Transcript PADM 7060
PADM 7060 Quantitative Methods for
Public Administration
Unit 4 Chapters 11-12
Jerry Merwin
Meier, Brudney & Bohte
Part IV: Inferential Statistics
Unit 4
Chapter 11: Introduction to Inference
Chapter 12: Hypothesis Testing
Unit 5
Chapter 13: Estimating Population
Proportions
Chapter 14: Testing the Difference
Between Two Groups
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference
Explain the difference between
descriptive statistics and inferential
statistics.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 2)
What are the basic concepts and
definitions associated with inferential
statistics?
Population
Parameters
Sample
Random selection
Statistic
Meier, Brudney & Bohte :
Chapter 11 Introduction to Inference (Page 3)
How important is random selection to
the concept of inference?
What are the difference in parameters
and statistics?
Symbols (See table 11.1)
Calculations
Mean?
Standard deviation?
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 4)
How do we estimate the population
mean? (177)
What do we mean by sampling error?
How can we reduce sampling error?
Ideal sample size is n 30.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 5)
How do we estimate the population
standard deviation? (see pages 178-179)
Why do we calculate s with the
denominator n-1?
How can we reduce sampling error?
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 6)
What is the standard error of the
mean? (pages 179-180)
How can we estimate the standard
error of the mean without taking
many samples?
See the formula on page 181
Also, note the explanation about using
the estimated standard deviation in the
computations.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 7)
Let’s look at the example on page
180 regarding the Yukon police:
The calculations for standard error of the
mean are on page 181
Next, we will talk about how we can use
this information.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 8)
What is the “Student’s t distribution”
(a.k.a. the t distribution)
Characteristics:
With n > = 30 normal distribution works
Resembles normal distribution but flatter
Differs for each sample size
Need to know the degrees of freedom (df)
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 9)
What is a confidence limit?
How is it calculated?
See formula
Using our example from Yukon:
First look up the t values in table 3 on 446
(see book about why we use .025 and d.f. = 4)
With the formula, we get
15.6 + (1.7 x 2.78) = 20.3 for the upper limit
15.6 – (1.7 x 2.78) = 10.9 for the lower limit
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 10)
With this information, what does it
tell us about the confidence limit?
15.6 + (1.7 x 2.78) = 20.3 for the upper
limit
15.6 – (1.7 x 2.78) = 10.9 for the lower
limit
We are 95% confident that…
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 11)
Problems 11.2, 11.6 11.8
Meier, Brudney & Bohte :
Chapter 12 Hypothesis Testing
How is hypothesis testing related to theory and
research? (Diagram courtesy of Dr. Nolan J. Argyle, from the text listed below)
David Nachmias & Chava Nachmias, Research Methods in the Social Sciences, 2nd ed. New York: St. Martins Press, 1981, p. 23.
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 2)
What is a hypothesis?
How is a hypothesis important to a
manager?
Explain the null hypothesis?
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 3)
What are the steps in hypothesis
testing?
Formulate the hypothesis
Collect the relevant data
Evaluate the hypothesis in light of the
data
Accept or reject the hypothesis
Revise your decisions in light of the new
information
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 4)
What is the primary type of
hypothesis testing we will do in
managerial situations?
Hypothesis testing with samples!
Example from Prudeville
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 5)
Who can explain the concept of onetailed and two-tailed tests?
When do we use the one-tailed test?
Figure 12.1
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 6)
What are the two types of errors we
can make testing a null hypothesis?
Type 1
Type 2
How can we decrease type 1 errors?
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 7)
How can we determine sample size?
Consider:
The amount of error that can be tolerated
The confidence one wants to have in the
error estimate
The standard deviation of the population
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
Problems 12.2, 12.6
(Page 8)