The sampling design process
- 1. The Sampling Design Process Define the Population Determine the Sampling Frame Select Sampling Technique(s) Determine the Sample Size Execute the Sampling Process
- 2. Define the Target Population The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements, sampling units, extent, and time. – An element is the object about which or from which the information is desired, e.g., the respondent. – A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process. – Extent refers to the geographical boundaries. – Time is the time period under consideration.
- 3. Define the Target Population Important qualitative factors in determining the sample size are: – the importance of the decision – the nature of the research – the number of variables – the nature of the analysis – sample sizes used in similar studies – incidence rates – completion rates – resource constraints
- 4. Classification of Sampling Techniques Sampling Techniques Nonprobability Sampling Techniques Probability Sampling Techniques Convenience Sampling Judgmental Sampling Quota Sampling Snowball Sampling Systematic Sampling Stratified Sampling Cluster Sampling Other Sampling Techniques Simple Random Sampling
- 5. Convenience Sampling Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. – use of students, and members of social organizations – mall intercept interviews without qualifying the respondents – department stores using charge account lists – “people on the street” interviews
- 6. A Graphical Illustration of Convenience Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Group D happens to assemble at a convenient time and place. So all the elements in this Group are selected. The resulting sample consists of elements 16, 17, 18, 19 and 20. Note, no elements are selected from group A, B, C and E.
- 7. Judgmental Sampling Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher. – test markets – purchase engineers selected in industrial marketing research – precincts selected in voting behavior research – expert witnesses used in court
- 8. Graphical Illustration of Judgmental Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 The researcher considers groups B, C and E to be typical and convenient. Within each of these groups one or two elements are selected based on typicality and convenience. The resulting sample consists of elements 8, 10, 11, 13, and 24. Note, no elements are selected from groups A and D.
- 9. Quota Sampling Quota sampling may be viewed as two-stage restricted judgmental sampling. – The first stage consists of developing control categories, or quotas, of population elements. – In the second stage, sample elements are selected based on convenience or judgment. Population Sample composition composition Control Characteristic Percentage Percentage Number Sex Male 48 48 480 Female 52 52 520 ____ ____ ____ 100 100 1000
- 10. A Graphical Illustration of Quota Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 A quota of one element from each group, A to E, is imposed. Within each group, one element is selected based on judgment or convenience. The resulting sample consists of elements 3, 6, 13, 20 and 22. Note, one element is selected from each column or group.
- 11. Snowball Sampling In snowball sampling, an initial group of respondents is selected, usually at random. – After being interviewed, these respondents are asked to identify others who belong to the target population of interest. – Subsequent respondents are selected based on the referrals.
- 12. A Graphical Illustration of Snowball Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Elements 2 and 9 are selected randomly from groups A and B. Element 2 refers elements 12 and 13. Element 9 refers element 18. The resulting sample consists of elements 2, 9, 12, 13, and 18. Note, there are no element from group E. Random Selection Referrals
- 13. Simple Random Sampling • Each element in the population has a known and equal probability of selection. • Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected. • This implies that every element is selected independently of every other element. This method is equivalent to a lottery system.
- 14. A Graphical Illustration of Simple Random Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Select five random numbers from 1 to 25. The resulting sample consists of population elements 3, 7, 9, 16, and 24. Note, there is no element from Group C.
- 15. Systematic Sampling • The sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame. • The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer. • When the ordering of the elements is related to the characteristic of interest, systematic sampling increases the representativeness of the sample.
- 16. Systematic Sampling • If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the representativeness of the sample. For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on.
- 17. A Graphical Illustration of Systematic Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Select a random number between 1 to 5, say 2. The resulting sample consists of population 2, (2+5=) 7, (2+5x2=) 12, (2+5x3=)17, and (2+5x4=) 22. Note, all the elements are selected from a single row.
- 18. Stratified Sampling • A two-step process in which the population is partitioned into subpopulations, or strata. • The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted. • Next, elements are selected from each stratum by a random procedure, usually SRS. • A major objective of stratified sampling is to increase precision without increasing cost.
- 19. Stratified Sampling • The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible. • The stratification variables should also be closely related to the characteristic of interest. • Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply.
- 20. A Graphical Illustration of Stratified Sampling A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Randomly select a number from 1 to 5 for each stratum, A to E. The resulting sample consists of population elements 4, 7, 13, 19 and 21. Note, one element is selected from each column.
- 21. Cluster Sampling • The target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters. • Then a random sample of clusters is selected, based on a probability sampling technique such as SRS. • For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage).
- 22. Cluster Sampling • Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population. • In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster.
