introduction to statistic

7/30/2019 Introduction to Statistic

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CHAPTER 1

INTRODUCTION

OBJECTIVES

After completing this chapter, students should be able to:

1. Describe the difference between descriptive andinferential statistics.

2. Identify and interpret the relationships between sampleand population, and statistics and parameter.

3. Identify and describe the different types of variables.

4. Identify and describe the different types of data.

5. Differentiate and identify the techniques of datacollection.

6. Identify and interpret the measurement scales.


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What is Statistics?

The word statistics derives from classical Latin roots,

status which means state.

Statistics has become the universal language of the

sciences.

As potential users of statistics, we need to master both

the science and the art of using statistical

methodology correctly.

These method include:

Carefully defining the situation

Gathering data

Accurately summarizing the data

Deriving and communicating meaningful conclusions

Specific definition:

Statistics is a collection of procedures and principles for

gathering data and analyzing information to help people

make decisions when faced with uncertainty.


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Nowadays statistics is used in almost all fields of human

effort such as:

education

health business agriculture..etc.

Example applications of Statistics

1. Sport=> A statistician may keeps records of the number of hits

a baseball player gets in a season.

2. Financial=> Financial advisor uses several statistic information to

make reliable predictions in investment.

3. Public Health=> An administrator would be concerned with the

number of residents who contract a new strain of flu

virus during a certain year.

4. Others

=>


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Statistics has Two Aspects

1) Theoretical / Mathematical Statistics

2) Applied Statistics

1) Theoretical / Mathematical Statistics

=> Deals with the development, derivation and proof of

statistical theorems, formulas, rules and laws.

2) Applied Statistics=> Involves the applications of those theorems,

formulas, rules and laws to solve real world problems.

** Applied Statistics can be divided into two main areas,

depending on how data are used.

(1) Descriptive statistics (2) Inferential statistics

What most people think of whenthey hear the wordstatistics

Includes the collection, presentation,and description of sample data.

Using graphs, charts and tables toshow data.

Refers to the technique of

interpreting the valuesresulting from the descriptive

techniques and making

decisions and drawingconclusions about the

o ulation


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Example 1Determine which of the following statements is descriptive

in nature and which is inferential.

a. Of all U.S kindergarten teachers, 32% say that knowing

the alphabet is an essential skill.Inferential

b. Of the 800 U.S kindergarten teachers polled, 32% say

that knowing the alphabet is an essential skill.

descriptive

ASPECTS OF STATISTICS

Theoretical/MathematicalStatistics Applied Statistics

Inferential Statistics

Deals with the development, derivationand proof of statistical theorems,

formulas, rules and laws.

Descriptive Statistics

Involves the applications of thosetheorems, formulas, rules and

laws to solve real world problems.

Consist of method for collecting,organizing, displaying and

summarizing data

Consist of methods that use resultsobtained from sample to make decisions

or conclusions about a population


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Why do we have to study statistics?

To read and understand various statistical studies in

related field.

To communicate and explain the results of study in

related field using our own words.

To become better consumers and citizens.


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Basic Terms of Statistics

1. Population versus Sample

Population=> a collection of all individuals about which

information is desired.

-individuals are usually people but could also be schools,

cities, pet dogs, agriculture fields, etc.

=> there are two kinds of population:

i. When the membership of a population can be (orcould be) physically listed.

- finite population:- e.g. the books in library.

ii. When the membership is unlimited.- infinite population:- e.g. the population of all people

who might use aspirin.

Sample=> a subset of the population.

2. Parameter versus Statistic

Parameter

=> a numerical value summarizing all the data of an entirepopulation.

- often a Greek letter is used to symbolize the name of

parameter.

e.g. the average age at time of admission for all students

who have ever attended our college.


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Statistics

=> a numerical value summarizing the sample data.

- english alphabet is used to symbolize the name of statistic

e.g. the average height, found by using the set of 25heights.

3. Variable

=>a characteristics of interest about each individual element

of a population or sample.

e.g. a students age at entrance into college, the color of

students hair, etc.

4. Data value

=> the value of variable associated with one element of a

population or sample. This value may be a number, a word,

or a symbol.

e.g. Farah entered college at age 23, her hair is brown,etc.

5. Data

=> the set of values collected from the variable from each of

the elements that belong to sample.

e.g. the set of 25 heights collected from 25 students.


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Example 2

A statistics student is interested in finding out something

about the average ringgit value of cars owned by the faculty

members of our university. Each of the seven terms just

describe can be identified in this situation.

i) population: the collection of all cars owned by all faculty

members at our university.

ii) sample: any subset of that population. For example, the

cars owned by members the statistics department.

iii) variable: the ringgit value of each individual car.

iv) data value: one data value is the ringgit value of a

particular car. Alis car, for example, is value at RM 45

000.

v) data: the set of values that correspond to the sample

obtained (45,000; 55,000; 34,0000;).

vi) parameter: which we are seeking information is the

average value of all cars in the population.

vii) statistic: will be found is the average value of the cars

in the sample.

