EDUC 203
ADVANCED STATISTICAL
METHODS
• Floricel V. Ulat, Ph D
• 05Feb2022
CHAPTER 1
INTRODUCTION
“STATISTICS is the most important science in the
whole world; for upon it depends the practical
application of every science and every art; the
one science essential to all political and social
administration, all education, all
organization
based on experience, for it only gives results of
our experience.”
-Florence Nightingale
STATISTICS
 originated from Latin word status, which means
“state.”
 the term itself became popular in the 18th century
 its original definition was “the science dealing with data
about the condition of a state or community”
 uses of statistics during biblical times:
 collecting data on taxes
 population count
 poultry and livestock
 agricultural products, labor and resources
from every citizen of the land
STATISTICS
The use of statistics in government is still evident these days:
• Countries now regularly compute for various socioeconomic
indicators such as:
- Consumer Price Index (CPI)
- Gross National Product (GNP)
- Gross Domestic Product (GDP)
- Birth rates and mortality rates,
- unemployment rates,
- literacy rates, and
- monetary exchange rates
STATISTICS
• At present, the government is not the only major user of statistics
• it expanded to almost every field of study
• it provides answers to research questions, helps in decision
making
• and aids in the process of choosing appropriate actions to be taken
through the analysis of available information.
* Medicine
* Business Sector
* Education
* Tourism Industry, Sports and etc.
BASIC CONCEPTS OF STATISTICS
STATISTICS – is the branch of science that deals with the
collection, presentation, organization, analysis and
interpretation of data.
POPULATION – the collection of all
elements under consideration
in a statistical inquiry.
SAMPLE – is a subset of population.
Sample
Population
Relationship Between the Population
and Sample
The elements of population can be
• individuals, objects, animals, geographic areas and so on
• Examples of populations under study:
1.
2.
3.
4.
5.
6.
Set of Farmers in Laguna Bay
Set of Public or Private School Teachers
Set of Fluorescent Bulbs manufactured for a month
Set of mango trees in a certain area
Set of Fishponds in Binangonan
Set of Rural health units in Rizal
• needs to have at least one of the characteristics or attributes of
the elements of the population
VARIABLE – is a characteristic or attribute of the elements in a
collection that can assume different values for the different
elements.
OBSERVATION – is a realized value of a variable.
DATA – is the collection of observations.
Examples:
Variable
1. Sex of a students
2. Employment Status
3. Monthly Income of a Person in Pesos
4. Height of Basketball players
Possible Observations
Male, Female
Temporary, Permanent, Contractual
i>0
h > 0 cms.
Exercise 1
Identify the population under study and variable/s of interest.
1. The Office of Admissions is studying the relationship between the
score in the entrance examination during application and the general
weighted average (GWA) upon graduation among graduates of the
university from 2015 to 2018.
2. The research division of a certain pharmaceutical company is
investing the effectiveness of a new diet pill in reducing weight on the
female adults.
3. The Department of Health is interested in determining the percentage
of children below 12 years old infected by the Hepatitis B virus in
Rizal 2017
4. A researcher from LGU wants to determine the awareness of the
residents of a certain barangay on the implemented projects
PARAMETER – is a summary measure describing a specific
characteristic of the population.
STATISTIC - is a summary measure describing a specific
characteristic of the sample.
PROPORTION – is the quotient obtained in dividing the
magnitude of a part by the magnitude of the whole.
Example:
* 28 out of 35 students own a cellphone in a class
* among 10 students, 7 own a cellphone
Exercise 2
1. A doctor claims that these tablespoons of pure virgin
coconut oil daily can reduce weight. To test the
doctor’s claim, a researcher studied two groups of 25
women aged 35 to 40 years with weights between 130
to 140 pounds. He administered the three tablespoons
of pure virgin coconut oil daily for a period of three
months to one group of women only. After three
months, he weighted the two groups of women.
a) Describe the two populations of interest.
b) What are the two samples?
2. Mr Donato Chan, a candidate for Vice-Mayor in Orion,
Bataan, wants to find out if there is a need to intensify
his campaign efforts against his opponents. He
requested the services of a group of students to
interview 1,000 of the 3,000 registered voters of Orion,
Bataan. The survey results showed that 75% of the
1,000 in the sample will vote for him as Vice-Mayor.
a) Identify the population and the sample
b) Identify the variable of interest
c) Identify the Parameter and the Statistic
3.The average weekly allowance of students last year at a
private high school was P600.00 per week, based on an
enrollment of 1,080 students. The grade 9 students who
did not have this information interviewed 50 students and
found their average weekly allowance last year to be
P550.00
a) Identify the population and the sample
b) Identify the variable of interest
c) Identify the Parameter and the Statistic
FIELDS OF STATISTICS
2 major fields of Statistics
1. Applied Statistics – is concerned with the procedures and
techniques used in the collection, presentation, organization,
analysis and interpretation of data.