- 23. A Graphical Illustration of Cluster Sampling (2-Stage) A B C D E 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 Randomly select 3 clusters, B, D and E. Within each cluster, randomly select one or two elements. The resulting sample consists of population elements 7, 18, 20, 21, and 23. Note, no elements are selected from clusters A and C.
- 24. Technique Strengths Weaknesses Nonprobability Sampling Convenience sampling Least expensive, least time-consuming, most convenient Selection bias, sample not representative, not recommended for descriptive or causal research Judgmental sampling Low cost, convenient, not time-consuming Does not allow generalization, subjective Quota sampling Sample can be controlled for certain characteristics Selection bias, no assurance of representativeness Snowball sampling Can estimate rare characteristics Time-consuming Probability sampling Simple random sampling (SRS) Easily understood, results projectable Difficult to construct sampling frame, expensive, lower precision, no assurance of representativeness. Systematic sampling Can increase representativeness, easier to implement than SRS, sampling frame not necessary Can decrease representativeness Stratified sampling Include all important subpopulations, precision Difficult to select relevant stratification variables, not feasible to stratify on many variables, expensive Cluster sampling Easy to implement, cost effective Imprecise, difficult to compute and interpret results Strengths and Weaknesses of Basic Sampling Techniques
- 25. Sampling: Final and Initial Sample Size Determination
- 26. Definitions and Symbols • Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population. A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken. • Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter. • Finite Population Correction: The finite population correction (fpc) is a correction for estimation of the variance of a population parameter, e.g., a mean or proportion, when the sample size is 10% or more of the population size.
- 27. Definitions and Symbols • Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter. • Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence. • Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.
- 28. Following are the points to be taken care of in deciding the sample size - Variability in population: larger the variability larger the sample size. - Confidence attached to the estimate: assuming the normal distribution the higher the confidence the researcher wants for the estimate larger will be the sample size. - Allowable margin of error: If the researcher seeks greater precision then larger will be the sample size.
- 29. Symbols for Population and Sample Variables Variable Populat ion Sam ple Mean µ X Proport ion ∏ p Variance σ2 s2 St andard deviat ion σ s Size N n St andard error of t he m ean σx Sx St andard error of t he proport ion σp Sp St andardized variat e ( z) (X-µ) / σ ( X-X) / S Coefficient of variat ion (C) σ/ µ S/ X __ _ _ _
- 30. Sample size estimation from population Mean The formula for estimating population proportion – n= Z2 σ2 e2 n=sample size Z= confidence level σ= population standard deviation e=margin of error
- 31. Ques1. An economist is interested in estimating the average monthly household expenditure on food items. Based on the past data, it is estimated that the std. deviation of the population on the monthly expenditure on food items is Rs. 30. with the allowable error set at Rs. 7, estimate the sample size required at a 90% confidence (Z= 1.645).
- 32. When population portion is not known n= 1 Z2 4 e2 A market researcher for a consumer electronics company would like to study the television viewing habits of the residents of a particular, small city. What sample size is needed if he wishes to be 95% confident of being within +0.035 of the true proportion who watch the evening news on at least three weeknights if no previous estimate is available. (95% confidence level Z= 1.96)
- 33. When population portion is known n= Z2 pq e2 p= the value of population portion known q= 1-p A consumer electronics co wants to determine the job satisfaction levels of its employees. For this, they ask a simple question, ‘Are you satisfied with your job?’ It was estimated that no more than 30% of the employees would answer yes. What should be the sample size for this co to estimate the population proportion to ensure a 95% confidence in result, and to be within 0.04 of the true population proportion? (95% confidence level, Z= 1.96) Here, e= 0.04, p= 0.3, q= 1-p= 1- 0.3 = 0.7
- 35. Sample Size Determination for Means and Proportions `Steps Means Proportions 1. Specify the level of precision D = ±$5.00 D = p - ∏ = ±0.05 2. Specify the confidence level (CL) CL = 95% CL = 95% 3. Determine the z value associated with CL z value is 1.96 z value is 1.96 4. Determine the standard deviation of the population Estimate σ: σ = 55 Estimate ∏: ∏ = 0.64 5. Determine the sample size using the formula for the standard error n = σ2 z2 /D2 = 465 n = ∏(1-∏) z2 /D2 = 355 6. If the sample size represents 10% of the population, apply the finite population correction nc = nN/(N+n-1) nc = nN/(N+n-1) 7. If necessary, reestimate the confidence interval by employing s to estimate σ = Χ ± zsx = p ± zsp 8. If precision is specified in relative rather than absolute terms, determine the sample size by substituting for D. D = Rµ n = C2 z2 /R2 D = R∏ n = z2 (1-∏)/(R2 ∏) _ -
