Transcript Population - fordham.edu

Chapter 1
Statistics & Problem
Solving
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Stat-Slide-Show, Copyright 1994-95 by Quant Systems Inc.
Outline
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Prayer, Course Information
Why Word Problems?
What is Stats?
Scientific Method for Finding Truth
Examples of Stats in Science (Joke:
Common sense still needed, Japanese
no-fat diet, French hi-fat, Italian Red
wine lower heart attacks than
US/Britain English-speaking)
Computers, Stats and Power
Definition pp 1 to 4 (Pop’n sample,
statistic, parameter, Greek symbols)
List of questions answered by
descriptive stats
Inferential Stats involves probability
theory and fills much of stats theory.
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Ancient Prayer for
Learning
• Written between 3000 BC Vedas
600 BC Budha (The Martin Luther
like figure for Hinduism who
protested against Yajna rituals with
animal sacrifices.
May our studies be brilliant and may
there be no animosity between the
teacher and the student.
I want to help you think, be creative, be
not afraid of math and word
problems. Remember knowledge
cannot be stolen and grows by giving
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Success in Life
• Ability is what you're
capable of doing...
• Motivation determines
what you do...
• Attitude determines how
well you do it.
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Course information
vinod/syllabus06.doc
• See /economics/vinod/syllabus06.doc
• Textbook, Getting access code for
Software, Exam Weights 27-25-43-5
for home-works (mostly computerbased word problems), midterm,
final, participation. Need calculator
• Policies: Attendance matters, Get
info if u miss a class, No make-ups,
final is made worth more points.
Need written proof for all excuses.
Lateness penalty (one point for each
business day) for doing homework
later than the day it is due.
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Why I like software word
problems and Let me know if
you do not understand
• They test your thinking in a practical
situation of a real world problem.
• Software is very good for self
learning at leisure and it uses word
problems.
• BTW, If you are not understanding
anything, please please, please let me
know ASAP, directly or by e-mail. I
am here to help you understand.
• Blackboard anonymous posting of
questions may be a good way if you
are shy
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What is Stats?
• Human brain (100 bill neurons) is a
Statistical Engine, it uses data to
solve problems and make decisions.
Visual , auditory, tactile data used to
drive a car.
• What do Statisticians Do?
• Taming of Uncertainty by using data.
• Helps all kinds of scientific inquiry
• Useful in Entertainment (sports stat)
• Statistical Methodology is designed to
work Even if there are exceptions,
unlike natural or deductive laws.
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Scientific Method
• Nothing on faith, question
everything, Socrates gave his life.
• Ancient Indian sages (Vedas
3000BC). Always permit questioning
of fundamental beliefs. Charvaka
believed in enjoying life, Sex in right
circumstances is not sin, Patanjali
promoted Yoga.
• How to look at the evidence even if
the evidence has exceptional cases?
• Evidence-based objective view of life.
You are not really literate without
stats!
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Examples of stats in
Science
• Smoking causes cancer?. We have
seen exceptions (Winston Churchill)
• President is popular? Polling
• A product redesign is popular?
• Why meditate and do Yoga? Quiet
mind easier during Yoga. In 1967
Herb Benson showed: Meditators use
17% less oxygen, increase theta brain
waves, are calmer & happier, they
deactivate frontal lobe. (Time
Magazine, Aug 4, 2003). Happiness
depends on Inner Self (humans are
designed to tolerate temp range 50 to
100 degrees, Learn not to complain)
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Computers, Stats and
Power
• Stats rivals simple writing as one of
the most profound innovations in
human history.
• In our information society stats is the
intellectual fuel for computers.
• Knowledge is Power, but knowledge
is created by using stats.
• 1) Collect data: In natural sciences
we use controlled experiments. In
social sciences we use historical data.
• 2) Describe Data
• 3) Use Data to make decisions under
uncertainty ( what stock to buy? even
who to marry), that is, for inference.
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To repeat, Statistical
methods involve:
• describing data
• designing experiments and collecting
data so that meaningful results can
be extracted
• making decisions, inferences, and
predictions using data instead of
opinion and speculation
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Definitions and
Jargon
A population is the total set of
measurements that we are
interested in studying.
A list containing all members
of the population is referred to
as a frame.
A census is a survey that
attempts to include all elements
or units in the frame.
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Definitions page 2
Population parameters are facts
about the population. Since
parameters are descriptions of the
population, a population can have
many parameters. (e.g., height wt)
A sample is a (proper) subset of
the population, which is used to
gain insight about the population.
Good Samples are “representative”
of underlying (large) population.
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Population
Population
Described by
Parameter
Sample
Described
by Statistic
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Definitions p. 3
A statistic is a fact or
characteristic about the sample.
E.g.sample mean, variance, etc
The objective of inferential
statistics is to make reasonable
guesses about population
characteristics using sample data.
(is quality good? What is
population opinion about
president?)
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Cycle for data and
inference
Population
Population
Sample
Parameter
Statistic
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Notational
Distinction
A parameter for population
mean is mu = , the m in
the Greek alphabet,
Distinguished from
‘statistic’ m, which comes
from a sample.
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Definition p.4: Two
types of stats
1. Descriptive Statistics is
the collection, organization,
analysis, and presentation
of data.
2.inferential statistics deals
with using samples to draw
conclusions and or make
decisions (infer) about
populations using
probability theory.
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Descriptive statistics tries to
answer questions such as:
• What is a typical value for the
measurements?
• How much variation do the measurements
possess?
• What is the shape or distribution of the
measurements?
• Are there any extreme values in the
measurements? If so, what are they
telling us?
• What is the relative position of a
particular measurement in the data?
• If there are two variables, is one variable
related to another? If so, what kind of
relationship exists?
• How strong is the relationship?
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Descriptive Statistics
• Collect data
– e.g. Survey, Observation,
Experiments
• Present data
– e.g. Charts and graphs
• Characterize data
– e.g. Sample mean =
x
i
n
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Data Sources
Primary
Secondar
y
Data
Collection
Data
Compilation
Print or
Electronic
Observat
ion
Surv
ey
Experimentat
ion
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Populations and Samples
• A Population is the set of all items or
individuals of interest
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Examples:
All likely voters in the next election
All parts produced today
All sales receipts for November
• A Sample is a subset of the population
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Examples: 1000 voters selected at random for interview
A few parts selected for destructive testing
Every 100th receipt selected for audit
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Population Inferential Stats
Population with
unknown
characteristics
uses sample
data to
make inferences
about unknown
population
characteristics.
Draw
Sample
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Inferential Stats occupies
much of statistical theory.
• Define a scientific hypothesis
• Hypotheses in Business and
Economics usually involving some
uncertainty where we want to know
what is “by and large” true, subject
to exceptions.
• Use probability theory to nail down
the uncertainty and test the
hypothesis.
• Conclude if the hypothesis is
accepted or not
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Why Sample?
• Less time consuming than a census
• Less costly to administer than a census
• It is possible to obtain statistical results
of a sufficiently high precision based on
samples.
• For example, a study for my Conference
on Entrepreneurship and Human Rights
in August 2005 used a sample of 79
countries not all 200+ countries in the
world. Data were missing for small
countries.
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Inferential Statistics
• Making statements about a
population by examining sample
results
Sample statistics
Population
parameters
(known)
Inference
(unknown,
but can
be estimated from
sample evidence)
Sample
Population
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Data Types
Data
Qualitative
(Categorical)
Quantitative
(Numerical)
Examples:

