VIEWS: 4 PAGES: 28 POSTED ON: 5/24/2010
Sampling in Marketing Research 1 Basics of sampling I A sample is a Samples offer many benefits: “part of a whole Save costs: Less expensive to study the to show what the sample than the population. rest is like”. Save time: Less time needed to study the Sampling helps to sample than the population . determine the Accuracy: Since sampling is done with corresponding care and studies are conducted by skilled value of the and qualified interviewers, the results are population and expected to be accurate. plays a vital role in Destructive nature of elements: For some marketing elements, sampling is the way to test, since research. tests destroy the element itself. 2 Basics of sampling II Limitations of Sampling Sampling Process Demands more rigid control in undertaking sample Defining the Developing operation. population a sampling Frame Minority and smallness in number of sub-groups often render study to be Specifying Determining suspected. Sample Sample Method Size Accuracy level may be affected when data is subjected to weighing. Sample results are good SELECTING THE SAMPLE approximations at best. 3 Sampling: Step 1 Sampling: Step 2 Defining the Universe Establishing the Sampling Frame Universe or population is the whole mass under study. A sample frame is the list of all elements in the population How to define a universe: (such as telephone directories, » What constitutes the units of electoral registers, club analysis (HDB apartments)? membership etc.) from which » What are the sampling units the samples are drawn. (HDB apartments occupied in the last three months)? A sample frame which does not fully represent an intended » What is the specific designation population will result in frame of the units to be covered (HDB error and affect the degree of in town area)? reliability of sample result. » What time period does the data refer to (December 31, 1995) 4 Step - 3 Determination of Sample Size Sample size may be determined by using: » Subjective methods (less sophisticated methods) – The rule of thumb approach: eg. 5% of population – Conventional approach: eg. Average of sample sizes of similar other studies; – Cost basis approach: The number that can be studied with the available funds; » Statistical formulae (more sophisticated methods) – Confidence interval approach. 5 Conventional approach of Sample size determination using Sample sizes used in different marketing research studies TYPE OF STUDY MINIMUM TYPICAL SIZE RANGE Identifying a problem (e.g.market segmentation) 500 1000-2500 Problem-solving (e.g., promotion) 200 300-500 Product tests 200 300-500 Advertising (TV, Radio, or print Media per commercial or ad tested) 150 200-300 Test marketing 200 300-500 Test market audits 10 10-20 stores/outlets stores/outlets Focus groups 2 groups 4-12 groups 6 Sample size determination using statistical formulae: The confidence interval approach To determine sample sizes using statistical formulae, researchers use the confidence interval approach based on the following factors: » Desired level of data precision or accuracy; » Amount of variability in the population (homogeneity); » Level of confidence required in the estimates of population values. Availability of resources such as money, manpower and time may prompt the researcher to modify the computed sample size. Students are encouraged to consult any standard marketing research textbook to have an understanding of these formulae. 7 Step 4: Specifying the sampling method Probability Sampling » Every element in the target population or universe [sampling frame] has equal probability of being chosen in the sample for the survey being conducted. » Scientific, operationally convenient and simple in theory. » Results may be generalized. Non-Probability Sampling » Every element in the universe [sampling frame] does not have equal probability of being chosen in the sample. » Operationally convenient and simple in theory. » Results may not be generalized. 