- 36. Sample Size for Estimating Multiple Parameters Variable Mean Household Monthly Expense On Department store shopping Clothes Gifts Confidence level 95% 95% 95% z value 1.96 1.96 1.96 Precision level (D) $5 $5 $4 Standard deviation of the population (σ) $55 $40 $30 Required sample size (n) 465 246 217
- 37. Adjusting the Statistically Determined Sample Size Incidence rate refers to the rate of occurrence or the percentage, of persons eligible to participate in the study. In general, if there are c qualifying factors with an incidence of Q1, Q2, Q3, ...QC,each expressed as a proportion: Incidence rate = Q1 x Q2 x Q3....x QC Initial sample size = Final sample size . Incidence rate x Completion rate
- 38. Improving Response Rates Prior Notification Motivating Respondents Incentives Questionnaire Design and Administration Follow-Up Other Facilitators Callbacks Methods of Improving Response Rates Reducing Refusals Reducing Not-at-Homes
- 39. Arbitron Responds to Low Response Rates Arbitron, a major marketing research supplier, was trying to improve response rates in order to get more meaningful results from its surveys. Arbitron created a special cross-functional team of employees to work on the response rate problem. Their method was named the “breakthrough method,” and the whole Arbitron system concerning the response rates was put in question and changed. The team suggested six major strategies for improving response rates: 1. Maximize the effectiveness of placement/follow-up calls. 2. Make materials more appealing and easy to complete. 3. Increase Arbitron name awareness. 4. Improve survey participant rewards. 5. Optimize the arrival of respondent materials. 6. Increase usability of returned diaries. Eighty initiatives were launched to implement these six strategies. As a result, response rates improved significantly. However, in spite of those encouraging results, people at Arbitron remain very cautious. They know that they are not done yet and that it is an everyday fight to keep those response rates high.
- 40. Adjusting for Nonresponse • Subsampling of Nonrespondents – the researcher contacts a subsample of the nonrespondents, usually by means of telephone or personal interviews. • In replacement, the nonrespondents in the current survey are replaced with nonrespondents from an earlier, similar survey. The researcher attempts to contact these nonrespondents from the earlier survey and administer the current survey questionnaire to them, possibly by offering a suitable incentive.
- 41. Adjusting for Nonresponse • In substitution, the researcher substitutes for nonrespondents other elements from the sampling frame that are expected to respond. The sampling frame is divided into subgroups that are internally homogeneous in terms of respondent characteristics but heterogeneous in terms of response rates. These subgroups are then used to identify substitutes who are similar to particular nonrespondents but dissimilar to respondents already in the sample.
- 42. Adjusting for Nonresponse • Subjective Estimates – When it is no longer feasible to increase the response rate by subsampling, replacement, or substitution, it may be possible to arrive at subjective estimates of the nature and effect of nonresponse bias. This involves evaluating the likely effects of nonresponse based on experience and available information. • Trend analysis is an attempt to discern a trend between early and late respondents. This trend is projected to nonrespondents to estimate where they stand on the characteristic of interest.
- 43. Use of Trend Analysis in Adjusting for Nonresponse Percentage Response Average Dollar Expenditure Percentage of Previous Wave’s Response First Mailing 12 412 __ Second Mailing 18 325 79 Third Mailing 13 277 85 Nonresponse (230) 91 Total 100 275 (57)
- 44. Adjusting for Nonresponse • Weighting attempts to account for nonresponse by assigning differential weights to the data depending on the response rates. For example, in a survey the response rates were 85, 70, and 40%, respectively, for the high-, medium-, and low income groups. In analyzing the data, these subgroups are assigned weights inversely proportional to their response rates. That is, the weights assigned would be (100/85), (100/70), and (100/40), respectively, for the high-, medium-, and low-income groups.
- 45. Adjusting for Nonresponse • Imputation involves imputing, or assigning, the characteristic of interest to the nonrespondents based on the similarity of the variables available for both nonrespondents and respondents. For example, a respondent who does not report brand usage may be imputed the usage of a respondent with similar demographic characteristics.
- 46. Finding Probabilities Corresponding to Known Values µ-3σ µ-2σ µ-1σ µ µ+1σ µ+2σ µ+3σ 35 -3 40 -2 45 -1 50 0 55 +1 60 +2 65 +3 Area is 0.3413 Z Scale Z Scale(µ=50,σ =5) σArea between µ and µ + 1 = 0.3431 Area between µ and µ + 2σ = 0.4772 Area between µ and µ + 3σ = 0.4986
- 47. Finding Probabilities Corresponding to Known Values Area is 0.500Area is 0.450 Area is 0.050 X 50 X Scale -Z 0 Z Scale
- 48. Finding Values Corresponding to Known Probabilities: Confidence Interval Area is 0.475Area is 0.475 X 50 X Scale -Z 0 Z Scale Area is 0.025Area is 0.025 -Z