INFERENTIAL
STATISTICS
ISTAT
BISU
BISU
M106
LIST OF
STUDENTS
BISU
MODE OF TEACHING AND LEARNING
FACE-TO-FACE
Discussion, Solving &
A Computation, Activities,
Group Work, etc
OFFLINE
B Task Completion, Problem
Sets, Group Works, etc
GRADING SYSTEM
30% 30% 40%
Major Exam Projects Quizzes
Quizzes, Participation,
Mini Research Solved Problems, Activity,
Midterm & Final (Problem Sets) Group work, etc
CLASS RULES
1. Attend each class regularly and participate actively in the discussion.
2. Expected to take all quizzes and examinations on the scheduled date.
3. No special quiz and exam except for a valid reason. If ever permitted to take the test or
exam, he/she must write a letter to the authority and the correspondence will be signed
by those people.
4. Should pass the assignments and project on time, any delay without a justifiable
reason means non-acceptance of the said work/s.
5. Cheating, lying, plagiarism and other forms of immoral and unethical behavior will not
be tolerated.
6. Any student found guilty of cheating and plagiarism (use of unauthorized books, notes
or otherwise securing help in a test, copying tests, assignments, reports or term papers,
representing the work of another person as one’s own, collaborating without authority,
with another student during an examination or in preparing academic work, signing
another student’s name on an attendance sheet, or otherwise practicing scholastic
dishonesty) will receive an F or Failure or 5.0 in the course requirement or in the course.
BISU
INFERENTIAL
STATISTICS
NATURE OF
STATISTICS
Chapter 1
BISU-MC
CHAPTER OUTLINE
1.1 Introduction
1.2 Division of Statistics
1.3 Parametric and Statistic
1.4 Sources of Data
1.5 Constant and Variable
1.6 Types of Data
1.7 Classification of Variables
1.8 Levels of Measurement
1.9 Sampling Techniques
1.10 Methods of Collecting Data
1.11 Methods of Presenting Data
1.12 Summation Notation, Sigma ⅀
Statistics is the grammar of science.
~ Karl Pearson (1857-1936)
1.1 Introduction
We define statistics as a branch of
mathematics that examines and
investigates ways to process and analyze
the data gathered. Statistics provides
procedure in data collection, presentation,
organization, and interpretation to have a
meaningful idea that is useful to business
decision-makers.
1.2 Division of Statistics
Descriptive Statistics is the totality of methods and
treatments employed in the collection, description, and
analysis of numerical data. The purpose of a descriptive
statistics is to tell something about the particular group of
observation.
Inferential Statistics is the logical process from sample
analysis to a generalization or conclusion about a
population. It is also called statistical inference or inductive
statistics.
1.2 Division of Statistics
A population consists of all the members of the group
about which you want to draw a conclusion, while sample is
a portion, or part, of the population of interest selected for
analysis.
Population
L B Sample
D N
G
A F E H
J T M N Q K C M
R S W Q V O P R W P D
C I K
1.3 Parameter and Statistic
Parameter is a numerical index describing
a characteristic of a population.
Statistic is a numerical index describing a
characteristic of a sample.
1.4 Sources of Data
Primary data are data that come from an original
source, and are intended to answer specific research
questions, can be taken by interview, mail-in questionnaire,
survey, or experimentations.
Secondary data are data that are taken from previously
recorded data, such as information is research conducted,
industry financial statements, business periodicals, and
government reports. It can also be taken electronically (e.g.
via internet websites, compact disk, etc.).
1.5 Constant and Variable
Constant. A constant is a characteristic of objects,
people, or events that does not vary. For example, the
temperature at which water boils (100 degrees Celsius)
is a constant.
Variable. A variable is a characteristic of objects,
people, or events that can take of different values. It can
vary in quantity (e.g., weight of people), or in quality (e.g,
hair color of people). Variables can be classified in
different ways.
Figure 1.2: Types of Variables
Variable
Qualitative Quantitative
Discrete Continuous
1.6 Types of Data
Qualitative Variable. A variable that is
conceptualized and analyzed as distinct categories
with no continuum implied. Also termed categorical
variable; observations that are put in the same or
different classes, each class being considered as
possessing some common characteristics that is not
shared by those in other classes.