8 Probability sampling Four types of probability sampling Appropriate for Appropriate for homogeneous population heterogeneous population » Simple random sampling » Stratified sampling – Requires the use of a random – Use of random number number table. table may be necessary » Systematic sampling » Cluster sampling – Requires the sample frame – Use of random number only, table may be necessary – No random number table is necessary 9 Non-probability sampling Four types of non-probability sampling techniques » Very simple types, based on subjective criteria – Convenient sampling – Judgmental sampling » More systematic and formal – Quota sampling » Special type – Snowball Sampling 10 Simple Random Sampling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Also called random sampling 1 37 75 10 49 98 66 03 86 34 80 98 44 22 22 45 83 53 86 23 51 2 50 91 56 41 52 82 98 11 57 96 27 10 27 16 35 34 47 01 36 08 Simplest method of 3 99 14 23 50 21 01 03 25 79 07 80 54 55 41 12 15 15 03 68 56 probability 4 70 72 01 00 33 25 19 16 23 58 03 78 47 43 77 88 15 02 55 67 5 18 46 06 49 47 32 58 08 75 29 63 66 89 09 22 35 97 74 30 80 sampling 6 65 76 34 11 33 60 95 03 53 72 06 78 28 14 51 78 76 45 26 45 7 83 76 95 25 70 60 13 32 52 11 87 38 49 01 82 84 99 02 64 00 8 58 90 07 84 20 98 57 93 36 65 10 71 83 93 42 46 34 61 44 01 9 54 74 67 11 15 78 21 96 43 14 11 22 74 17 02 54 51 78 76 76 10 56 81 92 73 40 07 20 05 26 63 57 86 48 51 59 15 46 09 75 64 Need to use Random 11 34 99 06 21 22 38 22 32 85 26 37 00 62 27 74 46 02 61 59 81 12 02 26 92 27 95 87 59 38 18 30 95 38 36 78 23 20 19 65 48 50 Number Table 13 43 04 25 36 00 45 73 80 02 61 31 10 06 72 39 02 00 47 06 98 14 92 56 51 22 11 06 86 88 77 86 59 57 66 13 82 33 97 21 31 61 15 67 42 43 26 20 60 84 18 68 48 85 00 00 48 35 48 57 63 38 84 11 How to Use Random Number Tables ________________________________________________ 1. Assign a unique number to each population element in the sampling frame. Start with serial number 1, or 01, or 001, etc. upwards depending on the number of digits required. 2. Choose a random starting position. 3. Select serial numbers systematically across rows or down columns. 4. Discard numbers that are not assigned to any population element and ignore numbers that have already been selected. 5. Repeat the selection process until the required number of sample elements is selected. 12 How to Use a Table of Random Numbers to Select a Sample Your marketing research lecturer wants to randomly select 20 students from your class of 100 students. Here is how he can do it using a random number table. Step 1: Assign all the 100 members of the population a unique number.You may identify each element by assigning a two-digit number. Assign 01 to the first name on the list, and 00 to the last name. If this is done, then the task of selecting the sample will be easier as you would be able to use a 2-digit random number table. NAME NUMBER NAME NUMBER Adam, Tan 01 Tan Teck Wah 42 ……………… …………………… … Carrol, Chan 08 Tay Thiam Soon 61 ………………. … ……………….. … Jerry Lewis 18 Teo Tai Meng 87 ………………. … …………………. … Lim Chin Nam 26 …………………… … ………………. … Yeo Teck Lan 99 Singh, Arun 30 Zailani bt Samat 00 13 How to use random number table to select a random sample Step 2: Select any starting point in the Random Number Table and find the first number that corresponds to a number on the list of your population. In the example below, # 08 has been chosen as the starting point and the first student chosen is Carol Chan. Starting point: 10 09 73 25 33 76 move right to the end of the row, then down 37 54 20 48 05 64 to the next row row; 08 42 26 89 53 19 move left to the end, 90 01 90 25 29 09 then down to the next row, and so on. 12 80 79 99 70 80 66 06 57 47 17 34 31 06 01 08 05 45 Step 3: Move to the next number, 42 and select the person corresponding to that number into the sample. #87 – Tan Teck Wah Step 4: Continue to the next number that qualifies and select that person into the sample. # 26 -- Jerry Lewis, followed by #89, #53 and #19 Step 5: After you have selected the student # 19, go to the next line and choose #90. Continue in the same manner until the full sample is selected. If you encounter a number selected earlier (e.g., 90, 06 in this example) simply skip over it and choose the next number. 