Sampling Design

1. Sampling Design

2. Sampling • The process of obtaining information from a subset (sample) of a larger group (population) • The results for the sample are then used to make estimates of the larger group • Faster and cheaper than asking the entire population • Two keys • Selecting the right people • Have to be selected scientifically so that they are representative of the population • Selecting the right number of the right people • To minimize sampling errors I.e. choosing the wrong people by chance

3. SAMPLING • Sample -- contacting a portion of the population (e.g., 10% or 25%) • best with a very large population (n) • easiest with a homogeneous population • Census -- the entire population • most useful if the population ("n") is small • or the cost of making an error is high

4. Population Vs. Sample Population of Interest Population Sample Parameter Statistic Sample We measure the sample using statistics in order to draw inferences about the parameters of the population.

5. Characteristics of Good Samples • Representative • Accessible • Low cost

6. …this (bad)… Population Sample

7. …or this (VERY bad)… Sample Population

8. Terminology • Population • The entire group of people of interest from whom the researcher needs to obtain information. • Element (sampling unit) • one unit from a population • Sampling • The selection of a subset of the population • Sampling Frame • Listing of population from which a sample is chosen Census • A polling of the entire population Survey • A polling of the sample

9. Terminology • Parameter • The variable of interest • Statistic • The information obtained from the sample about the parameter • Goal • To be able to make inferences about the population parameter from knowledge of the relevant statistic - to draw general conclusions about the entire body of units • Critical Assumption • The sample chosen is representative of the population

10. Steps in Sampling Process 1. Define the population 2. Identify the sampling frame 3. Select a sampling design or procedure 4. Determine the sample size 5. Draw the sample

11. Sampling Design Process Define Population Determine Sampling Frame Determine Sampling Method • Non-Probability Sampling • Convenience • Judgmental • Quota • Probability Sampling • Simple Random Sampling • Stratified Sampling • Cluster Sampling Determine Appropriate Sample Size Execute Sampling Design

12. 1. Define the Target Population Question: “Who, ideally, do you want to survey?” • Answer: those who have the information sought. • What are their characteristics. • Who should be excluded? • age, gender, product use, those in industry • Geographic area • It involves • defining population units • setting population boundaries • Screening (e.g. security questions, product use )

13. 1. Define the Target Population The Element ...... individuals families seminar groups sampling Unit…. individuals over 20 families with 2 kids seminar groups at “new” university Extent ............ individuals who have bought “one” families who eat fast food seminar groups doing MR Timing .......... bought over the last seven days

14. 1. Define the Target Population The target population for a toy store can be defined as all households with children living in Calgary. What’s wrong with this definition?

15. 2. Determine the Sampling Frame • Obtaining a “list” of population (how will you reach sample) • Students who eat at McDonalds? • young people at random in the street? • phone book • students union listing • University mailing list • Problems with lists • omissions • ineligibles • duplications • Procedures • E.g. individuals who have spent two or more hours on the internet in the last week

16. 2. Determine the Sampling Frame • Select “sample units” • Individuals • Household • Streets • Companies

17. 3. Selecting a Sampling Design • Probability sampling - equal chance of being included in the sample (random) • simple random sampling • systematic sampling • stratified sampling • cluster sampling • Non-probability sampling - - unequal chance of being included in the sample (non-random) • convenience sampling • judgement sampling • snowball sampling • quota sampling

18. 3. Selecting a Sampling Design Probability Sampling • An objective procedure in which the probability of selection is nonzero and is known in advance for each population unit. • also called random sampling. • Ensures information is obtained from a representative sample of the population • Sampling error can be computed • Survey results can be projected to the population • More expensive than non-probability samples

19. 3. Selecting a Sampling Design Simple Random Sampling (SRS) • Population members are selected directly from the sampling frame • Equal probability of selection for every member (sample size/population size) • 400/10,000 = .04 • Use random number table or random number generator

20. 3. Selecting a Sampling Design Simple Random Sampling • N = the number of cases in the sampling frame • n = the number of cases in the sample • f = n/N = the sampling fraction • NCn = the number of combinations (subsets) of n from N If you have a sampling frame of the 10,000 full-time students at the U of L and you want to survey .01 percent of them, how would you do it?

