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Basic Statistical Concepts& Decision-Making
DATA ANALYSIS17 September 2015
Basic statistical conceptsTERMS, DEFINITIONS, AND APPROACH
Basic statistical terms
Population versus sample.
Parameter versus statistic.
Inference of population parameters from sample statistics.
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.
Work within groups…
List 10 examples of
population/sample pairs.
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.
Work within groups…
List 10 examples of
parameters and associated statistics
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.
Hypothesis testingTHEORY, PROPOSITIONS, LOGIC
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.”
Hypotheses are…
The foundation of theory-building.
Statements of testable scientific propositions.
The focus for empirical work.
Well-stated hypotheses…Examine propositions in theory that
require verification.
Are specific.
Are testable.
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.
“Nomological net” of theory
“Nomological net” of theory
“Nomological net” of theory
Good (not easy) explanation Chapter 1 treats
concepts in the philosophy of science
Work within groups…
Describe 1 example of
theory and 1 example of a
pseudo-theory
Language of hypothesis testing… Hypotheses are“tested”
Hypotheses are never“proved”
Hypotheses only are“rejected”
Theories are built and verified by testing hypotheses
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.
A word about notation
Greek letters used to designate parameters.
Letters of English alphabet used to signify statistics.
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.
Work within groups…
Formulate 1 statistical null hypothesis &
and its alternative
Decision-by-truth tableD
ecis
ion Fail to
reject Ho
Reject Ho
Decision-by-truth tableTruth
Ho true Ho falseD
ecis
ion Fail to
reject Ho
Reject Ho
Decision-by-truth tableTruth
Ho true Ho falseD
ecis
ion Fail to
reject Ho
Reject Ho
Where are errors?
Decision-by-truth table
Error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
Decision-by-truth table
Error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
What do the errors cost?
Decision-by-truth table
Type 1error
Error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
Decision-by-truth table
Type 1error
Type 2error
TruthHo true Ho false
Dec
isio
n Fail to reject Ho
Reject Ho
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
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
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
Work within groups…In a decision-by-
truth table, describe possible
outcomes of a statistical null
hypothesis test
Basic Statistical Concepts& Decision-Making
DATA ANALYSIS17 September 2015