14 Systematic sampling Very similar to simple random sampling with one exception. In systematic sampling only one random number is needed throughout the entire sampling process. To use systematic sampling, a researcher needs: [i] a sampling frame of the population; and is needed. [ii] a skip interval calculated as follows: Skip interval = population list size Sample size Names are selected using the skip interval. If a researcher were to select a sample of 1000 people using the local telephone directory containing 215,000 listings as the sampling frame, skip interval is [215,000/1000], or 215. The researcher can select every 215th name of the entire directory [sampling frame], and select his sample. 15 Example: How to Take a Systematic Sample Step 1: Select a listing of the population, say the City Telephone Directory, from which to sample. Remember that the list will have an acceptable level of sample frame error. Step 2: Compute the skip interval by dividing the number of entries in the directory by the desired sample size. Example: 250,000 names in the phone book, desired a sample size of 2500, So skip interval = every 100th name Step 3: Using random number(s), determine a starting position for sampling the list. Example: Select: Random number for page number. (page 01) Select: Random number of column on that page. (col. 03) Select: Random number for name position in that column (#38, say, A..Mahadeva) Step 4: Apply the skip interval to determine which names on the list will be in the sample. Example: A. Mahadeva (Skip 100 names), new name chosen is A Rahman b Ahmad. Step 5: Consider the list as “circular”; that is, the first name on the list is now the initial name you selected, and the last name is now the name just prior to the initially selected one. Example: When you come to the end of the phone book names (Zs), just continue on through the beginning (As). 16 Stratified sampling I A three-stage process: Stratified samples can be: Step 1- Divide the population into Proportionate: involving the homogeneous, mutually exclusive selection of sample elements and collectively exhaustive subgroups from each stratum, such that or strata using some stratification the ratio of sample elements variable; from each stratum to the Step 2- Select an independent simple sample size equals that of the random sample from each stratum. population elements within Step 3- Form the final sample by each stratum to the total consolidating all sample elements number of population chosen in step 2. elements. May yield smaller standard errors of Disproportionate: the sample estimators than does the simple random is disproportionate when the sampling. Thus precision can be gained above mentioned ratio is with smaller sample sizes. unequal. 17 Selection of a proportionate Stratified Sample To select a proportionate stratified sample of 20 members of the Island Video Club which has 100 members belonging to three language based groups of viewers i.e., English (E), Mandarin (M) and Others (X). Step 1: Identify each member from the membership list by his or her respective language groups 00 (E ) 20 (M) 40 (E ) 60 (X) 80 (M) 01 (E ) 21 (X) 41 (X) 61 (M) 81 (E ) 02 ( X ) 22 (E ) 42 (X) 62 (M) 82 (E ) 03 (E ) 23 (X) 43 (E ) 63 (E ) 83 (M) 04 (E ) 24 (E ) 44 (M) 64 (E ) 84 (X) 05 (E ) 25 (M) 45 (E ) 65 (X) 85 (E ) 06 (M) 26 (E ) 46 (X) 66 (M) 86 (E ) 07 (M) 27 (M) 47 (M) 67 (E ) 87 (M) 08 (E ) 28 (X) 48 (E ) 68 (M) 88 (X) 09 (E ) 29 (E ) 49 (E ) 69 (E ) 89 (E ) 10 (M) 30 (E ) 50 (E ) 70 (E ) 90 (X) 11 (E ) 31 (E ) 51 (M) 71 (E ) 91 (E ) 12 ( X ) 32 (E ) 52 (X) 72 (M) 92 (M) 13 (M) 33 (M) 53 (M) 73 (E ) 93 (E ) 14 (E ) 34 (E ) 54 (E ) 74 (X) 94 (E ) 15 (M) 35 (M) 55 (E ) 75 (E ) 95 (X) 16 (E ) 36 (E ) 56 (M) 76 (E ) 96 (E ) 17 ( X ) 37 (E ) 57 (E ) 77 (M) 97 (E ) 18 ( X ) 38 (X) 58 (M) 78 (M) 98 (M) 19 (M) 39 (X) 59 (M) 79 (E ) 99 (E ) 18 Selection of a proportionate stratified sample II Step 2: Sub-divide the club members into three homogeneous sub-groups or strata by the language groups: English, Mandarin and others. EnglishLanguage Mandarin Language Other Language Stratum Stratum Stratum . 