PADM 7060 Quantitative Methods for Public Administration Unit 5 Chapters 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 )  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 )  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 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 (Page 7)  Problems 13.2,

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 Control Group Mean 526 books 475 books Std Dev

Meier & Brudney: Chapter 14 Testing the Difference Between Two Groups (Page 3)  Ware County Library example (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  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 (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 ) Conclusion?

Meier & Brudney: Chapter 14 Testing the Difference Between Two Groups (Page 9)  Problems: 14.6, 14.12