Chapter #1 /97
Download
Report
Transcript Chapter #1 /97
Elementary Statistics
M A R I O F. T R I O L A
Copyright © 1998, Triola, Elementary Statistics
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley
Wesley Longman Longman
Addison
1
Introduction To Statistics
Chapter 1
M A R I O F. T R I O L A
Copyright ©Copyright
1998,
Triola, Elementary Statistics
© 1998, Triola, Elementary Statistics
Addison Wesley Longman
Addison Wesley Longman
2
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
3
1-1
Overview
Statistics
Two Meanings
Actual numbers
Methods of analysis
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
4
Statistics
Actual numbers
numerical measurements determined by a
set of data
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
5
Statistics
Methods of analysis
a collection of methods for planning
experiments, obtaining data, and then
analyzing, interpreting, and drawing
conclusions based on the data
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
6
Definitions
Population
the complete collection of elements
(scores, people, measurements, etc.)
to be studied
Sample
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
7
Definitions
Population
the complete collection of elements
(scores, people, measurements, etc.)
to be studied
Sample
a subset of a population
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
8
Definitions
Parameter
a numerical measurement describing
some characteristic of a population
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
9
Definitions
Parameter
a numerical measurement describing
some characteristic of a population
population
parameter
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
10
Definitions
Statistic
a numerical measurement describing
some characteristic of a sample
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
11
Definitions
Statistic
a numerical measurement describing
some characteristic of a sample
sample
statistic
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
12
Definitions
• Population
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
13
Definitions
Population
Parameter
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
14
Definitions
Population
Parameter
Sample
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
15
Definitions
Population
Parameter
Sample
Statistic
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
16
Definitions
Population
Parameter
Sample
Statistic
Census
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
17
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
18
Definitions
Discrete
data which results from either a finite number of
possible values or a countable number of possible
values
0, 1, 2, 3, . . .
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
19
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
3
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
4
20
Quantitative Data
Discrete - Countable
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
21
Quantitative Data
Discrete - Countable
Continuous - Measurements with no
gaps
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
22
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
23
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
24
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.
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
25
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
26
Levels of Measurement
Nominal - names only
Ordinal - names with some order
Interval - differences but no ‘zero’
Ratio - differences and a ‘zero’
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
27
Levels of Measurement
Nominal - names only
Ordinal - names with some order
Interval - differences but no ‘zero’
Ratio - differences and a ‘zero’
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
28
Design of Experiments
Section 1-4
M A R I O F. T R I O L A
Copyright ©Copyright
1998,
Triola, Elementary Statistics
© 1998, Triola, Elementary Statistics
Addison Wesley
Wesley Longman Longman
Addison
29
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
population
30
Definitions
Observational Study
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
31
Definitions
Observational Study
observing and measuring specific characteristics
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
32
Definitions
Experiment
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
33
Definitions
Experiment
application of some treatment and then
observe its effects on the subject
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
34
Definitions
Experiment
application of some treatment and then
observe its effects on the subject
Treatment Group
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
35
Definitions
Experiment
application of some treatment and then
observe its effects on the subject
Treatment Group
Control Group
E.g. Drug v.s. placebo
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
36
Designing an Experiment
Experimental units (blocks)
Completely randomized design
Rigorously controlled design
Replication
Study the text book Section 1-4 for the details
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
37
Definitions
Confounding
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
38
Definitions
Confounding
effects from two or more variables that cannot
be distinguished from each other
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
39
Data carelessly collected may be so
completely useless that no amount of
statistical torturing can salvage them.
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
40
Random Sampling -
selection so
that each has an equal chance of being
selected
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
41
Stratified Sampling -
subdivide
population and draw sample from each stratum
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
42
Systematic Sampling
Every K th element
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
43
Cluster Sampling -
divide into
sections; choose a few of those sections; choose
all from selected sections
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
44
Convenience Sampling -
use
readily available results
Hey!
Do you believe
in the death
penalty?
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
45
Methods of Sampling
Random
Stratified
Systematic
Cluster
Convenience
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
46
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
Copyright © 1998, Triola, Elementary Statistics
Addison Wesley Longman
47