Example: eye color, gender, occupation, religious
preference, etc.
1.6 Types of Data
Quantitative Variable. A variable that is
conceptualized and analyzed a continuum
implied. It differs in amount of degree. Also termed
numerical variable; variates that yield frequencies
when counted, giving rise to discrete variable or
when measured yield metric continuous variable.
Example: height, weight, math aptitude, salary, etc.
1.7 Classification of Variables
Experimental Classification. A researcher may
classify variables according to the function they
serve in the experiment.
1. Independent variables are variables
controlled by the experimenter/researcher, and
expected to have an effect on the behavior of the
subjects. The independent variable is also called
explanatory variable.
1.7 Classification of Variables
2. Dependent variable is some measure of the
behavior of subjects and expected to be influenced
by the independent variable. The dependent variable
is also called outcome variable.
Example: To predict the value of fertilizer on the
growth of plants; the dependent variable is the
growth of the plants while the independent variable
is the amount of fertilizer used.
1.7 Classification of Variables
Mathematical Classification. Variables may also
be classified in terms of the mathematical values
they may take on within a given interval.
1. Continuous Variable is a variable which can
assume any of an infinite number of values, and can
be associated with points on a continuous line
interval.
Example: height, weight, volume, etc.
1.7 Classification of Variables
2. Discrete Variable is a variable which consist
of either a finite number of values or countable
number of values.
Example: gender, courses, Olympic Games, etc.
Figure 1.3: Classification of Numerical Data
Numerical Data
Qualitative Quantitative
Nominal Ordinal Interval Ratio
1.8 Levels of Measurement
The four widely recognized levels of measurement are
the nominal, ordinal, interval, and ratio.
A. Nominal level of measurement is mutually
exclusive and exhaustive meaning it is used to
differentiate classes or categories for purely classification
or identification purposes. It is the weakest form of
measurement because no attempt can be made to
account for differences within the particular category or
to specify any ordering or direction across the various
categories. Nominal data are discrete variables.
1.8 Levels of Measurement
Mutually Exclusive is a property of a set of
categories such that an individual or object is
included in only one category.
Exhaustive is a property of a set of
categories such that each individual or object
must appear in a category.
1.8 Levels of Measurement
Example:
Qualitative Variable Categories
Gender Male, Female
Automobile Ownership Yes, No
Type of Life Insurance Owned Term, Endowment, Straight-Life,
Others, None
1.8 Levels of Measurement
B. Ordinal level of measurement is used in ranking. It is
somewhat stronger form of measurement, because an
observed value classified into one category is said to
possess more of a property being scaled than does an
observed value classified into another category.
Nevertheless, within a particular category no attempt is
made to account for differences between the classified
values. Moreover, ordinal scaling is still a weak form of
measurement because no meaningful numerical statements
can be made about differences between the categories.
1.8 Levels of Measurement
Example:
Qualitative Variable Categories
Student Class Designation Freshman, Sophomore, Junior,
Senior
Faculty Rank Professor, Associate Prof., Asst.
Prof., Instructor
Product Satisfaction Unsatisfied, Neutral, Satisfied
Student Grades 1.0, 1.25, 1.50, 1.75, 2.0, ...
1.8 Levels of Measurement
C. Interval Level of Measurement is used to
classify order and differentiate between classes or
categories in terms of degrees of differences. Interval
data are either discrete or continuous variables.
Qualitative Variable
Temperature (in degree Celsius or Fahrenheit), IQ Level
Scores, Performance Rating
1.8 Levels of Measurement
D. Ratio level of measurement differs from interval
measurement only in one aspect; it has a true zero point
(complete absence of the attitude being measured). With an
absolute value point it can be said that the ratios of two
observations is "twice as fast", "half as long" or others. Ratio
data are either discrete or continuous variable.
Qualitative Variable
Weight (in pounds or kilograms)
Age (in years or days)
Salary (in Philippine peso)
Table 1.1: Characteristics of Levels of Measurement
1.10 Methods of Collecting Data
Direct or Interview Method. It is a face-to-face
encounter between the interviewer and the interviewee. The
interview may vary according to the preference of either or
both parties.
However, this method is time-consuming, expensive, and
has limited field coverage.
