# Statistics

(P.P. Leung)

Lecture notes are based on the following textbook:

N.A. Weiss (2012), Introductory Statistics, 9th edition, Pearson.

Chapter 1 The Nature of Statistics 統計本質

§1.1 Two kinds of Statistics

§1.4 Other Sampling Designs (其他抽樣方法)

Chapter 1 The Nature of Statistics 統計本質

What is Statistics? 何謂統計?

From Wikipedia, the free encyclopaedia:

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities. Statistics is also used for making informed decisions in government and business. Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

From Our textbook:

← Facts or data of a numerical kind, assembled (組合), classified (分類) and tabulated (表列) so as to present significant information about a given subject ← The science of assembling, classifying, and tabulating such facts or data ← Collecting and analyzing data for the purpose for making generalizations and decisions

From 《統計學原理，南開大學出版》:

統計學是搜集、描述和分析數據，並根據所得數據資料進行推斷的一門科學和藝術。

Statistic (in wider and simpler sense):

1. Let data talk. 讓數據說話。

2. Quantify the uncertainties. 數量化不準確程度。

3. Making decision without enough information. 在條件不足下做决定。

§1.1 Two kinds of Statistics

Descriptive Statistics (描述統計) – consists of methods for organizing (整理) and summarizing (摘要) information, e.g. the NBA/CBA season every year.

Inferential Statistics (推斷統計) – consists of methods for drawing and measuring the reliability (可靠性) of conclusions about a population based on information obtained from a sample of the population, e.g. the 1948 presidential election.

Technical Terms (專有名詞):

Population (總體) – the collection of all individuals or items under consideration in a statistical study.

Sample (樣本) – a subset (part) of the population from which information is collected.

Statistics in this course – either descriptive statistics or inferential statistics (they are applied statistics.)

§1.2 Simple Random Sampling (簡單隨機抽樣)

Census (全體普查) – acquire information on the entire population of interest. Sampling (抽樣) – acquire information on only part of the population of interest. Experimentation (統計實驗) – acquire information by making up an experiment.

Why sampling is needed?

Survey of the whole population is usually labouring, time-consuming, expensive, frequently impractical and sometimes impossible.

Simple Random Sampling (簡單隨機抽樣) – A sampling procedure for which each possible sample of a given size is equally likely to be the one obtained. (每個抽樣單位被抽到的可能性都相同的方法)

Simple Random Sample (簡單隨機樣本) – A sample obtained by simple random sampling.

Why random sample is so important?

The sample being considered must be a representative sample (代表性樣本), i.e. it should reflect as closely as possible the relevant characteristics (相關特質) of the population. Random sample is a representative sample.

Simple random sampling with replacement (可放回簡單隨機抽樣) Simple random sampling without replacement (不可放回簡單隨機抽樣) (In this course, unless we specify otherwise, assume that simple random sampling is done with replacement).

Example – Simple Random Sampling P.14 Ex1.7

Sampling Oklahoma State Officials As reported by The World Almanac, the top five state officials of Oklahoma are as shown in Table 1.2. Consider these five...

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