15 1 Chapter 15 Sampling Mc GrawHillIrwin 2006

15 -1 Chapter 15 Sampling Mc. Graw-Hill/Irwin © 2006 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

2 Learning Objectives Understand. . . • two premises on which sampling theory is based • accuracy and precision for measuring sample validity • five questions that must be answered to develop a sampling plan

3 Learning Objectives Understand. . . • two categories of sampling techniques and the variety of sampling techniques within each category • various sampling techniques and when each is used

4 The Nature of Sampling • • • Sampling Population Element Population Census Sampling frame

5 Why Sample? Availability of elements Greater speed Lower cost Sampling provides Greater accuracy

6 When Is A Census Appropriate? Feasible Necessary

7 What Is A Good Sample? Accurate Precise

8 Exhibit 15 -1 Sampling Design within the Research Process

9 Exhibit 15 -2 Types of Sampling Designs Element Selection Unrestricted Probability Nonprobability Simple random Convenience Restricted Complex random Purposive Systematic Judgment Cluster Quota Stratified Double Snowball

10 Steps in Sampling Design What is the target population? What are the parameters of interest? What is the sampling frame? What is the appropriate sampling method? What size sample is needed?

11 Larger Sample Sizes Population variance Number of subgroups Desired precision When Confidence level Small error range

12 Simple Random Advantages • Easy to implement with random dialing Disadvantages • Requires list of population elements • Time consuming • Uses larger sample sizes • Produces larger errors • High cost

13 Systematic Advantages • Simple to design • Easier than simple random • Easy to determine sampling distribution of mean or proportion Disadvantages • Periodicity within population may skew sample and results • Trends in list may bias results • Moderate cost

14 Stratified Advantages • Control of sample size in strata • Increased statistical efficiency • Provides data to represent and analyze subgroups • Enables use of different methods in strata Disadvantages • Increased error will result if subgroups are selected at different rates • Especially expensive if strata on population must be created • High cost

15 Cluster Advantages • Provides an unbiased estimate of population parameters if properly done • Economically more efficient than simple random • Lowest cost per sample • Easy to do without list Disadvantages • Often lower statistical efficiency due to subgroups being homogeneous rather than heterogeneous • Moderate cost

16 Exhibit 15 -5 Stratified and Cluster Sampling Stratified • Population divided into few subgroups • Homogeneity within subgroups • Heterogeneity between subgroups • Choice of elements from within each subgroup Cluster • Population divided into many subgroups • Heterogeneity within subgroups • Homogeneity between subgroups • Random choice of subgroups

17 Area Sampling

18 Double Advantages Disadvantages • May reduce costs if • Increased costs if first stage results in discriminately used enough data to stratify or cluster the population

19 Nonprobability Samples No need to generalize Limited objectives Feasibility Issues Time Cost

20 Nonprobability Sampling Methods Convenience Judgment Quota Snowball

21 Key Terms • • Area sampling Census Cluster sampling Convenience sampling • Disproportionate stratified sampling • Double sampling • Judgment sampling • • • Multiphase sampling Nonprobability sampling Population element Population parameters Population proportion of incidence • Probability sampling

22 Key Terms • Proportionate stratified sampling • Quota sampling • Sample statistics • Sampling error • Sampling frame • Sequential sampling • • • Simple random sample Skip interval Snowball sampling Stratified random sampling Systematic variance

15 -23 Appendix 15 a Determining Sample Size Mc. Graw-Hill/Irwin © 2006 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

24 Exhibit 15 a-1 Random Samples

25 Exhibit 15 a-2 Increasing Precision Reducing the Standard Deviation by 50% Quadrupling the Sample

26 Exhibit 15 a-3 Confidence Levels & the Normal Curve

27 Exhibit 15 a-4 Standard Errors Standard Error (Z score) % of Area Approximate Degree of Confidence 1. 00 68. 27 68% 1. 65 90. 10 90% 1. 96 95. 00 95% 3. 00 99. 73 99%

28 Central Limit Theorem

29 Exhibit 15 a-6 Estimates of Dining Visits Confidence Z score % of Area Interval Range (visits per month) 68% 1. 00 68. 27 9. 48 -10. 52 90% 1. 65 90. 10 9. 14 -10. 86 95% 1. 96 95. 00 8. 98 -11. 02 99% 3. 00 99. 73 8. 44 -11. 56

30 Calculating Sample Size for Questions involving Means Precision Confidence level Size of interval estimate Population Dispersion Need for FPA

31 Exhibit 15 a-7 Metro U Sample Size for Means Steps Desired confidence level Size of the interval estimate Expected range in population Information 95% (z = 1. 96) . 5 meals per month 0 to 30 meals Sample mean Standard deviation Need for finite population adjustment Standard error of the mean Sample size 10 4. 1 No. 5/1. 96 =. 255 (4. 1)2/ (. 255)2 = 259

32 Proxies of the Population Dispersion • Previous research on the topic • Pilot test or pretest • Rule-of-thumb calculation – 1/6 of the range

33 Exhibit 15 a-7 Metro U Sample Size for Proportions Steps Desired confidence level Size of the interval estimate Expected range in population Information 95% (z = 1. 96) . 10 (10%) 0 to 100% Sample proportion with given attribute Sample dispersion Finite population adjustment Standard error of the proportion Sample size 30% Pq =. 30(1 -. 30) =. 21 No. 10/1. 96 =. 051. 21/ (. 051)2 = 81

34 Appendix 15 a: Key Terms • • • Central limit theorem Confidence interval Confidence level Interval estimate Point estimate Proportion