Indirect or Questionnaire Method. Unlike direct method,
this method utilized questionnaires to obtain information. lt
can be done by mail or hand-carried to the intended
respondents.
1.10 Methods of Collecting Data
Registration Method. This method of gathering
information is governed by laws.
Example: birth certificates, death certificates, and
licenses, etc.
Observation Method. This method is used to data that
are pertaining to behaviors of an individual or a group of
individuals at the time of occurrence of a given situation that
are best obtained by observation. One limitation of this
method is that observation is made only at the time or
occurrence of the appropriate events.
1.10 Methods of Collecting Data
Experiment Method. This is used to determine
the cause and effect relationship of certain
phenomena under controlled conditions. This
method are usually employed by scientific
researchers.
1.11 Methods of Presenting Data
Textual Method. This method presents the collected data
in narrative and paragraphs forms.
Tabular Method. This method presents the collected
data in table which are orderly arranged in rows and
columns for an easier and more comprehensive comparison
of figures.
Graphical Method. This method presents the collected
data in visual or pictorial form to get a clear view of data
(e.g. histogram, pie chart, pareto chart, pictograph, etc.)
A Sample Controversy
Shere Hite’s book Women and Love: A Cultural Revolution in
Progress (1987) had a number of widely quoted results:
■ 84% of women are “not satisfied emotionally with their
relationships” (p. 804).
■ 70% of all women “married five or more years are
having sex outside of their marriages” (p. 856).
■ 95% of women “report forms of emotional and
psychological harassment from men with whom they are
in love relationships” (p. 810).
■ 84% of women report forms of condescension from the
men in their love relationships (p. 809).
A Sample Controversy
● The sample was self-selected.
● The questionnaires were mailed to such
organizations as professional women’s groups,
counseling centers, church societies, and senior
citizens’ centers..
● The survey has 127 essay questions, and most of the
questions have several parts.
● Many of the questions are vague, using words such
as “love.”
● Many of the questions are leading.
Good Sample
representative in the sense that
characteristics of interest in the
population can be estimated
from the sample with a known
degree of accuracy
Why do sampling?
● Sampling can provide reliable information at
far less cost than a census.
● Data can be collected more quickly, so
estimates can be published in a timely fashion.
● Estimates based on sample surveys are often
more accurate than those based on a census
because investigators can be more careful
when collecting data
Important Terms
● Population - consists of all the members of the group about
which you want to draw a conclusion,
● Coverage - The percentage of the population of interest that
is included in the sampling frame
● Census - A survey in which the entire population is measured
● Sample -a portion, or part, of the population of interest
selected for analysis
● Observation Unit or Element - An object on which a
measurement is taken.
● Target Population - The complete collection of observations
we want to study.
Important Terms
● Measurement error - The difference between the response
coded and the true value of the characteristic being
studied for a respondent.
● Nonresponse - Failure of some units in the sample to
provide responses to the survey.
● Nonsampling error - An error from any source other than
sampling error.
● Sampled Population - The collection of all possible
observation units that might have been chosen in a
sample; the population from which the sample was taken.
Important Terms
● Sampling Unit - A unit that can be selected for a sample.
● Sampling Frame - A list, map, or other specification of
sampling units in the population from which a sample
may be selected.
● Sampling error -Error in estimation due to taking a
sample instead of measuring every unit in the population
● Selection bias - Bias that occurs because the actual
probabilities with which units are sampled differ from the
selection probabilities specified by the investigator.
Good Sample
Figure 1.4: Sampling Techniques
Sampling Techniques
Random Non-random
Simple Convenience
Systematic Purposive
Stratified Quota
Cluster Snowball
Voluntary
Judgement
1.9 Sampling Techniques
Sampling refers to the process of selecting the sample of
individuals who will participate as a part of the study.
A. Random Sampling is a process whose members had an
equal chance of being selected from the population; it is also
called probability sampling.
1. Simple Random Sampling is a process of selecting n
sample size in the population via random numbers or
through lottery.
1.9 Sampling Techniques
1.9 Sampling Techniques
2. Systematic Sampling is a process of selecting a kth
element in the population until the desired number of
subjects or respondents is attained.
Example: For instance we have the data shown below;
say we want to consider every 5th on the list.
