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1. Basic Marketing Research: Using Microsoft Excel Data Analysis, 3rd edition Alvin C. Burns Louisiana State University Ronald F. Bush University of West Florida Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
2. Why Use Samples? Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall Marketing researchers, when collecting primary data, typically rely on a sample because taking a census of everyone in a market is time consuming, very costly, and often leads to measurement errors.
3. Basic Concepts in Sampling The population is the entire group under study as specified by the research project. A sample is a subset of the population that should represent the population. A census is defined as an accounting of everyone in the population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
4. Basic Concepts in Sampling, Continued... Sampling error is any error in a survey that occurs because a sample is used. Usually caused by method of sample selection or sample size. A sample frame is some master list of all the members of the population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
5. Basic Concepts in Sampling, Continued... Sample frame error: the extent to which the sample frame does not perfectly match the population due to misrepresentation, overrepresentation, and/or underrepresentation. It is the researchers responsibility to seek out a sample frame with the least amount of error at a reasonable costs. The researcher should also apprise the client of the degree of sample frame error involved. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
6. Determining Size of a Sample A convenient way to describe the amount of sample error due to the size of the sample, or the accuracy of a sample, is to treat it as a plus-or-minus percentage value. The accuracy of a sample is usually expressed as a ±% such as ±5%or±10%. Using a sample saves time, energy, and money while generating results that generalize the entire population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
7. Sample Size and Accuracy With small increases in sample size, we can gain large increases in sample accuracy up to a point (about 500). Beyond that point, there are diminishing returns in accuracy. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
8. Formula to Determine Sample Accuracy Sample Error Formula: ± Sample Error % = Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
9. How to Calculate Sample Size Sample Size Formula When Estimating a Percentage n = z2(p * q) e2 Where: n= sample size; z= Standard error associated with chosen level of confidence (1.96 or 2.58); p=estimated % in population; q=(100%-p); e= acceptable error (accuracy) Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
10. Variability: p times q Effect of “High v Low” estimates of variability in the population-- If survey respondents have very little (low) variability, then most will select one category and few will select the other (90% vs 10%). Note that “low” variability (90*10) or (10*90) gives you a lower number in the formula’s numerator. Therefore, n will be lower! Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
11. Variability: p times q, Continued... If there is high variability, as when no two respondents agree Then there is a 50% 50 % split, p times q becomes 50 times 50, or 2,500, which is the largest possible p times q number possible Again, since p times q is in the numerator of our formula we will have a higher n if we estimate variance (p*q) to be high. How do we estimate variance (p*q)? Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
12. Estimating Variability There are three ways to estimate p times q: Unless we have other information we can assume the most conservative case and use the maximum amount of variance we would expect in the population (p= 50%, q= 50%) Use data from a previous study conducted on the same population Conduct a small pilot study to estimate variance Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
13. Level of Confidence: z It is customary among marketing researchers to use the 95% level of confidence. For 95%, z= 1.96 OR, for the 99% level of confidence: For 99%, z= 2.58 We use the phrase “level of confidence” because it refers to how confident we are that the sample finding will repeat itself if we conducted a different survey tomorrow or again the next day. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
14. Level of Confidence: z, Continued... By setting z= 1.96, it means that if we were to conduct our survey over a 100 times, 95 of these times we would get a sample finding that would fall within our predetermined level of accuracy, e. This gives us some confidence in the reliability of our sample estimate. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
15. Desired Accuracy: e The term e is the amount of sample error (desired accuracy) that will be associated with the survey results. Like z, e is determined by the judgment of the researcher and the client. Most client’s are satisfied with an accuracy level of ±5%. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
16. Desired Accuracy: e, Continued... e is used to indicate how close your sample finding, in this case a percentage, will be to the true population percentage if it were repeated many times. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
17. Explaining the Logic of Our Sample Size Formula: Example Calculation Sample Size Example when p=50%; q=50% and e=5% n = 1.962(50 x 50) 52 = 3.84 (2500) 25 = 9600 25 = 384 Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
18. Explaining the Logic of Our Sample Size Formula, Continued... What does the n=384 mean? It means that if you wish to conduct a survey to determine the percentage of respondents who “prefer X” and you estimate the variance to be 50% (prefer X) and 50% (prefer other than X), and you want your sample findings to fall within a range of ±5% if you were to do the study over and over, then you would need a sample size of 384! Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
19. Explaining the Logic of Our Sample Size Formula, Continued... As long as our variance estimate is accurate, we will correctly predetermine the amount of accuracy we will have in our survey results. Just think how powerful this statement is. By being able to predetermine how accurate your results will be, you can confidently conduct surveys to estimate values of interest and be assured as to the accuracy of the sample findings. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
20. How to Calculate Sample Size When Estimating a Mean Sample Size Formula When Estimating a Mean n = s2 z2 e2 Where: n= sample size; z= Standard error associated with chosen level of confidence (1.96 or 2.58); s=variability estimated by one standard deviation; e= acceptable error (accuracy) Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
