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• 1. CHAPTER 1
INTRODUCTION
OBJECTIVES
After completing this chapter, students should be able to:
Describe the difference between descriptive and inferential statistics.
Identify and interpret the relationships between sample and population, and statistics and parameter.
Identify and describe the different types of variables.
Identify and describe the different types of data.
Differentiate and identify the techniques of data collection.
Identify and interpret the measurement scales.
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.
Nowadays statistics is used in almost all fields of human effort such as:
education
health
agriculture…..etc.
Example applications of Statistics
Sport
=> A statistician may keeps records of the number of hits a baseball player gets in a season.
Financial
=> Financial advisor uses several statistic information to make reliable predictions in investment.
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
=>
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.
Refers to the technique of interpreting the values resulting from the descriptive techniques and making decisions and drawing conclusions about the population (1) Descriptive statistics (2) Inferential statistics
What most people think of when
they hear the word statistics
Includes the collection, presentation,
and description of sample data.
Using graphs, charts and tables to
show data.
ASPECTS OF STATISTICSTheoretical/MathematicalStatisticsApplied StatisticsInferential StatisticsDeals with the development, derivation and proof of statistical theorems, formulas, rules and laws. Descriptive StatisticsInvolves the applications of those theorems, formulas, rules and laws to solve real world problems. Consist of method for collecting,organizing, displaying andsummarizing data Consist of methods that use results obtained from sample to make decisions or conclusions about a population ASPECTS OF STATISTICSTheoretical/MathematicalStatisticsApplied StatisticsInferential StatisticsDeals with the development, derivation and proof of statistical theorems, formulas, rules and laws. Descriptive StatisticsInvolves the applications of those theorems, formulas, rules and laws to solve real world problems. Consist of method for collecting,organizing, displaying andsummarizing data Consist of methods that use results obtained from sample to make decisions or conclusions about a population
Example 1
Determine which of the following statements is descriptive in nature and which is inferential.
Of all U.S kindergarten teachers, 32% say that “knowing the alphabet” is an essential skill. Inferential
Of the 800 U.S kindergarten teachers polled, 32% say that “knowing the alphabet” is an essential skill. descriptive
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.
Basic Terms of Statistics
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:
When the membership of a population can be (or could be) physically listed.
- finite population:- e.g. the books in library.
When the membership is unlimited.
- infinite population:- e.g. the population of all people
who might use aspirin.
Sample
=>a subset of the population.
Parameter versus Statistic
Parameter
=> a numerical value summarizing all the data of an entire population.
- 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.
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 25 heights.
Variable
=> a characteristics of interest about each individual element of a population or sample.
e.g. a student’s age at entrance into college, the color of
student’s hair, etc.
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.
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.
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. Ali’s 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.
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 each student for this semester’s 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.
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.
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”.
Exercise 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.
Describe the population.
What is sample?
Describe the variable.
Identify the statistics and give its value.
Identify the parameter and give its value.
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.”
Name the variable interest.
Identify the type of variable.
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 they experienced relief from their allergies as well as any adverse side effects (viral infection, nausea, drowsiness, etc)
What is the population being studied?
What is the sample?
What are the characteristics of interest about each element in the population?
Are the data being collected qualitative or quantitative?
Identify each of the following as an example of (1) attribute (qualitative) or (2) numerical (quantitative) variables.
The breaking strength of a given type of string
The hair color of children auditioning for the musical Annie.
The number of stop signs in town of less than 500 people.
Whether or not a faucet is defective.
The number of questions answered correctly on a standardized test.
The length of time required to answer a telephone call at a certain real estate office.
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:
Secondary data:data obtained from published material by governmental, industrial or individual sourcesPrimary data: necessary data obtained through survey conducted by researcher
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).
Appropriate for research that requires huge data collection.
Increase the number of answered questions.
Expensive.
Interviewer might influence respondent’s responses.
Respondent refuse to answer sensitive or personal question.
(ii) Telephone interview
Quick.
Less costly.
Wider respondent coverage.
Information obtained might not represent the whole population.
Limited interview duration.
Not appropriate for long and contemplate question.
Demonstration cannot be performing.
(iii) Postal questionnaire
A set of questions to obtain related information
of conducted study.
Questionnaires are posted to every respondent.
Wider respondent coverage.
Respondent have enough time to answer questions.
Interviewer influences can be avoided.
Lower cost.
One way interaction.
Low response rate.
Not suitable for numerous and hard questions.
Time consuming.
Questionnaire is answered by unqualified respondent.
(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.
SECONDARY DATA
Published records from governmental, industrial or individual sources.
Historical data.
Various resources.
Experiment is not required.
Lower cost.
Save time and energy.
Obsolete information.
Data accuracy is not confirmed.
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 and ratio.
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 ordered position, 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
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:
- 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
Exercise 2
1)Classify each as nominal-level, ordinal-level, interval-level or ratio-level.
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.
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.
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 hotel’s 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.
d.none of the above answers is correct.
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 on how the respondents answered the question.
d.none of the above answers is correct.
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.
b. 1200 randomly selected from adults
c. 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