Workforce Education and Development, Penn State

1. DATA ANALYSIS
20 September 2016

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, 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.

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. ROLE INTHEORY

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.

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

13.  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.

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

15.  Null hypothesis is H0: m1 - m2 = 0 stated
about parameters.
• Equivalent to m1 = m2
• Estimated by testing whether X1 = X2.
• E.g., estimated by testing if
Xon-the-job training = Xclassroom training.
 Alternate hypothesis is H1: m1 - m2 not equal 0.
• Equivalent to m1 ≠ m2.

16. DECISION-MAKING UNDER ERROR & UNCERTAINTY

17. Decision
Fail to
reject Ho
Reject Ho

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

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

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

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

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

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

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

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

26. TRADITIONALLY,
probability ofType 1
error set at .05
MinimizeType 2
error by
increasing
sample size
Truth
Ho true Ho false
Decision
Fail to
reject Ho
Reject Ho

27. In a decision-by-
truth table, describe
possible outcomes
of a statistical null
hypothesis test

29.  Test the following hypotheses with the mtcars
data:
• Does a difference exist in the quarter mile time by
transmission type?
• Is there a difference in horsepower between vertical
and straight engines?
• Does displacement differ by whether an engine is
vertical or straight?
 Report the findings of each hypothesis test in an
RPubs page.

30. DATA ANALYSIS
20 September 2016