1. DATA ANALYSIS
16 OCTOBER 2014

2. TERMS, DEFINITIONS, AND APPROACH

3.  Population versus sample.
 Parameter versus statistic.
 Inference of population parameters from
sample statistics.

4.  Population
• Any complete group with at least one characteristic in
common.
• Not just people.
• 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.

5.  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.

6.  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.

7. THEORY, PROPOSITIONS, LOGIC

8.  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.”

9.  The foundation of theory-building.
 Statements of testable scientific
propositions.
 The focus for empirical work.

10.  Examine propositions in theory that require
verification.
 Are specific.
 Are testable.

11. 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.

16.  Hypotheses are“tested”
 Hypotheses are never“proved”
 Hypotheses only are“rejected”
 Theories are built and verified by testing hypotheses

17.  Greek letters used to designate parameters.
 Letters of English alphabet used to signify
statistics.

18.  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.

19.  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 timeclassroomtraining.
 Alternate hypothesis is H1: m1 - m2 not equal 0.
• Equivalent to m1 ≠ m2.

20. Decision
Fail to
reject Ho
Reject Ho

21. Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

22. Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho
Where are errors?

23. Error
Error
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

24. Error
Error
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho
What do the
errors cost?

25. Type 1
error
Error
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

26. Type 1
error
Type 2
error
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

27. Minimize Type 1
error by selecting
low error rate
Type 2
error
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

28. Minimize Type 1
error by selecting
low error rate
Minimize Type 2
error by
increasing
sample size
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

29. TRADITIONALLY,
probability of Type 1
error set at .05
Minimize Type 2
error by
increasing
sample size
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

30. > prop.test(98, 162)
1-sample proportions test with continuity correction
data: 98 out of 162, null probability 0.5
X-squared = 6.7222, df = 1, p-value = 0.009522
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.5249531 0.6798650
sample estimates:
p
0.6049383
Compare p-value
with Type 1 error
chosen. If p-value
is < Type 1 error,
the reject null
hypothesis.
Otherwise, you
fail to reject the
null hypothesis.