copyright © 1998, triola, elementary statistics addison wesley longman 1 elementary statistics m a...
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Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman 1
Elementary Elementary StatisticsStatistics
M A R I O F. T R I O L ACopyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
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Addison Wesley Longman 2
Introduction To Introduction To StatisticsStatistics
Chapter 1Chapter 1
M A R I O F. T R I O L ACopyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
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1-1 Overview
1-2 The Nature of Data
1-3* Uses and Abuses of Statistics
1-4 Design of Experiments
Chapter 1 Introduction to Statistics
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Statistics
Two Meanings Actual numbers Methods of analysis
1-1 Overview
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Actual numbersnumerical measurements determined by a
set of data
Statistics
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Methods of analysisa collection of methods for planning
experiments, obtaining data, and then
analyzing, interpreting, and drawing
conclusions based on the data
Statistics
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Population
the complete collection of elements (scores, people, measurements, etc.) to be studied
Sample
Definitions
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Population
the complete collection of elements (scores, people, measurements, etc.) to be studied
Sample
a subset of a population
Definitions
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Definitions
Parameter
a numerical measurement describing some characteristic of a population
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Parameter
a numerical measurement describing some characteristic of a population
population
parameter
Definitions
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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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• Population
Definitions
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Population Parameter
Definitions
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Population Parameter
Sample
Definitions
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Population Parameter
Sample Statistic
Definitions
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Population Parameter
Sample Statistic
Census
Definitions
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Quantitative data
numbers representing counts or measurements
Qualitative (attribute) datanonnumeric data that can be separated into different categories
The Nature of Data
Definitions
1-2
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Discrete data which results from either a finite number of
possible values or a countable number of possible values
0, 1, 2, 3, . . .
Definitions
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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
Definitions
3 4
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Discrete - Countable
Quantitative Data
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Discrete - Countable
Continuous - Measurements with no gaps
Quantitative Data
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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)
Definitions
E.g. Blood types: O, A, B, AB
Genders: Male & Female
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ordinal level of measurementinvolves data that may be arranged in some
order, but differences between data values
either cannot be determined or are meaningless
Definitions
E.g. Taste of food: bad, so-so, good, delicious
Grades: A, B, C, D, F
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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.)
Definitions
E.g. year 2000, temperature 96.2 F etc.
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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.
Definitions
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 Design of ExperimentsExperiments
Section 1-4Section 1-4
M A R I O F. T R I O L ACopyright © 1998, Triola, Elementary Statistics
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Steps for Designing an Experiment
1. Identify the exact question and exact population
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
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Observational Study
Definitions
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Observational Study observing and measuring specific characteristics
Definitions
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Experiment
Definitions
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Experiment application of some treatment and then observe its effects on the subject
Definitions
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Experiment application of some treatment and then observe its effects on the subject
Definitions
Treatment Group
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Experiment application of some treatment and then observe its effects on the subject
Definitions
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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Confounding
Definitions
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Confounding effects from two or more variables that cannot be distinguished from each other
Definitions
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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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Every K th element
Systematic Sampling
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Cluster Sampling - divide into sections; choose a few of those sections; choose all from selected sections
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Hey!Do you believe
in the deathpenalty?
Convenience Sampling - use readily available results
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Random
Stratified
Systematic
Cluster
Convenience
Methods of Sampling
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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
Definitions