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統計學 Fall 2003

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統計學 Fall 2003

授課教師：統計系余清祥

日期：2003年9月16日

第一週：什麼是統計？

什麼是統計?

- 統計學是研究定義問題、運用資料蒐集、整理、陳示、分析與推論等科學方法, 在不確定(Uncertainty)情況下, 做出合理決策的科學。

- Applications in Business and Economics
- Data
- Data Sources
- Descriptive Statistics
- Statistical Inference

- Accounting
Public accounting firms use statistical sampling procedures when conducting audits for their clients.

- Finance
Financial advisors use a variety of statistical information, including price-earnings ratios and dividend yields, to guide their investment recommendations.

- Marketing
Electronic point-of-sale scanners at retail checkout counters are being used to collect data for a variety of marketing research applications.

- Production
A variety of statistical quality control charts are used to monitor the output of a production process.

- Economics
Economists use statistical information in making forecasts about the future of the economy or some aspect of it.

- Elements, Variables, and Observations
- Scales of Measurement
- Qualitative and Quantitative Data
- Cross-Sectional and Time Series Data

- Data are the facts and figures that are collected, summarized, analyzed, and interpreted.
- The data collected in a particular study are referred to as the data set.

- The elements are the entities on which data are collected.
- A variable is a characteristic of interest for the elements.
- The set of measurements collected for a particular element is called an observation.
- The total number of data values in a data set is the number of elements multiplied by the number of variables.

Stock Annual Earn/

Company Exchange Sales($M) Sh.($)

DataramAMEX73.10 0.86

EnergySouth OTC74.00 1.67

Keystone NYSE 365.70 0.86

LandCare NYSE 111.40 0.33

PsychemedicsAMEX17.60 0.13

Observation

Variables

Elements

Data Set

Datum

- Scales of measurement include:
- Nominal(名義) data are merely labels or assigned numbers
- Ordinal(順序) data can be arranged in order such as worst to best or best to worst
- Interval data can be arranged in order and the difference between numbers has meaning
- Ratio data differ from interval data in that there is a definite zero point

- The scale determines the amount of information contained in the data.
- The scale indicates the data summarization and statistical analyses that are most appropriate.

Numerical data

Qualitative

Quantitative

Data Types

Levels of Measurement

Nominal

Ordinal

Ratio

Interval

Discrete

Discrete or continuous

Types of Data

- Nominal
- Data are labels or names used to identify an attribute of the element.
- A nonnumeric label or a numeric code may be used.

- Nominal
- Example:
Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on.

Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).

- Example:

- Ordinal
- The data have the properties of nominal data and the order or rank of the data is meaningful.
- A nonnumeric label or a numeric code may be used.

- Ordinal
- Example:
Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

- Example:

- Interval
- The data have the properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure.
- Interval data are always numeric.

- Interval
- Example:
Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.

- Example:

- Ratio
- The data have all the properties of interval data and the ratio of two values is meaningful.
- Variables such as distance, height, weight, and time use the ratio scale.
- This scale must contain a zero value that indicates that nothing exists for the variable at the zero point.

- Ratio
- Example:
Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.

- Example:

- Data can be further classified as being qualitative or quantitative.
- The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.
- In general, there are more alternatives for statistical analysis when the data are quantitative.

- Qualitative data are labels or names used to identify an attribute of each element.
- Qualitative data use either the nominal or ordinal scale of measurement.
- Qualitative data can be either numeric or nonnumeric.
- The statistical analysis for qualitative data are rather limited.

- Quantitative data indicate either how many or how much.
- Quantitative data that measure how many are discrete.
- Quantitative data that measure how much are continuous because there is no separation between the possible values for the data..

- Quantitative data are always numeric.
- Ordinary arithmetic operations are meaningful only with quantitative data.

- Cross-sectional data are collected at the same or approximately the same point in time.
- Example: data detailing the number of building permits issued in June 2000 in each of the counties of Texas

- Time series data are collected over several time periods.
- Example: data detailing the number of building permits issued in Travis County, Texas in each of the last 36 months

- Existing Sources
- Data needed for a particular application might already exist within a firm. Detailed information is often kept on customers, suppliers, and employees for example.
- Substantial amounts of business and economic data are available from organizations that specialize in collecting and maintaining data.

- Existing Sources
- Government agencies are another important source of data , and the data types include census (普查) and survey (抽樣) data.
- Data are also available from a variety of industry associations and special-interest organizations.

- Internet
- The Internet has become an important source of data.
- Most government agencies, like the Bureau of the Census (www.census.gov), make their data available through a web site.
- More and more companies are creating web sites and providing public access to them.
- A number of companies now specialize in making information available over the Internet.

- Statistical Studies
- Statistical studies can be classified as either experimental or observational.
- In experimental studies the variables of interest are first identified. Then one or more factors are controlled so that data can be obtained about how the factors influence the variables.
- In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest.
- A survey is perhaps the most common type of observational study.

- Time Requirement
- Searching for information can be time consuming.
- Information might no longer be useful by the time it is available.

- Cost of Acquisition
- Organizations often charge for information even when it is not their primary business activity.

- Data Errors
- Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information.

- Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.

Example: Hudson Auto Repair

The manager of Hudson Auto would like to have

a better understanding of the cost of parts used in the

engine tune-ups performed in the shop. She examines

50 customer invoices for tune-ups. The costs of parts,

rounded to the nearest dollar, are listed below.

- Tabular Summary (Frequencies and Percent Frequencies)
Parts Percent

Cost ($)FrequencyFrequency

50-59 2 4

60-69 1326

70-791632

80-89 714

90-99 714

100-109 510

Total 50 100

- Graphical Summary (Histogram)

18

16

14

12

Frequency

10

8

6

4

2

Parts

Cost ($)

50 60 70 80 90 100 110

- Numerical Descriptive Statistics
- The most common numerical descriptive statistic is the average (or mean).
- Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).

Statistical Inference

- Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).

- Process of Statistical Inference

1. Population

consists of all

tune-ups. Average

cost of parts is

unknown.

2. A sample of 50

engine tune-ups

is examined.

3. The sample data

provide a sample

average cost of

$79 per tune-up.

4. The value of the

sample average is used

to make an estimate of

the population average.

Population (all votes cast)

Sample (selected votes for observation)

Population Verses a Sample

Basic Definitions

- Descriptive Statistics (敘述性統計量): the
collection and description of data

- Inferential Statistics(推論性統計量): analyzing, decision making or estimation based on the data
- Population(母體): the set of all possible measurements that is of interest
- Sample(樣本): the portion of the population from which information is gathered