21. 3. Selecting a Sampling Design Objective: To select n units out of N such that each NCn has an equal chance of being selected Procedure: Use a table of random numbers, a computer random number generator, or a mechanical device to select the sample

22. 3. Selecting a Sampling Design Systematic Sampling • Order all units in the sampling frame based on some variable and number them from 1 to N • Choose a random starting place from 1 to N and then sample every k units after that

23. systematic random sample number the units in the population from 1 to N decide on the n (sample size) that you want or need k = N/n = the interval size randomly select an integer between 1 to k then take every kth unit

24. 3. Selecting a Sampling Design Stratified Sampling (I) • The chosen sample contains a number of distinct categories which are organized into segments, or strata • equalizing "important" variables • year in school, geographic area, product use, etc. • Steps: • Population is divided into mutually exclusive and exhaustive strata based on an appropriate population characteristic. (e.g. race, age, gender etc.) • Simple random samples are then drawn from each stratum.

25. Stratified Random Sampling

26. Stratified Random Sampling • The sample size is usually proportional to the relative size of the strata. • Ensures that particular groups (e.g. males and females) within a population are adequately represented in the sample • Has a smaller sampling error than simple random sample since a source of variation is eliminated

27. 3. Selecting a Sampling Design Stratified Sampling (II) • DirectProportional Stratified Sampling • The sample size in each stratum is proportional to the stratum size in the population • Disproportional Stratified Sampling • The sample size in each stratum is NOT proportional to the stratum size in the population • Used if 1) some strata are too small 2) some strata are more important than others 3) some strata are more diversified than others

28. 3. Selecting a Sampling Design Cluster Sampling • The Population is divided into mutually exclusive and exhaustive subgroups, or clusters, usually based on geography or time period • Each cluster should be representative of the population i.e. be heterogeneous. • Means between clusters should be the same (homogeneous) • Then a sample of the clusters is selected. • then some randomly chosen units in the selected clusters are studied.

29. cluster or area random sampling • divide population into clusters (usually along geographic boundaries) • randomly sample clusters • measure units within sampled clusters

30. 3. Selecting a Sampling Design When to use stratified sampling • If primary research objective is to compare groups • Using stratified sampling may reduce sampling errors When to use cluster sampling • If there are substantial fixed costs associated with each data collection location • When there is a list of clusters but not of individual population members

31. 3. Selecting a Sampling Design Non-Probability Sampling • Subjective procedure in which the probability of selection for some population units are zero or unknown before drawing the sample. • information is obtained from a non-representative sample of the population • Sampling error can not be computed • Survey results cannot be projected to the population

32. 3. Selecting a Sampling Design Non-Probability Sampling Advantages • Cheaper and faster than probability • Reasonably representative if collected in a thorough manner

33. Types of Non-Probability Sampling (I) • Convenience Sampling • A researcher's convenience forms the basis for selecting a sample. • people in my classes • Mall intercepts • People with some specific characteristic (e.g. bald) • Judgement Sampling • A researcher exerts some effort in selecting a sample that seems to be most appropriate for the study.

34. Types of Non-Probability Sampling • Snowball Sampling • Selection of additional respondents is based on referrals from the initial respondents. • friends of friends • Used to sample from low incidence or rare populations. • Quota Sampling • The population is divided into cells on the basis of relevant control characteristics. • A quota of sample units is established for each cell. • 50 women, 50 men • A convenience sample is drawn for each cell until the quota is met. (similar to stratified sampling)

35. Quota Sampling Let us assume you wanted to interview tourists coming to a community to study their activities and spending. Based on national research you know that 60% come for vacation/pleasure, 20% are VFR (visiting friends and relatives), 15% come for business and 5% for conventions and meetings. You also know that 80% come from within the province. 10% from other parts of Canada, and 10% are international. A total of 500 tourists are to be intercepted at major tourist spots (attractions, events, hotels, convention centre, etc.), as you would in a convenience sample. The number of interviews could therefore be determined based on the proportion a given characteristic represents in the population. For instance, once 300 pleasure travellers have been interviewed, this category would no longer be pursued, and only those who state that one of the other purposes was their reason for coming would be interviewed until these quotas were filled.

