Slides Prepared by JOHN S. LOUCKS St. Edward’s University

1. Slides Prepared by JOHN S. LOUCKS St. Edward’s University

2. Chapter 18 Sample Survey • Terminology Used in Sample Surveys • Types of Surveys and Sampling Methods • Survey Errors • Simple Random Sampling • Stratified Simple Random Sampling • Cluster Sampling • Systematic Sampling

3. Terminology Used in Sample Surveys • An element is the entity on which data are collected. • A population is the collection of all elements of interest. • A sample is a subset of the population.

4. Terminology Used in Sample Surveys • The target populationis the population we want to make inferences about. • The sampled populationis the population from which the sample is actually selected. • These two populations are not always the same. • If inferences from a sample are to be valid, the sampled population must be representative of the target population.

5. Terminology Used in Sample Surveys • The population is divided into sampling unitswhich are groups of elements or the elements themselves. • A list of the sampling units for a particular study is called a frame. • The choice of a particular frame is often determined by the availability and reliability of a list. • The development of a frame can be the most difficult and important steps in conducting a sample survey.

6. Types of Surveys • Surveys Involving Questionnaires • Three common types are mail surveys, telephone surveys, and personal interview surveys. • Survey cost are lower for mail and telephone surveys. • With well-trained interviewers, higher response rates and longer questionnaires are possible with personal interviews. • The design of the questionnaire is critical.

7. Types of Surveys • Surveys Not Involving Questionnaires • Often, someone simply counts or measures the sampled items and records the results. • An example is sampling a company’s inventory of parts to estimate the total inventory value.

8. Sampling Methods • Sample surveys can also be classified in terms of the sampling method used. • The two categories of sampling methods are: • Probabilistic sampling • Nonprobabilistic sampling

9. Nonprobabilistic Sampling Methods • The probability of obtaining each possible sample can be computed. • Statistically valid statements cannot be made about the precision of the estimates. • Sampling cost is lower and implementation is easier. • Methods include convenience and judgment sampling.

10. Nonprobabilistic Sampling Methods • Convenience Sampling • The units included in the sample are chosen because of accessibility. • In some cases, convenience sampling is the only practical approach.

11. Nonprobabilistic Sampling Methods • Judgment Sampling • A knowledgeable person selects sampling units that he/she feels are most representative of the population. • The quality of the result is dependent on the judgment of the person selecting the sample. • Generally, no statistical statement should be made about the precision of the result.

12. Probabilistic Sampling Methods • The probability of obtaining each possible sample can be computed. • Confidence intervals can be developed which provide bounds on the sampling error. • Methods include simple random, stratified simple random, cluster, and systematic sampling.

13. Survey Errors • Two types of errors can occur in conducting a survey: • Sampling error • Nonsampling error

14. Survey Errors • Sampling Error • It is defined as the magnitude of the difference between the point estimate, developed from the sample, and the population parameter. • It occurs because not every element in the population is surveyed. • It cannot occur in a census. • It can not be avoided, but it can be controlled.

15. Survey Errors • Nonsampling Error • It can occur in both a census and a sample survey. • Examples include: • Measurement error • Errors due to nonresponse • Errors due to lack of respondent knowledge • Selection error • Processing error

16. Survey Errors • Nonsampling Error • Measurement Error • Measuring instruments are not properly calibrated. • People taking the measurements are not properly trained.

17. Survey Errors • Nonsampling Error • Errors Due to Nonresponse • They occur when no data can be obtained, or only partial data are obtained, for some of the units surveyed. • The problem is most serious when a bias is created.

18. Survey Errors • Nonsampling Error • Errors Due to Lack of Respondent Knowledge • These errors on common in technical surveys. • Some respondents might be more capable than others of answering technical questions.

19. Survey Errors • Nonsampling Error • Selection Error • An inappropriate item is included in the survey. • For example, in a survey of “small truck owners” some interviewers include SUV owners while other interviewers do not.

20. Survey Errors • Nonsampling Error • Processing Error • Data is incorrectly recorded. • Data is incorrectly transferred from recording forms to computer files.

21. Simple Random Sampling • A simple random sampleof size n from a finite population of size N is a sample selected such that every possible sample of size n has the same probability of being selected. • We begin by developing a frameor list of all elements in the population. • Then a selection procedure, based on the use of random numbers, is used to ensure that each element in the sampled population has the same probability of being selected.

