Sampling Design

1. Sampling Design

2. Sampling Terminology • Sample • A subset, or some part, of a larger population • Population or universe • Any complete group of entities that share some common set of characteristics • Population element • An individual member of a population • Census • An investigation of ALL the individual elements that make up a population

3. Why Sample? • Sampling • Cuts costs • Reduces labor requirements • Gathers vital information quickly • Most properly selected samples give sufficiently accurate results

4. Table 12.1 Sample Versus Census

5. Target Population • Relevant population • Operationally define • All women still capable of bearing children vs. • All women between the ages of 12 and 50 • Comic book reader? • Does this include children under 6 years of age who do not actually read the words?

6. Sampling Frame • A list of elements from which the sample may be drawn • A.K.A., the working population • Mailing lists - data base marketers • Sampling services or list brokers • Sampling frame error • Error that occurs when certain sample elements are excluded from or overrepresented in a sampling frame

7. Two Major Categories of Sampling • Probability sampling • Known, nonzero, & equal probability of selection for every population element • Nonprobability sampling • Probability of selecting any particular member is unknown

8. Nonprobability Sampling • Convenience • Judgment • Quota • Snowball

9. Convenience Sampling • Also called haphazard or accidental sampling • The sampling procedure of obtaining the people or units that are most conveniently available

10. Judgment Sampling • Also called purposive sampling • An experienced individual selects the sample based on his or her judgment about some appropriate characteristics required of the sample member

11. Quota Sampling • Ensures that the various subgroups in a population are represented on pertinent sample characteristics to the exact extent that the investigators desire • It should not be confused with stratified sampling.

12. Snowball Sampling • A variety of procedures • Initial respondents are selected by probability methods • Additional respondents are obtained from information (or referrals) provided by the initial respondents

13. Comparing the Nonprobability Techniques

14. Figure 12.8 Probability Sampling Techniques Most Commonly-Used Probability Sampling Techniques Probability Sampling Techniques Simple Random Sampling Systematic Sampling Stratified Sampling

15. Simple Random Sampling • A sampling procedure that ensures that each element in the population will have an equal chance of being included in the sample

16. Systematic Sampling • A simple process • Every nth name from the list will be drawn • Periodicity • Problem that occurs in systematic sampling when the original list has a systematic pattern (I.e., the original list is not random in character)

17. Stratified Sampling • Probability sample • Subsamples are drawn within different strata using simple random sampling • Each stratum is more or less equal on some characteristic • Do not confuse with quota sample

18. Comparing the Probability Techniques

19. What is the Appropriate Sample Design? • Degree of accuracy • Resources • Time • Advanced knowledge of the population • National versus local • Need for statistical analysis

20. Choosing Between Nonprobability & Probability Sampling

21. Internet Samples • Recruited Ad Hoc Samples • Opt-in Lists

22. Information Needed to Determine Sample Size • Variance (standard deviation) • Get from pilot study or rule of thumb (managerial judgment) • Magnitude of error • Managerial judgment or calculation • Confidence level • Managerial judgment

23. Sample Size Formula for Questions Involving Means

24. Sample Size Formula - Example Suppose a survey researcher is studying expenditures on lipstick Wishes to have a 95 percent confident level (Z) and Range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00.

25. Sample Size Formula - Example

26. Sample Size Formula - Example Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00 (rather than the original $2.00), sample size is reduced.

27. Sample Size Formula - Example

28. 2 2 é ù é ù ( 2 . 57 )( 29 ) ( 2 . 57 )( 29 ) = = n n ê ú ê ú 4 2 ë û ë û 2 2 é ù é ù 74 . 53 74 . 53 = = ê ú ê ú 4 2 ë û ë û ] [ [ ] 2 2 = = 6325 18 . 37 . 265 = = 347 1389 Calculating Sample Size 99% Confidence

29. Sample Size for a Proportion

30. 2 z pq = n 2 E Where: n = Number of items in samples Z2 = The square of the confidence interval in standard error units. p = Estimated proportion of success q = (1-p) or estimated the proportion of failures E2 = The square of the maximum allowance for error between the true proportion and sample proportion or zsp squared.

31. Sample Size for a Proportion:Example • A researcher believes that a simple random sample will show that 60 percent of a population (p = .6) recognizes the name of an automobile dealership. • Note that 40% of the population would not recognize the dealership’s name (q = .4) • The researcher wants to estimate with 95% confidence (Z = 1.96) that the allowance for sampling error is not greater than 3.5 percentage points (E = 0.035)

32. = p . 6 2 ( 96 )(. 1. ) (. 6 4 ) = n = ( . 035 ) 2 q . 4 ( 3 . 8416 )(. 24 ) = 001225 . 922 = . 001225 = 753 Calculating Sample Size at the 95% Confidence Level