1.1 Chapter 1. Introduction to Statistics - Final (1).pdf

Introduction to
Statistics
RICHARD T. ALCANTARA
MAEd-Math & Dev. Ed. D.

“There are three kinds of lies:
lies, damned lies, and statistics.“
- Mark Twain, USA.
[(Benjamin, Disraeli) 19th century British Prime
Minister]
Course Introduction

Larson & Farber, Elementary Statistics: Picturing the World, 3e 3
Why study statistics?
• Data are everywhere.
• Statistical techniques are used to
make many decisions that affect our
lives.
• No matter what your career, you will
make professional decisions that
involve data.
• An understanding of statistical
methods will help you make these
decisions effectively.

Applications of statistical concepts in the
BUSINESS WORLD
• Finance – correlation and regression, index
numbers, time series analysis
• Marketing – hypothesis testing, chi-square
tests, nonparametric statistics
• Personnel – hypothesis testing, chi-
square tests, nonparametric tests
• Operating management – hypothesis
testing, estimation, analysis of variance,
time series analysis

Origins

❑ The origin of descriptive statistics can be
traced to ancient Rome and China, the
Babylonians and Egyptians carried censuses in
4500-3000 B.C.
A Brief History of Statistics
❑Human Activities:
- registration of property
- surveys on births and deaths
- amount of livestock each owned
& the crops each harvested
- accidents in order to determine
insurance rates, etc.
- Counts of abled-
bodied fighting men,
- Taxes, etc.

❑ Statistics arose from the need of states to
collect data on their people and
economies, in order to administer them.
A Brief History of Statistics
❑ Its meaning broadened in the early 19th
century to include the collection and
analysis of data in general.
❑ Today statistics is widely employed in
government, business, in the natural and
social sciences, etc.

• A systematic collection of data on the
population and the economy was begun in the
Italian city-states of Venice and Florence during
the Renaissance.
• The term statistics, derived from the Italian
word statista which means state, was used to
refer to a collection of facts of interest to the
state.
• In 1662 the English tradesman
“John Graunt” published a
book entitled Natural and Political
Observations Made upon the Bills
of Mortality
 There was roughly 1 death
for every 88/3 people.

❑ The first SCIENTIFIC SCHOOL which was
much closer to the modern understanding of
statistics was an ENGLISH SCHOOL OF
POLITICAL ARITHMETIC. Its founders were
William Petty (1623 - 1687) and John Graunt
(1620 - 1674)
School of Political Arithmetic
❑ They developed early human statistical and
census methods that later provided a
framework for modern demography.
❑ John Graunt made first life table, giving
probabilities of survival to each age
❑ He discovered that slightly more males were
born than females, but that more males than
females died during the first year of life.

Gottfried Achenwall
❑ Gottfried Achenwall (20 October 1719 – 1
May 1772) was a German philosopher and
statistician. He is counted among the
inventors of the term “statistics”.
❑ He first began to read a new course
"statistics" in the University of Göttingen,
which explained how the state was arranged.
❑Statistics is considered to be not a subfield of
mathematics but rather a distinct field that uses
mathematics because of its origins in government and
its data-centric world view.

What is Statistics?
❑ Turtle defines statistics as “ the body of
principles and techniques of collecting,
classifying, presenting, comparing, and
interpreting quantitative data.”
❑ … “Statistics is the science which deals with
the classification and tabulation of
numerical facts as the basis for explanation,
description, and composition of
phenomenon.” (Lovit)

What is Statistics?
❑Statistics – is a branch of mathematics
that deals with the scientific collection,
organization, presentation of numerical
data in order to obtain useful and
meaningful information.
❑Statistics – is the art of learning from
the data.

What is Statistics?
❑ The purpose of statistics is to develop and
apply methodology for extracting useful
knowledge from both experiments and
data.
❑ In addition to its fundamental role in data
analysis, statistical reasoning is also
extremely useful in data collection (design
of experiments & surveys) and also guiding
proper scientific inference (Fisher, 1990)

What is Statistics?
❑ Statistics is neither really a science nor a
branch of mathematics. It is perhaps best
considered as a meta-science ( or meta-
language) for dealing with data collection,
analysis, and interpretation.
❑As such its scope is enormous and it provides
much guiding insight in many branches of
sciences, business, etc.

