Chapter 11 Sampling Design

2. Chapter 11 Sampling Design

3. Chapter Objectives • define sampling, sample, population, element, subject and sampling frame • describe and discuss the different probability and non-probability sampling designs • identify the use of appropriate sampling designs for different research purposes • discuss precision and confidence • estimate sample size • discuss efficiency in sampling • discuss generalisability in the context of sampling designs

4. The Principles of Sampling Design

5. Population, Element, Sampling Frame, Sample and Subject • Population (or target population) • entire group of people, events or things of interest that the researcher wishes to investigate • Element • a single member of the population • Sampling Frame • a listing of all the elements in the population from which the sample is drawn • Sample • a subset of the population • Subject • a single member of the sample

6. Relationship between Population, Sampling Frame and Sample

7. Relationship between Sample Statistics and Population Parameters

8. Advantages of Sampling • Less costs • cheaper than studying whole population • Less errors due to less fatigue • better results • Less time • quicker • Destruction of elements avoided • eg bulbs

9. Normal Distibution in a Population As the sample size n increases, the means of the random samples taken from practically any population approach a normal distribution with mean μand standard deviation

10. Representativeness of Samples • If the sample mean is much > than the population mean μthen the sample would overestimate the true population mean • If the sample mean is much < than the population mean μthen the sample would underestimate the true population mean • The more representative the sample is of the population, the more generalisable are the findings of the research.

11. Preparing a Sampling Design

12. Probability & Non-probability Sampling • Probability Sampling • the elements in the population have some known chance or probability of being selected as sample subjects • Non-probability Sampling • the elements do not have a known or predetermined chance of being selected as subjects

13. Probability Sampling • Simple random sampling • every element in the population has a known and equal chance of being selected as a subject • Complex (or restricted) probability sampling • procedures to ensure practical viable alternatives to simple random sampling, at lower costs, and greater statistical efficiency

14. Simple Random Sampling • Is the most representative of the population for most purposes • Disadvantages are: • Most cumbersome and tedious • The entire listing of elements in population frequently unavailable • Very expensive • Not the most efficient design

15. Complex Probability Sampling • Systematic sampling • Stratified random sampling • Cluster sampling • Area sampling • Double sampling

16. Systematic Sampling • Every nth element in the population starting with a randomly chosen element • Example: • Want a sample of 35 households from a total of 260 houses. Could sample every 7th house starting from a randomly chosen number from 1 to 10. If that random number is 7, sample 35 houses starting with 7th house (14th house, 21st house, etc) • Possible problem is that there could be systematic bias. eg every 7th house could be a corner house, with different characteristics of both house and dwellers.

17. Stratified Random Sampling • Comprises sampling from populations segregated into a number of mutually exclusive sub-populations or strata. Eg • University students divided into juniors, seniors, etc • Employees stratified into clerks, supervisors, managers, etc • Homogeneity within stratum and heterogeneity between strata • Statistical efficiency greater in stratified samples • Sub-groups can be analysed • Different methods of analysis can be used for different sub-groups.

18. Stratified Random Sampling Example StratumMotivation Level Clerks Low Middle Managers Very high Top Managers Medium Combined X would not discrimate among groups • Stratified Sampling • Proportionate sampling • Disproportionate sampling

19. Proportionate & Disproportionate Stratified Random Sampling

20. Cluster Sampling • Take clusters or chunks of elements for study • Eg, sample all students in MGMT 303 and MGMT 304 to study the characteristics of Management Science majors • Advantage of cluster sampling is lower costs • Statistically it is less efficient than other probability sampling procedures discussed so far Area Sampling: • Cluster sampling confined to a particular area • Eg, sampling residents of a particular locality, county, etc

21. Double Sampling • Collect preliminary data from a sample, and choose a sub-sample of that sample for more detailed investigation. • Example: • Conduct unstructured interviews with a sample of 50. • Repeat a structured interview with 30 from the 50 originally sampled.

22. Non-probability Sampling • Convenience sampling • Survey whoever is easily available • Used for quick diagnosis of situations • Simplest and cheapest • Least reliable • Purposive sampling • Judgement sampling • Snowball sampling • Quota sampling

23. Judgement Sampling • Involves the choice of subjects who are in the best position to provide the information required • Experts’ opinions could be sought • Eg, Doctors surveyed for cancer causes

24. Snowball Sampling • Used when elements in population have specific characteristics or knowledge, but are very difficult to locate and contact. • Initial sample group can be selected by probability or non-probability methods, but new subjects are selected based on information provided by initial subjects. • Eg, used to locate members of different stakeholder groups regarding their opinions of a new public works project.

25. Quota Sampling • Quotas for numbers or proportion of people to be sampled, established. • Examples: • survey for research on dual career families: 50% working men and 50% working women surveyed. • Women in management survey: 70% women surveyed and 30% men surveyed.

26. Choice Points in Sampling Design

27. Precision and Confidence • Precision • refers to how close the sample estimate eg X is to the true population characteristic()depends on the variablity in the sampling distribution of the mean, ie the standard error ( SX ) • indicates the confidence interval within which the population mean can be estimated (= X+ KS X ) • Confidence • reflectsthe level of certainty that the sample estimates will actually hold true for the population • bias is absent from the data • accuracy is reflected by the confidence level ( K )

28. = standard deviation of the sample = sample size = standard error or standard deviation of the sample mean Standard Error

29. Characteristics of the Standard Error • The smaller the standard deviation of the population, the smaller the standard error and the greater the precision • The standard error varies inversely with the square root of the sample size. Hence the larger the n, the smaller the standard error, and the greater the precision.

30. = population mean = sample mean = standard error = z statistic for large samples ≥ 30 = tstatistic for small samples < 30 Confidence Interval for the Mean

31. Confidence Levels • For large samples, K = z score = 1.65 for 90% confidence level = 1.96 for 95% confidence level = 2.58 for 99% confidence level • Example: a 95% confidence interval for mean purchases (μ) by customers based on a sample mean of $105 with a standard error of $1.43 is: μ = 105 ± 1.96*1.43 = 105 ± 2.80 Hence μ would fall between $102.20 and $107.80

32. Trade-off between Precision and Confidence

33. Example: Suppose a manager wants to be 95% confident that withdrawals from a bank will be within a confidence level of ± $500. From a sample of customers the standard deviation S was calculated as $3500. What sample size is needed? The expression is equivalent to the precision or admissible margin of error. Let this be E. or Determining the Sample Size

34. Substituting K=1.96 (95% confidence), S=3500, and E=500 into this equation, provides the sample size n: Determining the Sample Size (cont’d) Rearranging these terms, a formula for the sample size n is:

35. Roscoe’s Rules of Thumb for Determining Sample Size • Sample sizes larger than 30 and smaller than 500 are appropriate for most research • Minimum sample size of 30 for each sub-category is usually necessary • In multivariate research, the sample size should be several times as large as the number of variables in the study • For simple experimental research, successful research is possible with samples as small as 10 to 20

36. Efficiency in Sampling If n is constant, you should get a smaller or For the same , you should use a smaller n

37. Review of Sample Size Decisions • How much precision is wanted in estimating the population characteristics, ie what is the margin of admissible error or confidence interval? • How much confidence is really needed. How much risk can we take of making errors in estimating the population parameters (ie confidence level)? • How much variability is in the population? The greater the variability, the larger the sample size needed. • Cost and time constraints • The size of the population (N) itself