wf ed 540, class meeting 4, 17 september 2015
TRANSCRIPT
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Basic Statistical Concepts& Decision-Making
DATA ANALYSIS17 September 2015
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Basic statistical conceptsTERMS, DEFINITIONS, AND APPROACH
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Basic statistical terms
Population versus sample.
Parameter versus statistic.
Inference of population parameters from sample statistics.
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Population & sample Population• Any complete group with at least one characteristic in
common. • Not just people, but any entity. • Might consist of, but not limited to, people, animals,
businesses, buildings, motor vehicles, farms, objects, or events.
Sample• A group of units selected from a larger group (the
population). • Generally selected for study because the population is
too large to study in its entirety. • Good samples represent the population.
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Work within groups…
List 10 examples of
population/sample pairs.
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Parameters & statistics
Parameter• Information about a population.• Characteristic of a population.• A population value.• The “truth.”
Statistic• Information about a sample.• An estimate of a population value.
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Work within groups…
List 10 examples of
parameters and associated statistics
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Statistical reasoning Data usually are available from a sample, not a
population. That is, sample statistics are available, not
population parameters. We wish to infer (or estimate) parameters from
statistics. Because data are available from a sample, not the
population, error occurs when inferring (or estimating) population parameters from sample statistics.
Data analysis techniques help us make decisions under error and uncertainty.
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Hypothesis testingTHEORY, PROPOSITIONS, LOGIC
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Scientific theories…
Are composed of propositions that explain the empirical, observable world. A proposition is an “if–then” statement
Are networks showing relationship and causality among propositions.
Must have“empirical import.”
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Hypotheses are…
The foundation of theory-building.
Statements of testable scientific propositions.
The focus for empirical work.
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Well-stated hypotheses…Examine propositions in theory that
require verification.
Are specific.
Are testable.
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Hypotheses are testedto build a “nomological network”
The term "nomological" is derived from Greek and means "lawful.”
A nomological network is a"lawful network,” a network of propositions that describe how things work.
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“Nomological net” of theory
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“Nomological net” of theory
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“Nomological net” of theory
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Good (not easy) explanation Chapter 1 treats
concepts in the philosophy of science
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Work within groups…
Describe 1 example of
theory and 1 example of a
pseudo-theory
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Language of hypothesis testing… Hypotheses are“tested”
Hypotheses are never“proved”
Hypotheses only are“rejected”
Theories are built and verified by testing hypotheses
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An example…
Research is designed to evaluate whether on–the–job training reduces cycle time in product manufacturing.
Two groups of subjects:• One group receives on-the-job training.• The other group receives classroom
training.Dependent variable is cycle time;
independent variable is group membership.
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A word about notation
Greek letters used to designate parameters.
Letters of English alphabet used to signify statistics.
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An example…
Null hypothesis is H0: m1 - m2 = 0 stated about parameters.• Equivalent to m1 = m2
• Estimated by testing whether mean1 = mean2.• E.g., estimated by testing if mean cycle timeon-the-
job training = mean cycle timeclassroom training.Alternate hypothesis is H1: m1 - m2 not
equal 0.• Equivalent to m1 ≠ m2.
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Work within groups…
Formulate 1 statistical null hypothesis &
and its alternative
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Decision-by-truth tableD
ecis
ion Fail to
reject Ho
Reject Ho
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Decision-by-truth tableTruth
Ho true Ho falseD
ecis
ion Fail to
reject Ho
Reject Ho
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Decision-by-truth tableTruth
Ho true Ho falseD
ecis
ion Fail to
reject Ho
Reject Ho
Where are errors?
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Decision-by-truth table
Error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Decision-by-truth table
Error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
What do the errors cost?
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Decision-by-truth table
Type 1error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Decision-by-truth table
Type 1error
Type 2error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Decision-by-truth table
Minimize Type 1error by selecting
low error rate
Type 2error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Decision-by-truth table
Minimize Type 1error by selecting
low error rate
Minimize Type 2error by
increasing sample size
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Decision-by-truth table
TRADITIONALLY, probability of Type 1
error set at .05
Minimize Type 2error by
increasing sample size
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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Work within groups…In a decision-by-
truth table, describe possible
outcomes of a statistical null
hypothesis test
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Basic Statistical Concepts& Decision-Making
DATA ANALYSIS17 September 2015