Nishino Shinji, a Japanese, has always wanted to write an easy-to-understand statistical book to help ordinary people understand statistics, master basic statistical tools and cultivate statistical thinking. Nishinoki graduated from the University of Tokyo majoring in biostatistics, mainly engaged in xxx, and has rich experience in the practical application of statistics. His rich experience focuses on numerical statistics and statistical thinking. The former is more professional and in-depth, while the latter is more popular and practical.
Statistical thinking is a way of thinking in the process of obtaining data, extracting information from data and demonstrating the reliability of conclusions, which plays a great role in improving human cognition. In order to make readers understand statistical thinking, this book is mainly divided into two parts, one is the main body of the book, the relationship between various statistical methods, concepts and actual cases, and the other is the mathematical explanation of various statistical concepts and formulas in the "Mathematical Appendix".
The book mainly talks about several mathematical concepts: mean, standard deviation, hypothesis testing, regression analysis and so on. The front is ok, but the back is more difficult than the knowledge of mathematics in domestic high schools. For those who don't study advanced mathematics in some universities, it is still quite difficult to read.
In the Practical Reading Guide, Toshiyuki Dayan said that only about 20% of the content in a book is really valuable to us. If your math foundation is not good, then the way of thinking in the book may be relatively more useful.
Mean and median. Statistically, mean and median are concepts that describe several trends. However, the average value depends on the distribution, and it is often the most effective when the data is normally distributed. Median is more of a nonparametric concept. Median is a number that can divide the data into two halves after arranging the data from small to large. If the distribution is not nearly orthogonal, then the median is more effective than the average. Therefore, it is more important to use these concepts correctly to explain things in life in the right situation. When the data obeys normal distribution, the average is equal to the median.
There is a "28 rule" in the economy, and 80% of the world's wealth is in the hands of 20% people. If only the average personal income is calculated, many people's income is "on the high side". If we calculate the median at this time and compare personal income with the median, we can roughly know what level our income is in the country. This technique can also be used to calculate which company is expected to get higher income when applying for a job. If the average salary of Company A is 8,000, but the median is only 3,000, and the average salary of Company B is 6,000, but the median is 4,000, how do you choose?
Statistical inference has limitations. When making a decision, most people infer from their own relevant experience, that is, samples. It is often said that everyone has his own limitations, in other words, it is impossible for people to understand the totality of things. Then when inferring with samples, we must choose the appropriate samples, and we can't generalize by partiality.
1936 American election, literary digest magazine speculated that Alfred? Langdon will get 370 electoral votes in 53 1. Judging from this result, there is no pressure to defeat Roosevelt at all. In this survey, Literature Abstracts distributed a total of100,000 questionnaires, and 2.3 million questionnaires were collected. The practice of literary abstracts is correct. A large sample size will definitely improve the accuracy of the estimation, and there is nothing wrong with it. But the result was wrong. Roosevelt was elected. Why? Because among the readers of Literary Digest, the proportion of * * * and party member is much higher than that of * * * and party supporters in the total American population. In other words, this sample cannot be extended to the whole country at all. Then the corresponding conclusion is definitely untenable.
Ensure a certain probability under the error allowed by statistics. In statistics, randomness is everywhere. It allows mistakes, and if there is no mistake, people will suspect that it is false. Statistics will also guarantee a problem, but its guarantee is based on probability form. Moreover, the guaranteed probability is not 100%, and there is an error. In statistics, the p value is 5%, which does not have much mathematical basis in itself, but follows the habit of mathematician Fisher and thinks that it is more convenient to judge the p value with 5%. When the standard deviation se is less than the p value, a certain inference or result is credible.
Statistics has fixed rules, but in practical application, it may not be completely observed. Sometimes the conditions are idle and the inspection standard of 5% on both sides is not fully followed. For example, in the medical field, some operations have a low success rate. As long as they reach an agreement with patients for life, patients may still choose to try. In business promotion, it is also possible to make some high-risk decisions with large P value, and decision makers may choose to take chances. Be prepared to take risks at this time.
In the preface of A Brief History of Mathematical Statistics, Mr. Chen Xiru said: Statistics is not only a method or technology, but also contains elements of the world outlook-it is a way of looking at everything in the world. This is what we often say from a statistical point of view. But statistical thought also has a development process. Therefore, the cultivation of statistical ideas (or viewpoints) not only needs to learn some specific knowledge, but also can organically and clearly link these knowledge from the perspective of development and gain a sense of historical importance.