Statistical analysis paper on statistical analysis and decision 1
Abstract: Statistical analysis and decision-making are both related and different. To participate in decision-making, we must make a good analysis of statistical data. To do a good job of statistical analysis, we need to solve three problems: topic selection, analysis and writing report.
[Keywords:] statistical analysis method decision
The whole process of statistical work is divided into four stages, namely statistical design, statistical investigation, statistical arrangement and statistical analysis. Among them, statistical analysis is the last stage of statistical work and the stage of producing statistical results. It is now advocated that statistics should participate in decision-making. Does this mean that a decision-making stage should be added to statistical work? If not, what is the relationship between statistical analysis and decision making?
In a narrow sense, statistical analysis and decision-making are different. Statistical analysis is a process of scientific analysis and comprehensive research on social and economic conditions based on statistics and using statistical methods, so as to understand its essence and laws. Decision-making is a process of comparing, analyzing and studying two or more possible schemes to achieve the predetermined goal, so as to make a reasonable and scientific choice. If statistical analysis and decision-making are compared to doctors' treatment, statistical analysis is the diagnosis of diseases and decision-making is the prescription. Diagnosis? And then what? Prescription? There is a difference.
Broadly speaking, statistical analysis and decision-making are inseparable. On the one hand, statistical analysis runs through the decision-making process. A decision-making process can be roughly divided into the following three steps: first, diagnose the problem and determine the decision-making goal; Second, explore and draw up various possible alternatives; Third, choose the most suitable scheme from various alternatives. Judging from these three steps, although many methods and means are needed, they are all inseparable from statistical analysis. The first step is to diagnose the problem through statistical analysis and determine the decision-making target on the basis of analysis; The second step is to draw up an alternative plan, which should be adopted? Corridor creativity? And then what? Detail design? At this stage, we should preliminarily screen the schemes envisaged in the corridor and enrich the specific content of each scheme. Screening? And then what? Enriched? Have to go through statistical analysis; The third step is to choose the best scheme. First of all, each alternative should be evaluated and demonstrated, which requires statistical analysis. Therefore, it can be said that there is no scientific decision without statistical analysis. On the other hand, in a sense, decision-making is the result of statistical analysis. Generally speaking, statistical analysis report is to ask questions, analyze problems and point out solutions to problems. In fact, decision-making scheme is also a way to solve problems and achieve decision-making goals, but it is better than? Suggestions on several measures in the future. This method is more comprehensive, detailed and scientific. The purpose of doctors' diagnosis is to correct prescriptions and save lives, not just to diagnose without prescriptions. Statistical analysis is to find and solve problems and promote the smooth development of social economy; We can't just ask questions without looking for solutions. In this sense, statistical analysis also includes forecasting and decision making. You can't count for the sake of statistics, nor can you analyze for the sake of analysis. Statistics should participate in decision-making, and for scientific decision-making, statistical analysis must be done well.
To do a good job of statistical analysis, we need to solve three problems: topic selection, analysis and report writing.
I. Topics of statistical analysis
The so-called topic selection is to determine the content and scope of statistical analysis in complex social and economic phenomena. The topic selection of statistical analysis is very important. Successful topic selection is the premise of successful analysis.
How to choose a good topic? There are two criteria for choosing a good topic: the analysis object is meaningful and suitable for the needs of decision makers and the masses. The key is to grasp the principles and policies of the party and the state and the economic benefits of enterprises.
The topics of statistical analysis are very extensive. The topics of industrial statistical analysis include: plan execution analysis, industrial net output value statistical analysis, industrial product sales statistical analysis, industrial raw material supply and consumption statistical analysis, industrial energy consumption statistical analysis, industrial production equipment statistical analysis, industrial labor and wages statistical analysis, cost profit statistical analysis, comprehensive economic benefit statistical analysis, etc. The statistical analysis topics of commodity circulation enterprises include: market supply and demand analysis, market share analysis, life cycle analysis of major commodities, market commodity price analysis, plan execution analysis, purchase and sale contract execution analysis, commodity procurement quality analysis, commodity sales dynamic analysis, commodity sales composition analysis, commodity inventory analysis, enterprise economic benefit analysis, etc. For the above content, according to the time, place and conditions, you can choose according to two criteria.