00 22 40 64 82 06 35 66 02 42 01 24 43 67 85 07 44 68 12 46 03 26 45 69 86 10 47 72 17 52 04 29 48 70 89 13 51 77 18 60 05 30 49 71 91 15 53 78 21 65 08 31 50 73 93 19 56 80 23 74 09 32 54 75 94 20 58 83 28 84 11 34 55 76 96 25 59 87 38 88 14 36 57 79 97 27 61 92 39 90 16 37 63 81 99 33 62 98 41 95 1. Calculate the overall sampling fraction, f, in the following manner: f = n = 20 = 1 = 0.2 N 100 5 where n = sample size and N = population size 19 Selection of a proportionate stratified sample III Determine the number of sample elements (n1) to be selected from the English language stratum. In this example, n1 = 50 x f = 50 x 0.2 =10. By using a simple random sampling method [using a random number table] members whose numbers are 01, 03, 16, 30, 43, 48, 50, 54, 55, 75, are selected. Next, determine the number of sample elements (n2) from the Mandarin language stratum. In this example, n2 = 30 x f = 30 X 0.2 = 6. By using a simple random sampling method as before, members having numbers 10,15, 27, 51, 59, 87 are selected from the Mandarin language stratum. In the same manner, the number of sample elements (n3) from the „Other language‟ stratum is calculated. In this example, n3 = 20 x f = 20 X 0.2 = 4. For this stratum, members whose numbers are 17, 18, 28, 38 are selected‟ These three different sets of numbers are now aggregated to obtain the ultimate stratified sample as shown below. S = (01, 03, 10, 15, 16, 17, 18, 27, 28, 30, 38, 43, 48, 50, 51, 54, 55, 59, 75, 87) 20 Cluster sampling Is a type of sampling in which clusters or groups of elements are sampled at the same time. Such a procedure is economic, and it retains the characteristics of probability sampling. A two-step-process: » Step 1- Defined population is divided into number of mutually exclusive and collectively exhaustive subgroups or clusters; » Step 2- Select an independent simple random sample of clusters. One special type of cluster sampling is called area sampling, where pieces of geographical areas are selected. 21 Example : One-stage and two-stage Cluster sampling Consider the same Island Video Club example involving 100 club members: Step 1: Sub-divide the club members into 5 clusters, each cluster containing 20 members. Cluster No. English Mandarin Others 1 00, 22, 40, 64, 82 06, 35, 66 02, 42 01, 24, 43, 67, 85 07, 44, 68 12, 46 2 03, 26, 45, 69, 86 10, 47, 72 17, 52 04, 29, 48, 70, 89 13, 51, 77 18, 60 3 05, 30, 49, 71, 91 15, 53, 78 21, 65 08, 31, 50, 73, 93 19, 56, 80 23, 74 4 09, 32, 54, 75, 94 20, 58, 83 28, 84 11, 34, 55, 76, 96 25, 59, 87 38, 88 5 14, 36, 57, 79, 97 27, 61, 92 39, 90 16, 37, 63, 81, 99 33, 62, 98 41, 95 Step 2: Select one of the 5 clusters. If cluster 4 is selected, then all its elements (i.e. Club Members with numbers 09, 11, 32, 34, 54, 55, 75, 76, 94, 96, 20, 25, 58, 59, 83, 87, 28, 38, 84, 88) are selected. Step 3: If a two-stage cluster sampling is desired, the researcher may randomly select 4 members from each of the five clusters. In this case, the sample will be different from that shown in step 2 above. 22 Stratified Sampling vs Cluster Sampling Stratified Sampling Cluster Sampling 1. The target population is sub-divided 1. The target population is sub- into a few subgroups or strata, each divided into a large number of containing a large number of elements. sub-population or clusters, each containing a few elements. 2. Within each stratum, the elements are 2. Within each cluster, the elements homogeneous. However, high degree of are heterogeneous. Between heterogeneity exists between strata. clusters, there is a high degree of homogeneity. 3. A sample element is selected each time. 3. A cluster is selected each time. 4. Less sampling error. 4. More prone to sampling error. 5. Objective is to increase precision. 