Functions of Statistics
❑ Expression of Facts in Numbers. One of the principal function
of statistics is to express facts relating to different phenomena
in numbers.
❑ Simple Presentation. The data must be presented in a simple
from, so that it becomes easy to understand.
❑ It Compare Facts. Another function of statistics is to compare
data relating to facts.
❑ It helps other sciences also. Many laws of economics, law of
demand and supply have been verified with the help of
statistics.
❑ It helps forecasting. It helps in forecasting changes in future
with regard to a problem

Distrust in Statistics
❑ Consideration of Statistical Limitations. While
making use of statistics, limitations of statistics must
be taken care of, for instance, statistics should be
homogeneous.
❑ No biases. Researcher should be impartial. He should
make use only of proper data and draw conclusions
without any bias or prejudice.
❑ Application by Experts. Statistics should be used
only scientifically, the possibilities of errors will be
little.
Note: Misuse of statistics caused distrust in statistics.

Key Definitions
❑ Statistics
Plural Sense:
• Data themselves or numbers derived from the
collected & analyzed data
Singular Sense:
• Scientific method for collecting, organizing,
summarizing, presenting, and analyzing data
and drawing conclusion on the basis of such
analysis to arrive at effective decision.
• Art of learning from the data.

Branches of Statistics
The study of statistics has two major branches: descriptive
statistics and inferential statistics.
Statistics
Descriptive
statistics
Inferential
statistics
Involves the
organization,
summarization,
and display of data.
Involves using a
sample to draw
conclusions about a
population.

Descriptive and Inferential Statistics
Example:
In a recent study, volunteers who had less
than 6 hours of sleep were four times more likely
to answer incorrectly on a science test than were
participants who had at least 8 hours of sleep.
Decide which part is the descriptive statistic and
what conclusion might be drawn using
inferential statistics.
The statement “four times more likely to answer
incorrectly” is a descriptive statistic. An inference
drawn from the sample is that “all individuals sleeping
less than 6 hours are more likely to answer science
question incorrectly than individuals who sleep at
least 8 hours.”

Populations & Samples
Example: In a recent survey, 250 college students at City
College were asked if they smoked cigarettes regularly. 35 of
the students said yes. Identify the population and the sample.
Responses of all students at
City College (population)
Responses of students
in survey (sample)
A population is the collection of all outcomes,
responses, measurement, or counts that are of interest.
A sample is a subset of a population.

Parameters & Statistics
A parameter is a numerical description of a population
characteristic. Use Greek letters µ (myu), ∑ (sigma), etc.
Ex. Average height of all students is 5’ 5’’.
A statistic is a numerical description of a sample
characteristic. Use small letters: n, x, σ, etc.
Ex. Average height of transferee students.
Parameter Population
Statistic Sample

Parameters & Statistics
Example:
Decide whether the numerical value describes a population
parameter or a sample statistic.
a.) A recent survey of a sample of 450 college students
reported that the average weekly income for students
is P1, 325.
Because the average of P1,325 is based on a sample,
this is a sample statistic.
b.) The average weekly income for all students is P1,405.
Because the average of P1,405 is based on a population,
this is a population parameter.

Constant and Variables
❑ A constant is a characteristic of objects, people, or
events that does not vary. Ex. Days in a week, Boiling
point, etc.
❑ A variable is a characteristic of objects, people, or events
that can take of different values or can vary in quantity or
in quality. Ex. Weight, rank, habit, etc.
❑ A measurement is the process of determining the value or
label, either qualitative or quantitative of a particular variable
for a particular unit of analysis.
❑ A data set is the collection of all observation. (Ex. 5’4”, 5’7”)
❑ Data consists of information coming from observations,
counts, measurements, or responses.
❑ An observation is the realized value of the variable. Ex. Skin
complexion

Statistical data
 The collection of data that are relevant to the
problem being studied is commonly the most
difficult, expensive, and time-consuming part of the
entire research project.
 Statistical data are usually obtained by counting or
measuring items.
• Primary data are collected specifically for the
analysis desired
• Secondary data have already been compiled and are
available for statistical analysis

Qualitative and Quantitative Data
Example:
The grade point averages (GPA) of five students are listed in
the table. Which data are qualitative data and which are
quantitative data?
Student GPA
Sally 3.22
Bob 3.98
Cindy 2.75
Mark 2.24
Kathy 3.84
Quantitative data
Qualitative data

Qualitative Data / Variables
Qualitative data are generally described by
words or letters. They are not as widely used as
quantitative data because many numerical techniques
do not apply to the qualitative data.
For example, it does not make sense to find an
average hair color or blood type.
Qualitative data can be separated into two subgroups:
 dichotomic (if it takes the form of a word with two
options (gender / sex - male or female)
 polynomic (if it takes the form of a word with more than
two options (education - primary school, secondary
school and university).