Census: a survey includes every element in the population.

Sample survey: a survey includes every element in selected

sample only.


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Types of Variables

1. Quantitative (numerical) Variables

A variable that quantifies an element of a population.

- e.g. the total cost of textbooks purchased by eachstudent for this semesters classes.

Arithmetic operations such as addition and averaging

are meaningful for data that result from a quantitative

variable.

Can be subdivided into two classification: discrete

variables and continuous variables.


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Discrete Variables

A quantitative variable that can assume a countable

number of values.

Can assume any values corresponding to isolated

points along a line interval. That is, there is a gap

between any two values.

Example 3

Number of courses for which you are currently registered.

Continuous Variables

A quantitative variable that can assume an

uncountable number of values.

Can assume any value along a line interval, including

every possible value between any two values.

Example 4

Weight of books and supplies you are carrying as you

attend class today.


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2. Qualitative (attribute, categorical) variables

A variable that describes or categorizes an element of

a population.

Example 5

A sample of four hair-salon customers was surveyed for

their hair color, hometown and level of

satisfaction.


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Exercise 1

1. Of the adult U.S. population, 36% has an allergy. A

sample of 1200 randomly selected adults resulted in

33.2% reporting an allergy.

a. Describe the population.b. What is sample?c. Describe the variable.d. Identify the statistics and give its value.e. Identify the parameter and give its value.

2. The faculty members at Universiti Utara Malaysia were

surveyed on the question How satisfied were you with

this semester schedule? Their responses were to be

categorized as very satisfied, somewhat satisfied,

neither satisfied nor dissatisfied, somewhat

dissatisfied, or very dissatisfied.

a. Name the variable interest.b. Identify the type of variable.

3. A study was conducted by Aventis Pharmaceuticals Inc.

to measure the adverse side effects of Allegra, a drug

used for treatment of seasonal allergies. A sample of 679

allergy sufferers in the United States was given 60 mg of

the drug twice a day. The patients were to report whether


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they experienced relief from their allergies as well as any

adverse side effects (viral infection, nausea, drowsiness,

etc)

a. What is the population being studied?b. What is the sample?c. What are the characteristics of interest about each

element in the population?

d. Are the data being collected qualitative orquantitative?

4. Identify each of the following as an example of (1)

attribute (qualitative) or (2) numerical (quantitative)

variables.

a. The breaking strength of a given type of stringb. The hair color of children auditioning for the musical

Annie.

c. The number of stop signs in town of less than 500people.

d. Whether or not a faucet is defective.e. The number of questions answered correctly on a

standardized test.

f. The length of time required to answer a telephonecall at a certain real estate office.


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DATA

The set of values collected from the variable from each

of the elements that belong to sample.

e.g. the set of 25 heights collected from 25 students.

From a survey or an experiment.

Two types of data:

Primary data:

necessary data obtainedthrough survey

conducted by researcher

Secondary data:

data obtained from

published material by

governmental, industrial

or individual sources


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1. PRIMARY DATA

Primary Data Collection Techniques

Data is collected by researcher

Data is obtained from respondent

(i) Face to face interview

- Two ways communication.

- Researcher(s) asks question directly to

respondent(s).

Advantages:

Precise answer.

Appropriate for research that requires huge datacollection.

Increase the number of answered questions.

Disadvantages:

Expensive.

Interviewer might influence respondents responses.

Respondent refuse to answer sensitive or personalquestion.


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(ii) Telephone interview

Advantages:

Quick.

Less costly.

Wider respondent coverage.

Disadvantages:

Information obtained might not represent the

whole population.

Limited interview duration.

Not appropriate for long and contemplate

question.

Demonstration cannot be performing.

Telephone is not answered.

(iii) Postal questionnaire

- A set of questions to obtain related informationof conducted study.

- Questionnaires are posted to every respondent.


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Advantages:

Wider respondent coverage.

Respondent have enough time to answer

questions.

Interviewer influences can be avoided.

Lower cost.

Disadvantages:

One way interaction.

Low response rate.

Not suitable for numerous and hard questions.

Time consuming.

Questionnaire is answered by unqualifiedrespondent.

(iv) Observation

Observing and measuring specific

characteristics without attempting to modify the

subjects being studied.

Records human behaviors, objects and situations

without contact with respondent.

- not commonly used.

- precise information.


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2. SECONDARY DATA

- Published records from governmental, industrial orindividual sources.

- Historical data.

- Various resources.