5. Objective is to increase sampling efficiency by decreasing cost. 23 AREA SAMPLING A common form of cluster sampling where clusters consist of geographic areas, such as districts, housing blocks or townships. Area sampling could be one-stage, two-stage, or multi-stage. How to Take an Area Sample Using Subdivisions Your company wants to conduct a survey on the expected patronage of its new outlet in a new housing estate. The company wants to use area sampling to select the sample households to be interviewed. The sample may be drawn in the manner outlined below. ___________________________________________________________________________________ Step 1: Determine the geographic area to be surveyed, and identify its subdivisions. Each subdivision cluster should be highly similar to all others. For example, choose ten housing blocks within 2 kilometers of the proposed site [say, Model Town ] for your new retail outlet; assign each a number. Step 2: Decide on the use of one-step or two-step cluster sampling. Assume that you decide to use a two-stage cluster sampling. Step 3: Using random numbers, select the housing blocks to be sampled. Here, you select 4 blocks randomly, say numbers #102, #104, #106, and #108. Step 4: Using some probability method of sample selection, select the households in each of the chosen housing block to be included in the sample. Identify a random starting point (say, apartment no. 103), instruct field workers to drop off the survey at every fifth house (systematic sampling). 24 Non-probability samples Convenience sampling » Drawn at the convenience of the researcher. Common in exploratory research. Does not lead to any conclusion. Judgmental sampling » Sampling based on some judgment, gut-feelings or experience of the researcher. Common in commercial marketing research projects. If inference drawing is not necessary, these samples are quite useful. Quota sampling » An extension of judgmental sampling. It is something like a two-stage judgmental sampling. Quite difficult to draw. Snowball sampling » Used in studies involving respondents who are rare to find. To start with, the researcher compiles a short list of sample units from various sources. Each of these respondents are contacted to provide names of other probable respondents. 25 Quota Sampling To select a quota sample comprising 3000 persons in country X using three control characteristics: sex, age and level of education. Here, the three control characteristics are considered independently of one another. In order to calculate the desired number of sample elements possessing the various attributes of the specified control characteristics, the distribution pattern of the general population in country X in terms of each control characteristics is examined. Control Characteristics Population Distribution Sample Elements . Gender: .... Male...................... 50.7% Male 3000 x 50.7% = 1521 ................. Female .................. 49.3% Female 3000 x 49.3% = 1479 Age: ......... 20-29 years ........... 13.4% 20-29 years 3000 x 13.4% = 402 ................. 30-39 years ........... 53.3% 30-39 years 3000 x 52.3% = 1569 ................. 40 years & over .... 33.3% 40 years & over 3000 x 34.3% = 1029 Religion: .. Christianity ........... 76.4% Christianity 3000 x 76.4% = 2292 ................. Islam ..................... 14.8% Islam 3000 x 14.8% = 444 ................. Hinduism .............. 6.6% Hinduism 3000 x 6.6% = 198 ................. Others ................... 2.2% Others 3000 x 2.2% = 66 _________________________________________________________________________________ _ 26 Sampling vs non-sampling errors Sampling Error [SE] Non-sampling Error [NSE] Very small sample Size Larger sample size Still larger sample Complete census 27 Choosing probability vs. non-probability sampling Probability Evaluation Criteria Non-probability sampling sampling Conclusive Nature of research Exploratory Larger sampling Relative magnitude Larger non-sampling errors sampling vs. error non-sampling error High Population variability Low [Heterogeneous] [Homogeneous] Favorable Statistical Considerations Unfavorable High Sophistication Needed Low Relatively Longer Time Relatively shorter High Budget Needed Low 28