管理决策中的统计思维导论

Statistical,

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"Statistical Thinking for Managerial Decisions" 是一本专注于将统计学应用于管理决策的讲义，旨在帮助读者理解和掌握在不确定情况下进行明智决策所需的统计思维方式。该资源由教授Hossein Arsham编写，包含多个学习层次的统计概念和主题。这本书的内容丰富多样，涵盖了从基础到进阶的统计知识，包括以下几个关键章节： 1. Chapter 1: 向统计思维决策转变 - 这一章引导读者理解统计思维的重要性，以及如何将其融入到日常管理和决策过程中，以应对不确定性。 2. Chapter 2: 描述性抽样数据分析 - 这一部分讲解了如何收集、组织和分析数据，以便对数据集进行初步的理解和描绘，包括平均值、中位数、模式、分布等。 3. Chapter 3: 概率作为统计推断的信心度量工具 - 介绍了概率论的基础，以及如何使用概率来评估统计推断的可靠性，这对于理解统计假设检验至关重要。 4. Chapter 4: 统计决策的必要条件 - 讨论了在做出统计决策时需要考虑的关键因素，如样本大小、置信水平和显著性水平。 5. Chapter 5: 估计器及其质量 - 探讨了参数估计的概念，包括点估计和区间估计，以及评价估计器优劣的标准，如无偏性和有效性。 6. Chapter 6: 假设检验：拒绝假设 - 阐述了如何设置零假设和备择假设，并通过统计测试来判断是否拒绝零假设。 7. Chapter 7: 均值和比例的假设检验 - 展示了如何对单个或两个总体的均值或比例进行假设检验，以确定是否存在显著差异。 8. Chapter 8: 多个总体的统计平等性检验 - 讲解了比较三个或更多总体的方法，如方差分析（ANOVA）。 9. Chapter 9: 卡方统计量的应用 - 介绍了卡方检验的原理和用途，用于检验分类变量之间的关联性或独立性。 10. Chapter 10: 回归建模与分析 - 解释了线性回归模型，以及如何利用它来预测一个变量基于另一个或多个变量的变化。 11. Chapter 11: 统计决策技术的统一视角 - 提供了一个全面的框架，将前面章节中的各种统计方法联系起来，形成一个综合的决策工具箱。这本讲义不仅适合对统计感兴趣的读者，也特别适用于经理人和决策者，他们可以通过学习这些统计概念和方法，提升在不确定环境下制定策略的能力。通过深入学习和实践，读者将能够更好地运用统计学知识进行有效的管理决策。

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The actuarial tables published by insurance companies reflect their statistical analysis of the average life

expectancy of men and women at any given age. From these numbers, the insurance companies then

calculate the appropriate premiums for a particular individual to purchase a given amount of insurance.

Exploratory analysis of data makes use of numerical and graphical techniques to study patterns and

departures from patterns. The widely used descriptive statistical techniques are: Frequency Distribution;

Histograms; Boxplot; Scattergrams and Error Bar plots; and diagnostic plots.

In examining distribution of data, you should be able to detect important characteristics, such as shape,

location, variability, and unusual values. From careful observations of patterns in data, you can generate

conjectures about relationships among variables. The notion of how one variable may be associated with

another permeates almost all of statistics, from simple comparisons of proportions through linear

regression. The difference between association and causation must accompany this conceptual

development.

Data must be collected according to a well-developed plan if valid information on a conjecture is to be

obtained. The plan must identify important variables related to the conjecture, and specify how they are to

be measured. From the data collection plan, a statistical model can be formulated from which inferences

can be drawn.

As an example of statistical modeling with managerial implications, such as "what-if" analysis, consider

regression analysis. Regression analysis is a powerful technique for studying relationship between

dependent variables (i.e., output, performance measure) and independent variables (i.e., inputs, factors,

decision variables). Summarizing relationships among the variables by the most appropriate equation (i.e.,

modeling) allows us to predict or identify the most influential factors and study their impacts on the output

for any changes in their current values.

Frequently, for example the marketing managers are faced with the question, What Sample Size Do I

Need? This is an important and common statistical decision, which should be given due consideration,

since an inadequate sample size invariably leads to wasted resources. The sample size determination

section provides a practical solution to this risky decision.

Statistical models are currently used in various fields of business and science. However, the terminology

differs from field to field. For example, the fitting of models to data, called calibration, history matching,

and data assimilation, are all synonymous with parameter estimation.

Your organization database contains a wealth of information, yet the decision technology group members

tap a fraction of it. Employees waste time scouring multiple sources for a database. The decision-makers

are frustrated because they cannot get business-critical data exactly when they need it. Therefore, too many

decisions are based on guesswork, not facts. Many opportunities are also missed, if they are even noticed at

all.

Knowledge is what we know well. Information is the communication of knowledge. In every knowledge

exchange, there is a sender and a receiver. The sender make common what is private, does the informing,

the communicating. Information can be classified as explicit and tacit forms. The explicit information can

be explained in structured form, while tacit information is inconsistent and fuzzy to explain. Know that data

are only crude information and not knowledge by themselves.

