padm 7060 quantitative methods for public administration unit 4 chapters 11-12 jerry merwin

PADM 7060 Quantitative Methods for Public AdministrationUnit 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 one-tailed 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 (Page 8)

Problems 12.2, 12.6