21. How to Calculate Sample Size When Estimating a Mean, Continued... Allowable error (e) is expressed in terms of units being estimated instead of a percentage. For example, if we are estimating likelihood to purchase a car on a 7-point scale, we would express e in terms of scale units such as 0.25 or .05 scale units. If we were estimated the number of pounds of hamburger meat bought per week by consumers, e would be expressed in pounds. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
22. How do we Estimate Variability (s) in Populations? There are three ways to estimate variability (indicated by one standard deviation, s, in the population): 1. First, do you have a previous study on the same population from which we can calculate s? Second, do you have a pilot study to calculate s? …and, third… Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
23. How do we Estimate Variability (s) in Populations? Continued… … 3. When the first two choices are not available we estimate the range of values that may be derived from the question and divide this range by 6. Why 6? We are trying to estimate one standard deviation, and +/-3 standard deviations account for 99% of the area under the normal curve, so 6 standard deviations are synonymous with the range. By dividing the range by 6 we can estimate 1 s! Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
24. The Effects of Incidence Rate and Nonresponse on Sample Size Whenever you calculate the sample size, you are computing the number of respondents you should have complete your survey. Invariably, surveys run into difficulties that require an upward adjustment in terms of the size of your sample you should begin with, or order from a sampling firm. See MRA 9.2 written for you by the CEO of Survey Sampling International! Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
25. XL Data Analyst Can Calculate n When You are Estimating a Percentage! All you need do is tell the program what you estimate p to be, and… What you wish your allowable error, e, to be! See the next two slides for an illustration Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
26. Using XL Data Analyst to Calculate Sample Size Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
27. Using XL Data Analyst to Calculate Sample Size, Continued... Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
28. Sample Size and Ethics It is an ethical marketing researcher’s responsibility to try to educate a client on the wastefulness of excessively large samples. Unethical researchers may recommend very large samples as a way to increase their profits, which may be set at a percentage of the total cost of the survey. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
29. How to Select a Representative Sample The two sample size formulas you have learned are only applicable when we have a representative sample. How we draw a sample, the sample plan, determines whether the sample is representative. There are two major types of sampling plans: probability and nonprobability sampling plans Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
30. Probability Sampling Methods A random sample is one in which every member of the population has an equal chance, or probability, of being selected into the sample. Sample methods that embody random sampling are often termed probability sampling methods, because the chance of selection can be expressed as a probability. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
31. Probability Sampling Methods, Cont. The four probability sampling methods are: Simple random sampling Systematic sampling Cluster sampling Stratified sampling Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
32. Simple Random Sampling With simple random sampling the probability of being selected into the sample is “known” and equal for all members of the population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
33. Simple Random Sampling, Continued... Steps:First, assign a number to all members of the population listed in the sample frame; Second, use some random method to select numbers such that all members of the frame have a chance of being selected; Third, select numbers until you have reached your desired sample size, n. Members selected should be representative of all the members of the population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
34. Simple Random Sampling, Continued... Examples:a. Put all names into a “hat” and stir them and blindly draw names out. b. Lotteries often use Simple Random Sampling. Ping pong balls are numbered 1-51 (depending on the lottery). This constitutes numbering all members of the population and now represents the sample frame. Second, the balls are put in some sort of air-box that swirls them around and randomly, certain balls drop into a chute. The process stops when X number of balls fill the chute, i.e. 6. Notice that all the balls had a chance of ending up in the final sample..this is what makes it a representative sample! Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
35. When to Use Simple Random Sampling, Continued... Used when the population is small and can easily be counted or even when the population is large but is contained in an electronic database which can automatically “draw” a random sample Probability of selection = sample size/population size Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
36. Randomly Selecting Samples Many sampling plans use a method of random selection of population elements into the sample. You may use a table of random numbers: a listing of numbers whose nonsystematic (or random) order is assured. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
37. Randomly Selecting Samples, Continued... You may use XL Data Analyst to generate random numbers. Random digit dialing is used to randomly select telephone numbers. A variation of random digit dialing is “Plus One dialing.” Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
38. Using the XL Data Analyst to Generate Random Numbers You can use the XL Data Analyst to generate your own table of random numbers Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
39. XL Data Analyst Output forRandom Numbers Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
40. Random Digit Dialing Random Digit Dialing (RDD) is a method of randomly generating numbers to represent telephone numbers This approach is used in telephone surveys to overcome the problems of unlisted and new telephone numbers Plus-one dialing means that the number drawn from the directory has the last digit in the number replaced by a random number. This ensures that both listed and unlisted numbers are included in the sample Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
41. Systematic Sampling Systematic sampling is a way to select a simple random sample from a directory or physical list that is much more efficient than simple random sampling, because with a physical list, the researcher must first enumerate each listing (difficult when the population is large) in order to select them using a random number The “skip interval” = population list size/sample size Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
