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John Loucks St . Edward’s University

SLIDES . BY. . . . . . . . . . . . John Loucks St . Edward’s University. Chapter 22, Part A Sample Survey. Terminology Used in Sample Surveys . Types of Surveys and Sampling Methods. Survey Errors. Simple Random Sampling. Terminology Used in Sample Surveys.

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John Loucks St . Edward’s University

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  1. SLIDES.BY . . . . . . . . . . . John Loucks St. Edward’s University

  2. Chapter 22, Part A Sample Survey • Terminology Used in Sample Surveys • Types of Surveys and Sampling Methods • Survey Errors • Simple Random 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 costs 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: Nonprobabilistic sampling Probabilistic sampling

  9. Nonprobabilistic Sampling Methods The probability of obtaining each possible sample cannot 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 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 t = 2 for a 95% confidence interval.

  24. Simple Random Sampling • 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)

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

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

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

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

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

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

  31. Determining the Sample Size An important consideration is choice of sample size. The best choice usually involves a tradeoff 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.

  32. 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.

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

  34. Simple Random Sampling • Necessary Sample Size for Estimating the Population Total

  35. Simple Random Sampling • Necessary Sample Size for Estimating the Population Proportion

  36. Simple Random Sampling • Example: Steddy Investments Ben Steddy 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’ net worth and the proportion favoring fixed income investments.

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

  38. Simple Random Sampling • Point Estimate of Total Net Worth (TNW) • Approximate 95% Confidence Interval for TNW • Estimate of Standard Error of TNW = $3,394,113 = $89,211,774 to $102,788,226

  39. Simple Random Sampling • Point Estimate of Population Proportion Favoring Fixed-Income Investments • Estimate of Standard Error of Proportion • Approximate 95% Confidence Interval

  40. Simple Random Sampling One year later Steddy 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. What is the necessary sample size? • Example: Steddy Investments

  41. Example: Steddy Investments • Necessary Sample Size Steddy will need a sample size of 51.

  42. End of Chapter 22, Part A

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