Statistical analysis can be divided into thematic analysis and comprehensive analysis. To study all aspects of the population and their interrelationships, or to study the statistical analysis of the main aspects of the population, is comprehensive analysis; Studying only one aspect or part of it is thematic analysis. Both have their own characteristics and are necessary, but there should be more thematic analysis and less comprehensive analysis.
Second, statistical analysis methods
The key to statistical analysis is analysis. How to conduct statistical analysis? Statistical analysis has two characteristics: one is based on statistics, and the other is based on statistical methods. Therefore, after selecting a topic, statistical analysis should collect and sort out relevant digital data and specific situations according to the needs of analysis, and flexibly use statistical methods for analysis on the basis of full possession of materials.
There are many statistical analysis methods. In the principle of statistics, besides the contents of statistical investigation and arrangement, comprehensive indicators, statistical indexes, time series and sampling inference are all statistical analysis methods. From the perspective of methodology, statistical analysis is the application of statistical principles.
Statistical methods are compatible with human cognitive process. Human cognition can be divided into two stages: perceptual cognition and rational cognition. What is known in the perceptual knowledge stage is the phenomenon of things, which can be sorted out through statistical investigation and statistics. What we know in the stage of rational cognition is the essence and laws of things, and we need to form concepts, make judgments, reason and other thinking activities. In line with this, different statistical analysis methods should be adopted respectively.
Generally, descriptive comprehensive index method is used to form concepts, namely total index, relative index and average index, to explain the scale, level, speed, internal structure and proportional relationship of the phenomenon. Judgment reasoning is to judge the essence of things, analyze the reasons for the changes of things, and find out the laws of their development. This is generally done by grouping analysis, dynamic analysis, factor analysis, correlation regression analysis and equilibrium analysis.
We should master all kinds of statistical analysis methods in statistical principles and use them flexibly. How to use it flexibly? There is a technical problem here. Skill is a clever combination of qualitative analysis and quantitative analysis.
The so-called qualitative analysis refers to the analysis of the nature of things and the factors affecting their development and changes. Quantitative analysis is to analyze the scale, level, speed, structure and proportion of things, as well as the direction and degree of influence of various factors on the overall change of things. The ingenious combination of qualitative analysis and quantitative analysis has two meanings, one is that they cannot be neglected, and the other is that they are inseparable.
Without qualitative analysis, quantitative analysis has no direction. Without quantitative analysis, qualitative analysis is inaccurate. The purpose of combination is to explore the internal relations of things in the dialectical unity of quality and quantity.
Fundamentally speaking, statistical analysis is to complete the leap from perceptual knowledge to rational knowledge and from phenomenon to essence. Only by completing this leap can we have high-quality statistical analysis. The quality of some statistical analysis is not high, and often this leap has not been completed, and it still stays on the surface.
Third, the writing of statistical analysis report
Statistical analysis report is the final product of statistics. If the accuracy of statistics is the life of statistics, then the quality of statistical analysis reports is related to the exertion of statistical functions. The requirements for high-quality statistical analysis reports can be summarized in five words, namely? Accurate, fast, new, deep and lively? .
Accuracy: it is to reflect the objective reality realistically. Make the figures accurate, the situation accurate and the arguments accurate.
Fast: It is to provide analysis report in time before the decision-making level makes a decision.
New: continuous innovation. It is required to constantly explore new fields, study new topics, and reflect new situations and problems.
Depth: on the basis of full possession of materials, it is to improve the depth of analysis, so that understanding can not only reflect phenomena, but also reveal the essence and laws of things, guide materials with opinions, and explain opinions with materials to achieve the unity of materials and opinions.
Live: refers to the lively words and flexible forms. The materials should be diversified, vivid and concrete, the language should be easy to understand and the text should be refined.