Data is known to be crude information and not knowledge by itself. The sequence from data to knowledge

is: from Data to Information, from Information to Facts, and finally, from Facts to Knowledge. Data

becomes information, when it becomes relevant to your decision problem. Information becomes fact, when

the data can support it. Facts are what the data reveals. However the decisive instrumental (i.e., applied)

knowledge is expressed together with some statistical degree of confidence.

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Fact becomes knowledge, when it is used in the successful completion of a decision process. Once you

have a massive amount of facts integrated as knowledge, then your mind will be superhuman in the same

sense that mankind with writing is superhuman compared to mankind before writing. The following figure

illustrates the statistical thinking process based on data in constructing statistical models for decision

making under uncertainties.

Click on the image to enlarge it and THEN print it.

The Path from Statistical Data to Managerial Knowledge

The above figure depicts the fact that as the exactness of a statistical model increases, the level of

improvements in decision-making increases. That's why we need Business Statistics. Statistics arose from

the need to place knowledge on a systematic evidence base. This required a study of the rules of

computational probability, the development of measures of data properties and relationships, and so on.

Statistical inference aims at determining whether any statistical significance can be attached that results

after due allowance is made for any random variation as a source of error. Intelligent and critical inferences

cannot be made by those who do not understand the purpose, the conditions, and applicability of the

various techniques for judging significance.

Considering the uncertain environment, the chance that"good decisions" are made increases with the

availability of"good information." The chance that"good information" is available increases with the level

of structuring the process of Knowledge Management. The above figure also illustrates the fact that as the

exactness of a statistical model increases, the level of improvements in decision-making increases.

Knowledge is more than knowing something technical. Knowledge needs wisdom. Wisdom is the power to

put our time and our knowledge to the proper use. Wisdom comes with age and experience. Wisdom is the

accurate application of accurate knowledge and its key component is to knowing the limits of your

knowledge. Wisdom is about knowing how something technical can be best used to meet the needs of the

decision-maker. Wisdom, for example, creates statistical software that is useful, rather than technically

brilliant. For example, ever since the Web entered the popular consciousness, observers have noted that it

puts information at your fingertips but tends to keep wisdom out of reach.

The notion of "wisdom" in the sense of practical wisdom has entered Western civilization through biblical

texts. In the Hellenic experience this kind of wisdom received a more structural character in the form of

philosophy. In this sense philosophy also reflects one of the expressions of traditional wisdom.

Business professionals need a statistical toolkit. Statistical skills enable you to intelligently collect, analyze

and interpret data relevant to their decision-making. Statistical concepts enable us to solve problems in a

diversity of contexts. Statistical thinking enables you to add substance to your decisions.

That's why we need statistical data analysis in probabilistic modeling. Statistics arose from the need to

place knowledge management on a systematic evidence base. This required a study of the rules of

computational probability, the development of measures of data properties, relationships, and so on.

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The purpose of statistical thinking is to get acquainted with the statistical techniques, to be able to execute 
procedures using available JavaScript, and to be conscious of the conditions and limitations of various 
techniques. 
Statistical Decision-Making Process
Unlike the deterministic decision-making process, such as linear optimization by solving systems of 
equations, Parametric systems of equations and in decision making under pure uncertainty, the variables are
often more numerous and more difficult to measure and control. However, the steps are the same. They are:
1. Simplification 
2. Building a decision model 
3. Testing the model 
4. Using the model to find the solution: 
o It is a simplified representation of the actual situation 
o It need not be complete or exact in all respects 
o It concentrates on the most essential relationships and ignores the less essential ones. 
o It is more easily understood than the empirical (i.e., observed) situation, and hence permits the problem to 
be solved more readily with minimum time and effort. 
5. It can be used again and again for similar problems or can be modified. 
Fortunately the probabilistic and statistical methods for analysis and decision making under uncertainty are more numerous 
and powerful today than ever before. The computer makes possible many practical applications. A few examples of business 
applications are the following: 
 An auditor can use random sampling techniques to audit the accounts receivable for clients. 
 A plant manager can use statistical quality control techniques to assure the quality of his production with a minimum
of testing or inspection. 
 A financial analyst may use regression and correlation to help understand the relationship of a financial ratio to a set 
of other variables in business. 
 A market researcher may use test of significace to accept or reject the hypotheses about a group of buyers to which 
the firm wishes to sell a particular product. 
 A sales manager may use statistical techniques to forecast sales for the coming year. 
Questions Concerning Statistical the Decision-Making Process: 
1. Objectives or Hypotheses: What are the objectives of the study or the questions to be answered? What is the 
population to which the investigators intend to refer their findings? 
2. Statistical Design: Is the study a planned experiment (i.e., primary data), or an analysis of records ( i.e., secondary 
data)? How is the sample to be selected? Are there possible sources of selection, which would make the sample 
atypical or non-representative? If so, what provision is to be made to deal with this bias? What is the nature of the 
control group, standard of comparison, or cost? Remember that statistical modeling means reflections before 
actions. 
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