Mass observation method
This is the basic method of collecting data in the process of statistical activities (that is, the stage of statistical investigation): that is, observing and studying enough individuals in the phenomenon population under study to understand the regular quantitative characteristics of the population. The mathematical basis of a large number of observations is the law of large numbers, which means that although each individual is influenced by different accidental factors and has a little difference in quantity, they can cancel each other out and present a stable regularity on the whole. Therefore, only when a sufficient number of individuals are observed, the comprehensive results of observation will tend to be stable, and general conclusions will be given based on a large number of observed data. All kinds of statistical investigation methods belong to a large number of observation methods.
Statistical grouping method
Because of the complexity, difference and multi-level of the phenomena studied, we need to study the phenomena in groups or classifications in order to explore the differences between different groups or classifications on the basis of homogeneity. Statistical grouping plays an important role in the whole process of statistical activities. In the stage of statistical investigation, different kinds of data can be collected by statistical grouping method to improve the sample representativeness of sampling investigation (that is, stratified sampling method). In the stage of statistical arrangement, various data can be processed and stored by statistical grouping, which provides the basis for compiling distribution series; In the stage of statistical analysis, we can divide the phenomenon types, study the overall internal structure, compare the differences between different classes or groups (significance test), and analyze the correlation between different variables by statistical grouping method. The statistical grouping methods in statistics include traditional grouping method, discriminant analysis method and cluster analysis method.
Comprehensive index method
The quantitative characteristics of statistical research phenomena are reflected by statistical comprehensive indicators. The so-called comprehensive index refers to the categories and numerical values used to reflect the quantitative characteristics and quantitative relations of the studied phenomena as a whole, and the common ones are total index, relative index, average index and symbolic variation index. The comprehensive index method plays a very important role in statistics, especially socio-economic statistics, and is the core content of descriptive statistics. How to record, describe and reflect the quantitative characteristics and quantitative relations of the studied phenomena most truly and objectively is a major topic in the theoretical research of statistical indicators.
Statistical model method
When using statistical indicators to reflect the quantitative characteristics of the studied phenomena, we often need to make quantitative research on the quantitative relationship between related phenomena in order to understand the relationship between the quantitative change of one phenomenon and the quantitative change of another phenomenon and the degree of influence of this change. When studying this quantitative relationship, it is necessary to use appropriate mathematical equations to simulate it according to specific research objects and certain assumptions. This method is called statistical model method.
Statistical inference method
In statistical cognitive activities, what we observe is often only a part of the phenomenon we study, and we only have random sample observation data, and understanding the quantitative characteristics of the population is the purpose of statistical research, which requires us to infer the quantitative characteristics of the population from the sample observation data by using the methods of parameter estimation or hypothesis testing according to probability theory and sample distribution theory. This method of inferring a population from a sample is called statistical inference. Statistical inference method has been applied in many fields of statistical research. In addition to the most common general index inference, the estimation and test of statistical model parameters and the estimation and test of original time series in statistical prediction also belong to the category of statistical inference, and there are problems of error and confidence. In practice, this is an effective and economical method, with a wide range of applications and rapid development. Statistical inference has become the basic method of modern statistics.
References:
Baidu encyclopedia statistics