The statistical analysis report is written on the basis of statistical analysis. Without good analysis, it is impossible to write a good report. Through the analysis stage, find out the facts, find out the nature, explore the law and draw a conclusion. On this basis, you can write a statistical analysis report. But good analysis does not mean that the report is well written. There is also a problem of writing skills, that is, accurately stating the facts, thoroughly clarifying the essence, profoundly revealing the law, and making appropriate suggestions.
1. State the facts accurately
Every statistical analysis report needs to express the analyzed phenomenon, that is, explain it? What is this? . Accurately stating facts can give readers a clear concept. So we must pay attention to the following points: (1) The figures should be true; (2) Use numbers appropriately, and don't pile them up to make them literal; (3) The language elements are accurate.
2. Thoroughly clarify the essence
Phenomenon only shows one-sided things, and essence only shows the whole things. Writing a statistical analysis report must profoundly reveal the essence of things, which is the embodiment of the correct degree and depth of statistical understanding of things. If you can't profoundly clarify the essence of things, it can only be a list of phenomena, which is of little value.
To understand the essence of things is to understand the basic nature of things. The nature of things is determined by the main aspects of internal contradictions. For example, do enterprises increase profits by raising prices or reducing costs? Through analysis, it is realized that the increase of profit mainly depends on reducing costs, which is the main aspect of contradiction and reflects the essence of things. Therefore, the report should clarify the important role of reducing costs in improving economic efficiency. Another example is an enterprise, the essential problem is the serious waste of steel, and the report should reveal several aspects and severity of waste.
3. Deeply reveal the law
Law is an inherent, essential and inevitable connection within things. There is a relationship between cost and output. After reasoning, this relationship is inherent and essential, reflecting the regularity of the development and change of things, and there is a certain regression relationship. Regression equation reflects this relationship, so in statistical analysis report, regression equation should be used to reveal this inevitable relationship and its regression relationship.
Make appropriate suggestions
The purpose of knowing the world is to transform it. After statistical analysis, we should understand the nature and laws of things through phenomena, and also put forward suggestions to solve problems, such as? Future opinions? 、? Some suggestions. 、? Decision plan? Wait a minute. What are the appropriate suggestions? Appropriate suggestions should meet three conditions: (1) it meets the purpose of analysis; (2) Conforming to objective laws; (3) It is feasible.
The above four points can generally be used as the structure and order of the analysis report, but they cannot be the same.
Statistical analysis report is the reflection of statistical analysis results. We should not only pay attention to improving the writing level, but also exercise the ability to analyze and solve problems.
Statistical analysis The second part is about the application of statistical analysis methods.
The application of statistical analysis methods in various fields has solved many practical problems in industry, agriculture, economy, medicine and other fields. This paper analyzes the main application of multivariate statistical analysis method and the necessity of constructing multivariate statistical test system, and puts forward some problems that need attention, which has strong practical significance.
Keywords statistical analysis; Application; Check the system; * * * sexual problems; A preface with practical significance
With the popularization and wide application of information technology, the development of society, economy and science and technology has been promoted, and the problem of multivariate statistical analysis method has been broken, which has been widely used in various fields and promoted the rapid development of all walks of life.
Second, the main application of multivariate statistical analysis method
Statistical method is an important tool in scientific research, and its application is quite extensive. In industrial, agricultural, economic, biological, medical and other practical problems, it is often necessary to deal with the observation data of multiple variables, so it is particularly important to comprehensively deal with the multivariate statistical analysis method of multiple variables. With the popularization of computer technology and the development of society, economy and science and technology, multivariate statistical analysis methods, which used to be considered difficult in mathematics, have been more and more widely used in practice.