42. Cluster Sampling In cluster sampling: the population is divided into subgroups, called “clusters.” If each cluster is representative of the population, one or a few clusters can be selected and a census can be performed. This is a one-step area sample. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
43. Cluster Sampling, Continued... If the clusters are not similar, more clusters can be selected and samples taken from each. This is a two-step area sample. This is desirable when geographic areas need to be surveyed because it can lower research costs. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
44. Stratified Sampling In marketing research it is common to work with populations that contain subgroupings. Stratified sampling is appropriate when we expect each subgroup to respond to research questions differently. When we divide the population into these subgroupings we form different strata; each subgroup represents a stratum. The researcher should use some basis for dividing the population into strata that results in different responses to the key question(s) across strata. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
45. Stratified Sampling, Continued... Why are stratified samples more accurate than random simple samples, given a sample size n? In figure 9.7 notice that the answers to the research questions differ between the strata. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
46. The mean response is different for each stratum… Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
47. Stratified Sampling, Continued... Secondly, notice that the distributions vary in shape; the small firm has the flattest distribution, meaning there is more variance, and the most peaked distribution is for large firms, with the medium firms distribution fitting somewhere in between. How much sample size should we allocate to each stratum? Having sample sizes for each stratum based upon the variances within each will result in a disproportionate sample size for each stratum. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
48. The flatter the distribution; the greater the variance… Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
49. Stratified Sampling, Continued... A proportionate sample size would occur if we allocated sample size based upon each stratum’s proportionate share of the total population. A disproportionate sample is any other allocation that would occur if we based our sample size per stratum not on its proportionate share of the population but on its variance as per our sample size formula. We should use a disproportionate sample size allocation in order to achieve the statistical efficiency possible by using a stratified sample plan….continued.. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
50. Stratified Sampling, Continued... In other words, we would allocate more sample size to the strata with the higher variances and take sample size away from strata with lower variances. This process gives us “statistical efficiency.” We are able to estimate population facts for each stratum accurately without increasing the total sample size required to do the study. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
51. Stratified Sampling, Continued... In a stratified sample, we would be estimating sample findings per stratum. How would we calculate the overall mean for the entire population? A weighted average Weighted average formula: AveragePopulation = (AverageA)(ProportionA) + (AverageB)(ProportionB) Where: A signifies stratum A and B signifies stratum B Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
52. Nonprobability Sampling Method With a nonprobability sampling method, all members of the population do not have a chance of being selected into the sample. Because of this we cannot say that a sample drawn using a nonprobability sampling method is representative of some larger population. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
53. Nonprobability Sampling Method, Cont. Nonprobability sampling plans are sometimes used: First, they are fast, simple to use, and less costly than probability sampling plans Second, many managers are perfectly happy to ask n number of persons a question to help them make a decision Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
54. Nonprobability Sampling Method, Cont. There are four nonprobability sampling methods: Convenience samples Judgment samples Referral samples Quota samples Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
55. Convenience Samples A convenience sample is drawn at the convenience of the researcher or interviewer Mall-intercept companies often use a convenient sampling method to recruit respondents Sample selection error occurs in the form of the absence of members of the population who are infrequent or nonusers of that location Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
56. Judgment Samples A judgment sample is somewhat different from a convenience sample in concept because a judgment sample requires a judgment or “educated guess” as to who should represent the population Subjectivity enters in here, and perhaps the judgment includes more members of the population than a convenience sample, still certain members of the population will not have a probability of being selected into the sample Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
57. Referral Samples A referral sample is sometimes called a “snowball sample”, because it requires respondents to provide the names of additional respondents Referral samples are most appropriate when there is a limited sample frame and when respondents can provide the names of others who would qualify for the survey Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
58. Referral Samples, Continued... Members of the population who are less well known, disliked, or whose opinions conflict with the respondent have a low probability of being selected into a referral sample. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
59. Quota Samples The quota sample establishes a specific quota for various types of individuals to be interviewed. The quotas are determined through application of the research objectives and are defined by key characteristics used to identify the population Often, quota sampling is used as a means of ensuring that convenience samples will have the desired proportions of different respondent classes, thereby reducing the sample selection error but not eliminating it. Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
60. Online Sampling Techniques Random online intercept sampling relies on a random selection of website visitors Invitation online sampling is when potential respondents are alerted that they may fill out a questionnaire that is hosted at a specific website Online panel sampling refers to consumer or other respondent panels that are set up by marketing research companies for the explicit purpose of conducting online surveys with representative samples Copyright ©2010 Pearson Education, Inc. publishing as Prentice Hall
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