- Experiment is not required.

Advantages:

Lower cost. Save time and energy.

Disadvantages:

Obsolete information.

Data accuracy is not confirmed.


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Data also can be classified by how they are categorized,

counted or measured.

This type of classification uses measurement scales with

4 common types of scales: nominal, ordinal, interval

andratio.

Nominal Level of Measurement

A qualitative variable that characterizes (or

describes/names) an element of a population.

Arithmetic operations not meaningful for data.

Order cannot be assigned to the categories.

Example: - Survey responses:- yes, no, undecided,

- Gender:- male, female

Ordinal Level of Measurement

A qualitative variable that incorporates and orderedposition, or ranking.

Differences between data values either cannot be

determined or are meaningless.

Example: - Level of satisfaction:- very satisfied,satisfied, somewhat satisfied, etc.

- Course grades:- A, B, C, D, or F


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Interval Level of Measurement

Involve a quantitative variable.

A scale where distances between data are meaningful.

Differences make sense, but ratios do not (e.g., 30-

20=20-10, but 20/10 is not twice as hot!).

No natural zero

Example:

- Temperature scales are interval data with 25oC warmer

than 20oC and a 5oC difference has some physical

meaning. Note that 0oC is arbitrary, so that it does not

make sense to say that 20oC is twice as hot as 10oC.

- The year 0 is arbitrary and it is not sensible to say that

the year 2000 is twice as old as the year 1000.

Ratio Level of Measurement

A scale in which both intervals between values and ratios

of values are meaningful.

A real zero point.

Example:


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- Temperature measured in degrees Kelvin is a ratio

scale because we know a meaningful zero point (absolute

zero).

- Physical measurements of height, weight, length are

typically ratio variables. It is now meaningful to say that

10 m is twice as long as 5 m. This is because there is a

natural zero.

Levels of Measurement

Nominal - categories only

Ordinal - categories with some order

Interval - differences but no natural starting point

Ratio - differences and a natural starting point


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Exercise 2

1) Classify each as nominal-level, ordinal-level, interval-

level or ratio-level.

2) Data obtained from a nominal scale

a. must be alphabetic.

b. can be either numeric or nonnumeric.

c. must be numeric.

d. must rank order the data.

3) The set of measurements collected for a particular

element is (are) called

a. variables.

b. observations.c. samples.

d. none of the above answers is correct.

a. Ratings of newscasts in Malaysia.

(poor, fair, good, excellent)

b. Temperature of automatic popcorn poppers.

c. Marital status of respondents to a survey on

saving accounts.

d. Age of students enrolled in a marital arts course.

e. Salaries of cashiers of C-Mart stores.


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4) The scale of measurement that is simply a label for the

purpose of identifying the attribute of an element is the

a. ratio scale.

b. nominal scale.

c. ordinal scale.d. interval scale.

5) Some hotels ask their guests to rate the hotels services

as excellent, very good, good, and poor. This is an

example of the

a. ordinal scale.

b. ratio scale.c. nominal scale.

d. interval scale.

6) The ratio scale of measurement has the properties of

a. only the ordinal scale.

b. only the nominal scale.

c. the rank scale.

d. the interval scale.

7) Arithmetic operations are inappropriate for

a. the ratio scale.

b. the interval scale.

c. both the ratio and interval scales.

d. the nominal scale.

8) A characteristic of interest for the elements is called a(n)

a. sample.

b. data set.

c. variable.



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9) In a questionnaire, respondents are asked to mark their

gender as male or female. Gender is an example of a

a. qualitative variable.

b. quantitative variable.

c. qualitative or quantitative variable, depending onhow the respondents answered the question.


10) The summaries of data, which may be tabular, graphical,

or numerical, are referred to as

a. inferential statistics.

b. descriptive statistics.c. statistical inference.

d. report generation.

11) Statistical inference

a. refers to the process of drawing inferences about the

sample based on the characteristics of the population.

b. is the same as descriptive statistics.

c. is the process of drawing inferences about the

population based on the information taken from the

sample.

d. is the same as a census.


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Answer Exercise 1

1) a. all adults of U.S. population

b. 1200 randomly selected from adultsc. allergy

d. 33.2% effected by allergy

e. 36.0% has an allergy

2) a. satisfaction

b. ordinal

3) a. all allergy sufferers in the U.S.

b. 679 allergy sufferers in the U.S.

c. to measure the adverse side effects of allergy

d. qualitative

4) a. quantitative

b. qualitative

c. quantitative

d. qualitative

e. quantitative

f. quantitative


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Answer Exercise 2

1) a. Ordinal b. Interval c. Nominal

a. Ratio e. ratio

2) b 3) c

4) b 5) a

6) d 7) d

8) c 9) a

10) b 11) c

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