### Chapter #1 /97

```Elementary Statistics
M A R I O F. T R I O L A
Wesley Longman Longman
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Introduction To Statistics
Chapter 1
M A R I O F. T R I O L A
1998,
Triola, Elementary Statistics
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Chapter 1
Introduction to Statistics
1-1 Overview
1-2 The Nature of Data
1-3* Uses and Abuses of Statistics
1-4 Design of Experiments
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1-1
Overview
Statistics
Two Meanings
 Actual numbers
 Methods of analysis
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Statistics
 Actual numbers
numerical measurements determined by a
set of data
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Statistics
 Methods of analysis
a collection of methods for planning
experiments, obtaining data, and then
analyzing, interpreting, and drawing
conclusions based on the data
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Definitions
 Population
the complete collection of elements
(scores, people, measurements, etc.)
to be studied
 Sample
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Definitions
 Population
the complete collection of elements
(scores, people, measurements, etc.)
to be studied
 Sample
a subset of a population
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Definitions
 Parameter
a numerical measurement describing
some characteristic of a population
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Definitions
 Parameter
a numerical measurement describing
some characteristic of a population
population
parameter
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Definitions
 Statistic
a numerical measurement describing
some characteristic of a sample
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Definitions
 Statistic
a numerical measurement describing
some characteristic of a sample
sample
statistic
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Definitions
• Population
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Definitions
Population
Parameter
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Definitions
Population
Parameter
Sample
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Definitions
Population
Parameter
Sample
Statistic
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Definitions
Population
Parameter
Sample
Statistic
Census
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1-2 The
Nature of Data
Definitions
 Quantitative data
numbers representing counts or
measurements
 Qualitative (attribute) data
nonnumeric data that can be separated into
different categories
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Definitions
 Discrete
data which results from either a finite number of
possible values or a countable number of possible
values
0, 1, 2, 3, . . .
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Definitions
 Discrete
data which results from either a finite number of
possible values or a countable number of possible
values
0, 1, 2, 3, . . .
 Continuous
data which results from infinitely many possible
values that can be associated with points on a
continuous scale in such as way that there are no
gaps or interruptions
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4
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Quantitative Data
 Discrete - Countable
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Quantitative Data
 Discrete - Countable
 Continuous - Measurements with no
gaps
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Definitions
 nominal level of measurement
characterized by data that consist of names,
labels, or categories only. Data cannot be
arranged in an ordering scheme (such as low
to high)
E.g. Blood types: O, A, B, AB
Genders: Male & Female
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Definitions
 ordinal level of measurement
involves data that may be arranged in some
order, but differences between data values
either cannot be determined or are meaningless
E.g. Taste of food: bad, so-so, good, delicious
Grades: A, B, C, D, F
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Definitions
 interval level of measurement
like the ordinal level, with the additional property
that we can determine meaningful amounts of
differences between data. However, there is no
inherent (natural) zero starting point (where
none of the quantity is present.)
E.g. year 2000, temperature 96.2 F etc.
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Definitions
 ratio level of measurement
the interval level modified to include the inherent
zero starting point where zero indicates that
none of the quantity is present. For values at
this level, differences and ratios are meaningful.
E.g. weights of grains, heights of people
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Levels of Measurement
 Nominal - names only
 Ordinal - names with some order
 Interval - differences but no ‘zero’
 Ratio - differences and a ‘zero’
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Levels of Measurement
 Nominal - names only
 Ordinal - names with some order
 Interval - differences but no ‘zero’
 Ratio - differences and a ‘zero’
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Design of Experiments
Section 1-4
M A R I O F. T R I O L A
1998,
Triola, Elementary Statistics
Wesley Longman Longman
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Steps for Designing an
Experiment
1.
Identify the exact question and exact
2.
Develop a plan for collecting data that is representative of the
population
3.
Collect data minimizing errors that result in biased data
4.
Analyze the data and draw conclusions
population
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Definitions
 Observational Study
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Definitions
 Observational Study
observing and measuring specific characteristics
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Definitions
 Experiment
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Definitions
 Experiment
application of some treatment and then
observe its effects on the subject
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Definitions
 Experiment
application of some treatment and then
observe its effects on the subject
Treatment Group
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Definitions
 Experiment
application of some treatment and then
observe its effects on the subject
Treatment Group
Control Group
E.g. Drug v.s. placebo
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Designing an Experiment
 Experimental units (blocks)
 Completely randomized design
 Rigorously controlled design
 Replication
Study the text book Section 1-4 for the details
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Definitions
 Confounding
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Definitions
 Confounding
effects from two or more variables that cannot
be distinguished from each other
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Data carelessly collected may be so
completely useless that no amount of
statistical torturing can salvage them.
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Random Sampling -
selection so
that each has an equal chance of being
selected
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Stratified Sampling -
subdivide
population and draw sample from each stratum
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Systematic Sampling
Every K th element
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Cluster Sampling -
divide into
sections; choose a few of those sections; choose
all from selected sections
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Convenience Sampling -
use
Hey!
Do you believe
in the death
penalty?
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Methods of Sampling
 Random
 Stratified
 Systematic
 Cluster
 Convenience
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Definitions

Sampling Error
the difference between a sample result and the
true population result due to chance sample
fluctuations

Non-sampling Error
sample data that is incorrectly collected, recorded,
or analyzed