37. Probability Vs. Non-Probability Sampling Disadvantages • The probability of selecting one element over another is not known and therefore the estimates cannot be projected to the population with any specified level of confidence. • Quantitative generalizations about population can only be done under probability sampling. • In practice, however, marketing researchers also apply statistics to study non-probability samples.

38. Generalization • You can only generalize to the population from which you sampled • U of L students not university students • geographic, different majors, different jobs, etc. • University students not Canadian population • younger, poorer, etc. • Canadians not people everywhere • less traditional, more affluent, etc.

39. Drawing inferences from samples • Population estimates • % who smoke, buy your product, etc • 25% of sample • what % of population? • very dangerous with a non-representative sample or with low response rates

40. Errors in Survey • Random Sampling Error • random error- the sample selected is not representative of the population due to chance • the level of it is controlled by sample size • a larger sample size leads to a smaller sampling error. Population mean (μ) gross income = $42,300 Sample 1 (400/250,000) mean (Χ) = $41,100 Sample 2 (400/250,000) mean (Χ) = $43,400 Sample 3 (400/250,000) mean (Χ) = $36,400

41. Non-Sampling Errors (I) • Non-sampling Error • systematic error • the level of it is NOT controlled by sample size. • The basic types of non-sampling error • Non-response error • Response or data error • A non-responseerror occurs when units selected as part of the sampling procedure do not respond in whole or in part • If non-respondents are not different from those that did respond, there is no non-response error

42. Non-Sampling Errors (II) • A response or data error is any systematic bias that occurs during data collection, analysis or interpretation • Respondent error (e.g., lying, forgetting, etc.) • Interviewer bias • Recording errors • Poorly designed questionnaires

43. Data Preparation

44. Steps in Data Preparation Editing Coding EnteringData Data Tabulation Reviewing Tabulations Statistically adjusting the data (e.g. weighting)

45. Editing • Carefully checking survey data for • Completeness (no omissions) • Non-ambiguous (e.g. two boxes checked instead of one) • Right informant (e.g. under age, when all supposed to be over 18) • Consistency • e.g. charging something on a credit card when the person does not own a credit card • Accuracy (e.g. no numbers out of range) • Most important purpose is to eliminate or at least reduce the number of errors in the raw data.

46. Solutions • Ideally re-interview respondent • Eliminate all unacceptable surveys (case wise deletion) (if sample is large and few unacceptable) • In calculations only the cases with complete responses are considered (pair wise deletion) (means that some statistics will be based on different sample sizes) • Code illegible or missing answers into a a “no valid response” category • substitute a neutral value - typically the mean response to the variable, therefore the mean remains unchanged

47. Coding • The process of systematically and consistently assigning each response a numerical score. • The key to a good coding system is for the coding categories to be mutually exclusive and the entire system to be collectively exhaustive. • To be mutually exclusive, every response must fit into only one category. • To be collectively exhaustive, all possible responses must fit into one of the categories. • Exhaustive means that you have covered the entire range of the variable with your measurement.

48. Coding • Coding Missing Numbers: When respondents fail to complete portions of the survey. • Whatever the reason for incomplete surveys, you must indicate that there was no response provided by the respondent. • For single digit responses code as “9”, 2 digit code as “99”

49. Coding Open-Ended Questions: When open-ended questions are used, you must create categories. • All responses must fit into a category • similar responses should fall into the same category. • e.g. Who services your car? ______________ • Possible categories: self, garage, husband, wife, friend, relative etc. • To make it collectively exhaustive add an “other” or “none of the above” category • Only a few i.e. < 10% should fit into this category

50. Precoded Questionnaires:Sometimes you can place codes on the actual questionnaire, which simplifies data entry. This… Becomes this… Are you: Male Female How satisfied are you with our product? ___Very Satisfied ___Somewhat Satisfied ___Somewhat Dissatisfied ___Very Dissatisfied ___No opinion Are you: (1) Male (2) Female How satisfied are you with our product? _1__Very Satisfied _2__Somewhat Satisfied _3__Somewhat Dissatisfied _4__Very Dissatisfied _5__No opinion