StatisticsStatistics

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Introductory StatisticsIntroductory StatisticsChapter 1 Introduction to StatisticsChapter 2 Describing Data SetsChapter 3 Using Statistics to Summarize Data SetsChapter 4 ProbabilityChapter 5 Discrete Random VariablesChapter 6 Normal Random VariablesChapter 7 Distributions of Sampling StatisticsChapter 8 Estimation Chapter 9 Testing Statistical HypothesesChapter 10 Hypothesis Tests Concerning Two PopulationsChapter 11 Analysis of VarianceChapter 12 Linear RegressionChapter 13 Chi-Squared Goodness-of-Fit TestsChapter 14 Nonparametric Hypotheses Tests

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Some Special Features of the Some Special Features of the TextText Introduction Statistics in Perspective ( 觀點 )

Real Data◦ Throughout the text discussions, examples, perspective

highlights, and problems, real data sets are used to enhance the students’ understanding of the material.

◦ These data sets provide information for the study of current issues in a variety of disciplines, such as health, medicine, sports, business, and education.

Historical Perspectives Problems/Review Problems Summary/Key Terms Formula Summary Program CD-ROM

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Chapter 1 Introduction to Chapter 1 Introduction to StatisticsStatistics1.1 Introduction1.2 The Nature of Statistics1.3 Populations and Samples1.4 A Brief History of Statistics

◦ This chapter introduces the subject matter of statistics, the art ( 技術 ) of learning from data.

◦ It describes the two branches of statistics, descriptive ( 描述 ) and inferential ( 推理 ).

◦ The idea of learning about a population ( 母群 ) by sampling and studying certain of its members is discussed.

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IntroductionIntroduction Is it better for children to start school at a younger or

older age?◦ Achievement tests◦ The total number of years spent in school (Table

1.1)

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IntroductionIntroductionConclusions:

◦ Using the census ( 記錄 ) data, the age at which a child enters school has very little effect on the total number of years that a child spends in school.

◦ One must collect relevant information (data), and these data must then be described and analyzed.

◦ Such is the subject matter of statistics.

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The Nature of StatisticThe Nature of StatisticDefinition (Statistics)

◦ Statistics ( 統計學 ) is the art of learning from data.

◦ Statistics is concerned with the collection of data, their description, and their analysis, which often leads to the drawing of

conclusions.

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Data CollectionData CollectionDefinition (descriptive statistics)

◦ The part of statistics concerned with the description and summarization of data is called descriptive statistics ( 描述統計 ).

For example: ◦ The efficacy of a new drug needs to be determined

Divide the volunteers into two groups by “random” one group receives the drug, the other group receives a placebo ( 安慰劑 )

Control group: The group that does not receive any treatment (that is,

the volunteers that receive a placebo).

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Inferential Statistics and Inferential Statistics and Probability ModelsProbability ModelsDefinition (inferential statistics)

◦ The part of statistics concerned with the drawing of conclusions from data is called inferential statistics ( 推論統計 ).

◦ When the experiment is completed and the data are described and summarized, we hope to be able to draw a conclusion about the efficacy of the drug. It is usually necessary to make some assumptions

about the chances (or probabilities) of obtaining the different data values.

The totality of these assumptions is referred to as a probability model for the data.

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Inferential Statistics and Inferential Statistics and Probability ModelsProbability ModelsConclusions

◦ The basis of statistical inference is the formulation of a probability model to describe the data.

◦ An understanding of statistical inference requires some knowledge of the theory of probability.

◦ Statistical inference starts with the assumption that important aspects

of the phenomenon( 現象 ) under study can be described in terms of probabilities, and

then it draws conclusions by using data to make inferences about these probabilities.

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Populations and Populations and SamplesSamplesDefinition

◦ The total collection of all the elements that we are interested in is called a population ( 母群 ).

◦ A subgroup of the population that will be studied in detail is called a sample ( 樣本 ).

A given sample generally cannot be considered to be representative of a population unless that sample has been chosen in a random manner.

This is because any specific nonrandom rule for selecting a sample often results in one that is inherently biased ( 偏見 ) toward some data values as opposed to ( 與 ... 對照 ) others.

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Populations and Populations and SamplesSamplesDefinition

◦ A sample of k members of a population is said to bea random sample, sometimes called a simple random sample, if the members are chosen in such a way that all possible choices of the k members are equally likely.

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A Brief History of StatisticsA Brief History of Statistics A systematic collection of data on the population and

the economy was begun in the Italian city-states of Venice ( 威尼斯 ) and Florence ( 佛羅倫斯 ) during the Renaissance. (Renaissance: 文藝復興時期 , 從 14 世紀末期到大約 1600 年之間 )

The term statistics, derived from the word state, was used to refer to a collection of facts of interest to the state.

In 1662 the English tradesman John Graunt published a book entitled Natural and Political Observations Made upon the Bills of Mortality ( 死亡率清單 ).

Table 1.2, which notes the total number of deaths in England and the number due to the plague ( 瘟疫 )for five different plague years, is taken from this book.

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A Brief History of StatisticsA Brief History of Statistics Graunt used the London bills of mortality ( 死亡率清單 )

to estimate the city’s population. To estimate the population of London in 1660,

Graunt surveyed households ( 家庭 ) in certain London parishes ( 地方行政區 ) and discovered that, on average, there were approximately 3 deaths for every 88 people.

There was roughly 1 death for every 88/3 people. Since the London bills cited 13,200 deaths in London

for that year, Graunt estimated the London population to be about

13,200 X 88 / 3 = 387,200

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A Brief History of StatisticsA Brief History of StatisticsGraunt also used the London bills of

mortality to infer ages at death.

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A Brief History of StatisticsA Brief History of Statistics In the early 20th century, two of the most important areas of

applied statistics were population biology ( 生物學 ) and agriculture ( 農耕 ).

Nowadays the ideas of statistics are everywhere. ◦ Descriptive statistics are featured in every newspaper and

magazine. ◦ Statistical inference has become indispensable ( 必需的 )

to public health and medical research, to marketing ( 行銷 ) and quality control ( 品管 ), to education, to accounting( 會計 ), to economics( 經濟 ), to meteorological forecasting( 氣象預報 ), to polling ( 投票 ) and surveys ( 調查 ), to sports, to insurance( 保險 ), to gambling( 賭博 ), and to all research that makes any claim to being scientific.

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KEY TERMSKEY TERMS Statistics: The art of learning from data. Descriptive statistics: The part of statistics that deals with the

description and summarization of data. Inferential statistics: The part of statistics that is concerned with

drawing conclusions from data. Probability model: The mathematical assumptions relating to the

likelihood of different data values. Population: A collection of elements of interest. Sample: A subgroup of the population that is to be studied. Random sample of size k: A sample chosen in such a manner

that all subgroups of size k are equally likely to be selected.

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