Transcript PADM 7060

PADM 7060 Quantitative Methods for
Public Administration
Unit 5 Chapters 13-14
Fall 2004
Jerry Merwin
Meier & Brudney
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: Chapter 13
Estimating Population Proportions
 What do we mean by Estimating
Population Proportions?
 Dealing with percentage of population
rather than mean
 Examples: Percentage of
 Vehicles that will pass inspection
 Recidivism rates
 Volunteers who will show up
Meier & Brudney: Chapter 13
Estimating Population Proportions
(Page 2)
 So how do we Estimate Population
Proportions and set confidence limits?
 Ramsey Prison example (Page 193)
 Warden wants to know recidivism rate
 Expects good results and wants to brag
 Journal of Law ‘n’ Order
 Sample of 100
 FBI data system trace on re-arrests within 1
year after release
 Results of search shows 68 arrested again
Meier & Brudney: Chapter 13
Estimating Population Proportions
(Page 3)
 Continued
 Ramsey Prison example (Pages 193-195)
 Question 1: best estimate of population
proportion?
 Consider 100 samples with an n of 1
 Sample Proportion = .68 (estimate of population
proportion)
 Question 2: standard deviation?
 See formula on page 194
 Does the typical idea of standard deviation fit?
 Standard deviation is calculated here only to use in
calculating the standard error of the proportion.
Meier & Brudney: Chapter 13
Estimating Population Proportions
(Page 4)
 Continued
 Ramsey Prison example
(Pages 193-195)
 Question 3: standard error of proportion?
 Same formula as standard error of mean (see
it on page 195)
 Question 4: the 95% confidence limits?
 Can proportions be normally distributed?
 Each person is either recidivist or not!
 See formula on 195 with limits
Meier & Brudney: Chapter 13
Estimating Population Proportions
(Page 5)
 Let’s talk about the Worcester
example with hypotheses.
 Steps on pages 195-196
 Do we accept or reject the null
hypothesis?
 Who can explain the digression
?
(on 196)
Meier & Brudney: Chapter 13
Estimating Population Proportions
(Page 6)
 How do we determine sample size? or
 How big a sample does one need to
find out information for our research?
 See page 197 for method of calculating n
 Key is proportion of .5
Meier & Brudney: Chapter 13
Estimating Population Proportions
 Problems 13.2, 13.4 13.12
(Page 7)
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
 Why would we want to test the
difference between two groups?
 Examples on page 201
 Could be comparison of scores before and
after some event
 Might be how two groups fare with different
treatment (mental health)
 How different units of an organization do
with some factor different
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 2)
 How can we compare the means from
two groups to see if they are different?
 Ware County Library example
 Bookmobile routes selected at random
 Some routes get poster ads, others do not
 See data in Table 14.1 on page 202
Experimental Group
Mean
526 books
Std Dev
125
Control Group
475 books
115
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
 Ware County Library example
(Page 3)
(Continued)
 The null hypothesis is?
 When testing the means of the two groups,
what are we really asking? *(Probability that they
are drawn from same population.)
 See the steps on page 202-203
 This procedure is called “Analysis of
Variance”
 Note how degrees of freedom are
determined: df = (n - 1) + (n - 1)
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 4)
 What other tests are used to compare
means?
 Distinctions?
 First test: two independent samples and
might not have same population variances
(thus, analysis of variance)
 Second test: equal variances
 Third test: dependent samples
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 5)
 What other tests are used to compare
means? (Continued)
 Example from Stone Creek, SD, re.
hiring procedures
 Sample 10 city bureaus
 Average time to hire employee before and
after new procedures (See page 204 for data)
 Steps on page 204 (for test with independent
samples & unequal variances)
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 6)
 What other tests are used to compare
means? (Continued)
 Example from Stone Creek, SD, re.
hiring procedures
 Steps on page 205
(for test with independent
samples & equal variances)
 How does this compare to the previous
test?
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 7)
 What other tests are used to compare
means? (Continued)
 Example from Stone Creek, SD, re.
hiring procedures
 Steps on pages 205-206
(for test with
dependent samples)
 How are data different?
 Why are we doing test of paired samples?
 Solving for “d” (Difference of two items)
 Get mean and standard deviation of differences
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
(Page 8)
 How is the t test used for two sample
proportions?
 See example with Morgan City Parole
Board (pages 206-208)
 Conclusion?
Meier & Brudney: Chapter 14
Testing the Difference Between Two Groups
 Problems: 14.6, 14.12
(Page 9)