Quantitative Data / Variables
❑ Quantitative data are always numbers and are the
result of counting or measuring attributes of a
population.
❑ Quantitative data can be separated into two
subgroups:
> discrete (if it is the result of counting Ex. the
number of students of a given ethnic group in a
class, the number of books on a shelf, ...)
> continuous (if it is the result of measuring
Ex. distance traveled, weight of luggage, …)

Types of Variables
❑ Qualitative Variables
- describes quality or attribute of person or object
- assign label or name
- Ex. Gender – male or female; Civil Status – single,
married, or widow)
❑ Quantitative Variables
- describes amount or number of something
- any attribute measured in numbers
- Ex. Weight – 80 kg, 140 lbs; Age – 23 years & 9 months

Types of variables
Variables
Quantitative
Qualitative
Dichotomic Polynomic Discrete Continuous
Gender, marital
status
Brand of Pc, hair
color
Children in family,
Strokes on a golf
hole
Amount of income,
tax paid, weight of
a student

Levels of Measurement
The level of measurement determines which statistical
calculations are meaningful. The four levels of
measurement are: nominal, ordinal, interval, and ratio.
Levels
of
Measurement
Nominal
Ordinal
Interval
Ratio
Lowest
to
highest

Nominal Level of Measurement
Data at the nominal level of measurement are qualitative
only.
Levels
of
Measurement
Nominal
Calculated using names, labels,
or qualities. No mathematical
computations can be made at
this level.
Colors in
the Phil.
flag
Names of
students in your
class
Textbooks title
you are using
this semester

Ordinal Level of Measurement
Data at the ordinal level of measurement are qualitative
or quantitative.
Levels
of
Measurement Arranged in order, but
differences between data
entries are not meaningful.
Class standings:
freshman,
sophomore,
junior, senior
Numbers on the
back of each
player’s shirt
Ordinal
Top 50 songs
played on the
radio

Interval Level of Measurement
Data at the interval level of measurement are quantitative.
A zero entry simply represents a position on a scale; the
entry is not an inherent zero or zero point is arbitrary.
Levels
of
Measurement
Arranged in order, the differences
between data entries can be calculated.
Temperatures Years on a
timeline
Interval
Intelligent
Quotient (IQ)
Note: Addition and subtraction, but not multiplication and
division are meaningful operations.
Anxiety Level
Test
Scores

Ratio Level of Measurement
Data at the ratio level of measurement are similar to the
interval level, but a zero entry is meaningful.
Levels
of
Measurement
A ratio of two data values can be
formed so one data value can be
expressed as a ratio.
Ages Grade point
averages
Ratio
Weights

Summary of Levels of Measurement
No
No
No
Yes
Nominal
No
No
Yes
Yes
Ordinal
No
Yes
Yes
Yes
Interval
Yes
Yes
Yes
Yes
Ratio
Determine if
one data value
is a multiple of
another
Subtract
data values
Arrange
data in
order
Put data
in
categories
Level of
measurement

Dyad Activity
1) Which of the ff. are variables or constants? Justify your
answers.
A. employee job position in a company
B. number of children in a family
C. number of centimeters in a meter
D. annual family income
E. number of days in a week
2.) For each of the ff. variables, indicate whether is qualitative
or quantitative and classify them further as dichotomic or
polynomic and as discrete or continuous. Identify also their
level of data measurement.
A. household size D. blood glucose level
B. ethnicity E. sex
C. height in cm

1.1 Chapter 1. Introduction to Statistics - Final (1).pdf

Individual Report
1. Name of the Statistical Test; Ex. Z-Test
2. Definition, Uses, and Purpose
3. Assumptions or Conditions or Requirements
4. Sample Problem and Data
5. Research Study or Article [Title, Abstract, Data Presentation, & Conclusion]
6. MS Excel or SPSS Calculations (Sir)

1.1 Chapter 1. Introduction to Statistics - Final (1).pdf

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