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
Marital Status
Political Party
Eye Color
(Defined
categories)
Discrete
Examples:


Number of
Children
Defects per
hour
(Counted
items)
Continuous
Examples:


Weight
Voltage
(Measured
characteristic
s)
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Data Types
• Time Series Data
– Ordered data values observed over time
• Cross Section Data
– Data values observed at a fixed point in
time
• Pooled cross section of time series or
Panel (longitudinal) data
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Data Types
Sales (in $1000’s)
2003
2004
2005
2006
Atlanta
435
460
475
490
Boston
320
345
375
395
Clevelan
d
Denver
405
390
410
395
260
270
285
280
Tim
e
Seri
es
Dat
a
Cross
Section
Data
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Data Measurement Levels
Measurement
s
Rankings
Ordered
Categories
Categorical
Codes ID
Numbers
Category
Names
Highest Level
Ratio/Interval
Data
Complete
Analysis
Higher Level
Ordinal Data
Nominal Data
Mid-level
Analysis
Lowest Level
Basic
Analysis
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Mahatma Gandhi
(1869-1948):
"The greatness of a nation and its moral
progress can be judged by the way its
animals are treated.”
“You must not lose faith in humanity.
Humanity is an ocean; if a few drops of
the ocean are dirty, the ocean does not
become dirty.”
“The only devils in this world are those
running around inside our own hearts,
and that is where all our battles should
be fought.”
“An eye for an eye makes the whole world
blind.”
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