Cluster analysis
It is a multivariate statistical method to study classification problems. The basic idea of clustering analysis is to treat each sample as a class first, then calculate the distance between the new class and other classes according to the similarity between samples, and then select an approximator, and reduce one class every time a class is merged, and continue this process until all samples are merged into one class. Therefore, clustering analysis depends on the understanding of proximity or similarity between observations, and different clustering results can be produced by defining different distance measures and similarity measures. It is very important for enterprises to find out which enterprises are direct competitors and which are indirect competitors in the same market when making marketing strategies. To solve this problem, enterprises can first obtain themselves and all their main competitors through market research, so as to find opportunities for enterprises in the market.
discriminant analysis
Discriminant analysis is to divide the known research objects into several types and get a batch of observation data of various types of known samples. On this basis, the discriminant is established according to certain criteria, and then the samples of unknown types are discriminant analyzed. In market forecasting, enterprises often use discriminant analysis to judge whether products are best-selling or slow-selling in the next quarter according to various indicators of previous surveys. Generally speaking, discriminant analysis is often combined with cluster analysis.
principal component analysis
Principal component analysis is an attempt to recombine the original indicators into a new set of irrelevant comprehensive indicators to replace the original indicators. At the same time, according to the actual needs, we can extract several less comprehensive indicators to reflect the information of the original indicators as much as possible. In market research, principal component analysis is often used to analyze customers' preferences and the differences between products and customers in the current market, so as to provide information on the development direction of new products for production enterprises.
factor analysis
Factor analysis is the generalization and application of principal component analysis. It combines complex random variables into a small number of random variables to describe, and the correlation between multiple variables reproduces the relationship between original indicators and factors. Factor analysis can also be considered as classifying indicators according to the internal structure of original data. For example, the number of commercial outlets, population, services of financial institutions, income and other N indicators in Y survey areas were analyzed by factor analysis. According to the general analysis method, N indicators need to be processed and given different weights. In this way, not only the workload becomes larger, but also the correlation between dry indicators is high, which will bring deviation to the analysis results and give many indicators with high correlation, so as to calculate the average comprehensive strength score of each investigation area and decide what type of sales point to build in a certain investigation area.
Third, the necessity of building a multivariate statistical analysis method testing system
(A) the construction of multivariate statistical analysis method testing system, improve the quality of multivariate statistical analysis.
Multivariate statistical analysis method has been used more and more widely, but there are many cases of blindly applying analysis method in application, and only care about the application of model method. Many textbooks only focus on introducing the ideas, principles and analysis steps of multivariate statistical analysis methods, and rarely describe the statistical test of the application results of multivariate statistical analysis methods. This directly affects the application effect and credibility of multivariate statistical analysis methods. Therefore, this paper intends to discuss the statistical test of multivariate statistical analysis methods. The purpose of constructing the examination system of multivariate statistical analysis method is to further enrich and improve the content system of multivariate statistical analysis method; In practice, the application of multivariate statistical analysis method is more reasonable and standardized. Promote the improvement of the application quality of multivariate statistical analysis methods and the wider application of multivariate statistical analysis methods.
(B) the basic theory of multivariate statistical analysis and statistical test system
Sample distribution of multivariate normal distribution population, i.e. Wichita distribution, hotelling distribution, Wilkes distribution and multivariate normal population mean vector hypothesis test, includes one normal population mean vector hypothesis test, two normal population mean vector hypothesis tests and multiple normal population mean vector hypothesis tests; The hypothesis test of multivariate normal population covariance matrix includes one normal population covariance matrix hypothesis test and multiple covariance matrix equality hypothesis tests.