2 Major areas of Interest of Applied Statistics:
a. Descriptive Statistics – includes all the
techniques used in organizing, summarizing and
presenting the data on hand.
b. Inferential Statistics - includes all the techniques
used in analyzing the sample data that will lead to
generalizations about a population from which the
sample came from.
FIELDS OF STATISTICS
2. Theoretical or Mathematical Statistics
is concerned with the development of the
mathematical foundations used in applied
statistics.
• Establish new theories that will validate the use of
new statistical methods or modifications of existing
statistical methods in solving problems that are more
complex.
Some illustrations of the applications of Descriptive
Statistics
1. Daily Sales performance for a product for the previous year, draw a line
chart or column chart to emphasize the upward/downward of the series
and calculate a quantity index per quarter to compare the sales by
quarter for the previous year.
2. Compare the total area of Watershed Forest Reserves in Regions IV and
VIII for a specified period, cover all the provinces in Regions IV and VIII
then measure the area of each one of the watershed forest reserve in
both regions.
It can be interpreted using horizontal bar chart
or computing for the ratios.
3. The PAGASA measures daily amount of rainfall in millimeters.
It
computes the average daily amount of rainfall
every month for the
past years.
Some examples of the applications of
Inferential Statistics
1. To examine the performance of the country’s financial
system to arrive at conclusions that apply to the entire
economy using the data gathered from a sample of
companies or business in the country.
2. Determine if reforestation is effective, take a
representative portion of denuded forests and draw
conclusions about the effect of reforestation on all
denuded forests.
STEPS IN A STATISTICAL INQUIRY
STATISTICAL INQUIRY - is a designed research that provides information
needed to solve a research problem.
Partial List of General Research Objectives that can accomplish by
performing a Statistical Inquiry:
1. Identify different groups of interrelated variables under study.
2. Compare the characteristics of the elements in the different subgroups in
the population through contrasts of their respective summary measures.
3. Determine the nature and relationship among the different variables of
interest.
4. Predict the value of a variable based upon its relationship with another
variable
5. Forecast future values of a variable using a sequence of observation on the
same variable taken over time.
STEPS IN A STATISTICAL INQUIRY
Regardless of the complexity of the research
problems, the following basic steps in performing
statistical inquiry:
1. Identify the problem
2. Plan the Study
3. Collect the data
4. Explore the data
5. Analyze data and interpret the result
6. Present the results
STEP 1: IDENTIFY THE PROBLEM
• Define and state the problem in a clear manner. In this step
establish the heart of the whole research process.
• A detailed review of literature is necessary in this stage.
• Provides insights on the feasibility of pursuing the problem
• Must identify the specific information needed to answer the
problem
• Brainstorm on various issues such as importance and rationale
for conducting the investigations, scope and limitations of the
study.
• Define the exact population of interest to delimit the scope of the
study
STEP 2: PLAN THE STUDY
• Take all the consideration all the outputs in Step 1, the stated
research problem and specific objectives
• The concrete output in Step 2 is the research design (detailed
methods and strategies for data collection and analysis)
• Effective research design is as simple as possible, at the same
time, cost-efficient.
With simple RD, avoids complications and
errors in its implementation. With cost-efficient RD, investigators
are confident of completing the study within the allotted budget
and time.
• Includes the list of variables, instruments, data collection method,
sampling design and methods of data analysis
STEP 3: COLLECT THE DATA
• Carry out the plans specified in the research design
• Take extra measures to ensure the quality of the data collected
• If the collected data were incomplete, outdated, inaccurate, or
worse yet, fabricated, then it will be useless to proceed with data
analysis
• Make sure that everyone involved in data collection has a
genuine appreciation for quality data.
• Ways to collect data: (surveys, observation, experiments, and use
of available documented data)
STEP 4: EXPLORE THE DATA
• Need to explore and understand the essential features of their
data
• Allows to determine if their data satisfy the assumptions made in
the derivation of the statistical techniques
• Reveals if their data exhibit peculiarities that will create problems
in the analysis
• Arrange the observations according to magnitude
• Construct a frequency distribution which shows the number of
observations in different categories
• May used graphical method (usually easier to discover patterns
trough visual inspection of chart)
STEP 5: ANALYZE AND INTERPRET
THE RESULT
• Examine all the results on the table, charts, estimated summary
measures and tests of hypotheses.
• Need to check to meet all the specific objectives stated in Step1
• Must be able to answer the research problems and give
recommendations on how can be useful in decision making
• Double-check the result that contradict existing theory or the
earlier hypothesis made
• May propose possible explanations for the results or suggest
future statistical inquiries that could help explain the inconsistency.
STEP 6: PRESENT THE RESULT
• Present the result in a clear and concise manner to the users of
the research
• Must include a discussion of the whole research process from
Step 1 to 5
• The three ways of presenting the results:
1. Textual – paragraph form.
2.
Tabular – showing the figures in rows and columns so
that the reader can easily comprehend the points
made
3.
Graphical – involves placing of the data without
having to look at too many figures
THANK YOU!