23 34 12 14 13 23 24 39 27 23
12 15 16 23 26 28 23 22 19 34
25 22 18 30 23 24 17 18 15 12
Therefore, the samples from every 5th from left to right
are 13, 23, 26, 34, 23, and 12.
1.9 Sampling Techniques
1.9 Sampling Techniques
3. Stratified Sampling is a process of
subdividing the population into subgroups
or strata and drawing members at
random from each subgroup or stratum.
1.9 Sampling Techniques
Example: Given that a population of a certain university.
Field of Specialization Population
Nursing 6,000
Accountancy 500
Management 2,000
Marketing 1,000
Education 2,500
Total 12,000
1.9 Sampling Techniques
Field of Specialization Population Percentage Sample Size Found by
Nursing 6,000 50.00 2,728 0.5000 ⨉ 5,455
Accountancy 500 4.16 227 0.0416 ⨉ 5,455
Management 2,000 16.66 909 0.1666 ⨉ 5,455
Marketing 1,000 8.33 455 0.0833 ⨉ 5,455
Education 2,500 20.33 1,136 0.2033 ⨉ 5,455
Total 12,000 100.00 5,455
Therefore, the total sample size is 5,455.
1.9 Sampling Techniques
1.9 Sampling Techniques
4. Cluster sampling is a process of selecting
clusters from a population which is very large or
widely spread out over a wide geographical area.
Example: If we want to know the opinion of the
residents of Manila regarding the improvement of
living in the city. We may use the cluster sampling
by subdividing the city into district then select at
random the number of district to be used as
sample.
1.9 Sampling Techniques
1.9 Sampling Techniques
1.9 Sampling Techniques
1.9 Sampling Techniques
B. Non-random sampling is a sampling procedure where
samples are selected in a deliberate manner with little or no
attention to randomization; it is also called non-probability
sampling.
1. Convenience sampling is a process of selecting a
group of individuals who (conveniently) are available for
study.
Example: A researcher may only include close friends and
clients to be included in the sample population.
1.9 Sampling Techniques
1.9 Sampling Techniques
2. Purposive sampling is a process of selecting based
from judgment to select a sample which the
researcher believed, based on prior information, will
provide the data they need.
Example: A human resource director interviews the
qualified applicants in a supervisory position. (Note:
Qualified applicants are selected by the HR Director
which is based from his own judgment.)
1.9 Sampling Techniques
Judgement sampling is a technique when the
researcher relies on his/her personal/sound judgement in
choosing to participate in the study or the sample
selected is based on the opinion of an expert.
Example: In a study wherein a researcher wants to know
what it takes to be a topnotcher in a bar examination, the
only people who can give the researcher first hand
advice are individuals who are bar topnotcher.
1.9 Sampling Techniques
1.9 Sampling Techniques
3. Quota sampling is applied when an investigator survey
collects information from an assigned number, or quota
of individuals from one of several sample units fulfilling
certain prescribed criteria or belonging to one stratum.
Their advantage is that they are cheaper to administer.
Example: When the respondents are composed of men
aged over 30 or 20 people who have bought cellular
phones in the last week. It is in the interviewer's discretion
which men or cellular phone buyers they select.
1.9 Sampling Techniques
1.9 Sampling Techniques
4. Snowball sampling is technique in which one or
more members of a population are located and used
to lead the researchers to other members of the
population.
Example: Imagine attempting to obtain the frame that
includes all homeless people in Metro Manila. To obtain
a sample of homeless individuals, for example, the
researcher will interview individuals on the street or at
homeless shelter.
1.9 Sampling Techniques
1.9 Sampling Techniques
5. Voluntary sampling is a technique when sample
are composed of respondents who are self-select
into the study/survey. Most of the time samples have
a strong interest in the topic of the study.
Example: Consider a news show asks their viewers to
participate in an online poll. The samples are viewers
who have chosen themselves and not the survey
administrator.
1.9 Sampling Techniques
1.9 Sampling Techniques
5. Theoretical sampling. When a solid
understanding of the target population is not known,
or when the target population is incredibly complex,
it may be necessary to start with an individual
respondent and start to build a theoretical model
from there..
Example:
It is unknown what may be required in respondent 3,
until respondent 2 has been studied
Thank You!
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
1.12 Summation Notation, Sigma ⅀