22. Simple Random Sampling We will see in the upcoming slides how to: • Estimate the following population parameters: • Population mean • Population total • Population proportion • Determine the appropriate sample size

23. Simple Random Sampling • In a sample survey it is common practice to provide an approximate 95% confidence interval estimate of the population parameter. • Assuming the sampling distribution of the point estimator can be approximated by a normal probability distribution, we use a value of z = 2 for a 95% confidence interval. • The interval estimate is: Point Estimator +/- 2 (Estimate of the Standard Error of the Point Estimator) • The bound on the sampling error is: 2 (Estimate of the Standard Error of the Point Estimator)

24. Simple Random Sampling • Population Mean • Point Estimator • Estimate of the Standard Error of the Mean

25. Simple Random Sampling • Population Mean • Interval Estimate • Approximate 95% Confidence Interval Estimate

26. Simple Random Sampling • Population Total • Point Estimator • Estimate of the Standard Error of the Total

27. Simple Random Sampling • Population Total • Interval Estimate • Approximate 95% Confidence Interval Estimate

28. Simple Random Sampling • Population Proportion • Point Estimator • Estimate of the Standard Error of the Proportion

29. Simple Random Sampling • Population Proportion • Interval Estimate • Approximate 95% Confidence Interval Estimate

30. Determining the Sample Size • An important consideration in sample design is the choice of sample size. • The best choice usually involves atradeoff between cost and precision (size of the confidence interval). • Larger samples provide greater precision, but are more costly. • A budget might dictate how large the sample can be. • A specified level of precision might dictate how small a sample can be.

31. Determining the Sample Size • Smaller confidence intervals provide more precision. • The size of the approximate confidence interval depends on the bound B on the sampling error. • Choosing a level of precision amounts to choosing a value for B. • Given a desired level of precision, we can solve for the value of n.

32. Simple Random Sampling • Necessary Sample Size for Estimating the Population Mean Hence,

33. Example: Innis Investments • Simple Random Sampling Innis is a financial advisor for 200 clients. A sample of 40 clients has been taken to obtain various demographic data and information about the clients’ investment objectives. Statistics of particular interest are the clients’ age, clients’ total net worth, and the proportion favoring fixed income investments.

34. Example: Innis Investments • Simple Random Sampling For the sample, the mean age was 52 (with a standard deviation of 10), the mean net worth was $480,000 (with a standard deviation of $120,000), and the proportion favoring fixed-income investments was .30.

35. Example: Innis Investments • Estimate of Standard Error of Mean Age • Approximate 95% Confidence Interval for Mean Age

36. Example: Innis Investments • Point Estimate of Total Net Worth (TNW) of Clients • Estimate of Standard Error of TNW = $3,394,113 • Approximate 95% Confidence Interval for TNW = $89,211,774 to $102,788,226

37. Using Excel for Simple Random Sampling: Population Total • Formula Worksheet Note: Rows 13-41 are not shown.

38. Using Excel for Simple RandomSampling: Population Total • Value Worksheet Note: Rows 13-41 are not shown.

39. Example: Innis Investments • Point Estimate of Population Proportion Favoring Fixed-Income Investments p = .30 • Estimate of Standard Error of Proportion • Approximate 95% Confidence Interval

40. Using Excel for Simple RandomSampling: Population Proportion • Formula Worksheet Note: Rows 13-41 are not shown.

41. Using Excel for Simple RandomSampling: Population Proportion • Value Worksheet Note: Rows 13-41 are not shown.

42. Example: Innis Investments One year later Innis wants to again survey his clients. He now has 250 clients and wants to set a bound of $30,000 on the error of the estimate of their mean net worth. • Necessary Sample Size He will need a sample size of 51.

43. Stratified Simple Random Sampling • The population is first divided into H groups, called strata. • Then for stratum h, a simple random sample of size nh is selected. • The data from the H simple random samples are combined to develop an estimate of a population parameter. • If the variability within each stratum is smaller than the variability across the strata, a stratified simple random sample can lead to greater precision. • The basis for forming the various strata depends on the judgment of the designer of the sample.

44. Example: Mill Creek Co. • Stratified Simple Random Sampling Mill Creek Co. has used stratified simple random sampling to obtain demographic information and preferences regarding health care coverage for its employees and their families. The population of employees has been divided into 3 strata on the basis of age: under 30, 30-49, and 50 or over. Some of the sample data is shown on the next slide.

45. Example: Mill Creek Co. • Data Annual Family Dental Expense Proportion Stratum Nhnh Mean St.Dev. Married Under 30 100 30 $250 $75 .60 30-49 250 45 400 100 .70 50 or Over 125 30 425 130 .68 475 105

46. Stratified Simple Random Sampling • Population Mean • Point Estimator where: H= number of strata = sample mean for stratum h Nh = number of elements in the population in stratum h N = total number of elements in the population (all strata)

47. Stratified Simple Random Sampling • Population Mean • Estimate of the Standard Error of the Mean

48. Stratified Simple Random Sampling • Population Mean • Interval Estimate • Approximate 95% Confidence Interval Estimate

49. Example: Mill Creek Co. • Point Estimate of Mean Annual Dental Expense = $375 • Estimate of Standard Error of Mean = 9.27

50. Example: Mill Creek Co. • Approximate 95% Confidence Interval for Mean Annual Dental Expense An approximate 95% confidence interval for mean annual family dental expense is $356.46 to $393.54.