(3) About the statistical inspection system
The basic framework of multivariate statistical analysis method inspection system is formed by organically combining the above statistical inspection systems. Construct the assessment system of multivariate statistical analysis method, cooperate with multivariate statistical analysis method, give full play to the application value of multivariate statistical analysis method, and improve the application quality. We suggest that the corresponding statistical test should be carried out according to the above framework when applying. Of course. The above statistical inspection system is still a preliminary framework. With the gradual improvement of the theory of multivariate statistical analysis methods, the above-mentioned inspection system needs to be continuously improved, and more colleagues need to pay attention to such problems and continue to study. On the other hand, in practical application, even if a certain method is statistically tested according to the above contents, there will still be many shortcomings in application due to the defects or limitations of various methods. Should attract attention. However, the result of factor analysis is still subjective. In particular, the interpretation of the professional practical significance of the public's main factors still retains an artistic flavor, and there is no unified approach, so it is often not satisfactory. In a word, when we apply it, we have the applicability of factor analysis, the estimation method of common factors and the number of common factors to choose. A series of problems, such as the practical meaning explanation of common factors, should be paid enough attention to. Inspection systems are classified as follows:
A. Statistical test system of principal component analysis
B. Factor analysis statistics test paper cracks
C. Statistical test system for systematic cluster analysis
D. discriminant analysis and statistical test of bulk cracks
E. correspondence analysis statistical test system
F. Statistical test system of canonical correlation analysis
Four, multivariate statistical analysis methods need to pay attention to several * * * problems.
1. Overall distribution of original data variables.
Various methods have different requirements for the overall distribution of original variables. Some methods have no special requirements for the overall distribution of original data variables, such as principal component analysis, cluster analysis, correspondence analysis and so on. Some methods have different requirements for the distribution of original variables in different situations. For example, in factor analysis, different estimation methods of common factors have different requirements for the distribution of original variables. When the main variable is estimated by maximum likelihood estimation method, it is assumed that the original variable obeys multivariate normal distribution. So pay attention to the application. For example, canonical correlation analysis requires that the original variables obey normal distribution, but strictly speaking, if the distribution form of variables, such as high skewness, will not reduce other variables.
Sample size problem.
At present, there is no unified conclusion as to how much sample size n is appropriate for multivariate statistical analysis. Some people think that the sample size should be 10 ~ 20 times of the number of variables, some people think that the sample size should be greater than 100, some people think that the sample size in bartlett test should be greater than 150, and some people think that it is unnecessary to ask for too many sample sizes. For example, in principal component analysis and factor analysis, when the correlation between the original variables is small, it is difficult to get satisfactory results even if the sample size is enlarged.
Correlation and nonlinear relationship between original variables.
In multivariate statistical analysis methods, some need the correlation of original variables. Others don't need the correlation of the original variables. For example, in cluster analysis, the correlation between original data variables is also needed when clustering analysis of Q-type system is carried out. For example, when choosing Euclidean distance, Mintz distance and Langer distance, the original variables are required to be irrelevant. Only after the relevant processing of the original data can you choose to use the above distance. If the original variables are related, it is more appropriate to choose Mahalanobis distance. In addition, the nonlinear relationship between the original variables is also a problem that needs attention. Such as principal component analysis, factor analysis and canonical correlation analysis. When calculating based on correlation matrix, the correlation matrix here is actually Pearson's product moment correlation. However, if the relationship between variables is not linear, but non-linear, then the analysis and conclusion will lose their due significance.
Data processing problems.
Multivariate statistical analysis involves many variables, and different variables often have different dimensions and different quantification levels. When analyzing, it is meaningless to combine variables of different dimensions linearly, when analyzing variables of different orders of magnitude. Will lead to. Eat big and eat small? That is, the influence of order of magnitude variables will be ignored, thus affecting the rationality of the analysis results. Therefore. In order to eliminate the influence of dimension and order of magnitude, the original data must be processed in multivariate statistical analysis. The most common thing is to do standardized transformation first, and then do corresponding analysis.
Verb (abbreviation of verb) conclusion
In the application of statistical analysis methods, many variables will be involved, which must be processed according to the original quantity before the corresponding analysis conclusions can be drawn. Based on the theoretical basis of multivariate statistical analysis method, this paper analyzes the relevant inspection system and analysis system, which has practical theoretical guiding significance.
refer to
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[2] Gao Huixuan. The application of multivariate statistical analysis [M]. Beijing, Peking University Publishing House, 2005: 343? 366.
[3] Guo Zhigang. Social science analysis method -SPSS software application [M]. Renmin University of China Press, 1999.
[4] Fu Deyin. Statistical test in principal component analysis [J]. Statistical Education, 2007 (9): 4? 7.
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