Transcript Inferential statistics

Statistics
1
2
Introductory Statistics
Chapter 1 Introduction to Statistics
Chapter 2 Describing Data Sets
Chapter 3 Using Statistics to Summarize Data Sets
Chapter 4 Probability
Chapter 5 Discrete Random Variables
Chapter 6 Normal Random Variables
Chapter 7 Distributions of Sampling Statistics
Chapter 8 Estimation
Chapter 9 Testing Statistical Hypotheses
Chapter 10 Hypothesis Tests Concerning Two Populations
Chapter 11 Analysis of Variance
Chapter 12 Linear Regression
Chapter 13 Chi-Squared Goodness-of-Fit Tests
Chapter 14 Nonparametric Hypotheses Tests
3
Some Special Features of the Text



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
4
Chapter 1 Introduction to Statistics
1.1 Introduction
1.2 The Nature of Statistics
1.3 Populations and Samples
1.4 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.
5
Introduction

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)
6
Introduction

Conclusions:
◦ 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.
7
The Nature of Statistic

Definition (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.
8
Data Collection

Definition (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).
9
Inferential Statistics and
Probability Models

Definition (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.
10
Inferential Statistics and
Probability Models

Conclusions
◦ 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.
11
Populations and Samples

Definition
◦ 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.
12
Populations and Samples

Definition
◦ A sample of k members of a population is said to be
a 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.
13
A 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.
(John Graunt 1662)
14
A 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
15
A Brief History of Statistics

Graunt also used the London bills of mortality to infer
ages at death.
16
A 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.
17
KEY 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.
18