BRM_Sampling Procedures.ppt
- 1. Alpha University College Business Research Methods 1 5/11/2022
- 2. Meaning and Concepts Reasons for Sampling The Sampling Process Types of Sampling Sample size determination methods Chapter Four: Sampling Procedures and Techniques 5/11/2022 2
- 3. Basic Concepts How to choose an adequate subset of the total population? There are several concepts in the study and practice of sampling design in research. Population (universe) ◦ all units/elements relevant to the research ◦ includes all members of the group under study or the set of entities under study and their characteristics. ◦ inferences from the sample are made about the population 5/11/2022 3
- 4. Concepts… Census ◦ information on the whole population; enumeration of the entire population Sample is part of the population and all its characteristics. A sample is “a smaller (but hopefully representative) collection of units from a population used to determine truths about that population” (Field, 2005) Sampling units/elements ◦ non-overlapping components of the population ◦ ‘units/elements’ used because it is not only people or households organizations... that are sampled 5/11/2022 4
- 5. Concepts… Sampling frame ◦ the list of all sampling units/elements in the population ◦ the sample is selected from this list Representative sample ◦ a sample that represents the population accurately For example, if the study is on ‘households welfare’: ◦ Population = all households in the study area ◦ Sampling unit = a household ◦ Sampling frame = list of the households 5/11/2022 5
- 6. The sampling process Step 1: Define the population, sampling units, extent and time. Step 2: Get a research permit if this is required in the place you work in. Step 3: Construct the sampling frame. Step 4: Determine the sample size. Step 5: Select a sampling procedure. Step 6: Select the sample. 6 5/11/2022
- 7. Identifying and defining the relevant population ◦ To whom do you want to generalize your results? ◦ The first thing the sample plan must include is a definition of the population to be investigated. ◦ Defining the target population implies specifying the subject of the study. ◦ Specification of a population involves identifying which elements (items) are included, as well as where and when. ◦ When one wants to undertake a sample survey the relevant population from which the sample is going to be drawn need to be identified. Example: if the study concerns income, then the definition of the population as individuals or households can make a difference. All university students 5/11/2022 7
- 8. Population… Census Vs. Sample Once the population has been defined, the researcher must decide whether the survey is to be conducted among all members of the population or only a subset of the population. That is, a choice must be made between census and sample Census is used when the population is small and definite. Sample is preferable if the population is large. 5/11/2022 8
- 9. Population… The Need for Census Universality/Wide applicability- the data collected has a wide application. sampling units are only applicable on average. For the safety of the consumer - census remains the only option in case of some products w/c are so critical to the life of consumers. Representativeness:- to eliminate the possibility that by chance a randomly/purposely selected sample may not representative of the population. Less sampling error: - The only possible errors can be due to computation of the elements. 5/11/2022 9
- 10. Population… Limitation of census Expensiveness: Huge resources (HR, financial, resources, etc. ) requirements Excessive time and energy: Beside cost factor, it takes too long time and consumes too much energy. Not appropriate for short term study. 5/11/2022 10
- 11. Sampling Sampling is the selection of elements (research units) from a population. Sampling is the process of systematically selecting that which will be examined during the course of a study. Strong research design and analytical approach require: Use of one or more of the sampling strategies Include an iterative sampling approach whereby the research team moves back and forth (iterating) between sampling and analyzing data such that preliminary analytical findings shape subsequent sampling choices. 5/11/2022 11
- 14. Reasons for Sampling The reasons for taking sampling instead of census: Economy- finance, manpower, etc. Speed- When the time between the recognition of the need of information and the availability of that information is short, sampling helps not to miss the information Indispensability- Sampling remains the only choice when a test involves the destruction of the item under study. Practicality- Sampling remains the only way when the population are infinitely Homogeneity: If all units of the population are alike, sampling technique is easy to use. Administrative convenience 5/11/2022 14
- 15. Defining and securing a sampling frame Ideally, the sampling frame would list every research unit in the target population separately and only once. In practice, such lists can seldom be constructed, and we end up with an incomplete list (the study population) It is a list of elements from which the sample is actually drawn is important and necessary. The sampling frame is the list from which the potential respondents are drawn. Example ◦ Registrar’s office ◦ Class rosters Sampling frame has the property that we can identify every single element and include any in our sample The sampling frame must be representative of the population 5/11/2022 15
- 16. Identifying parameters of interest What specific population characteristics (variables and attributes) may be of interest. Parameter: ◦ A Measurable characteristics of a population. ◦ A descriptive measure of the population under study. E.g. population mean (), proportions Statistic: Is a descriptive measure of a sample Example, when we work out certain measurement like, mean from a sample they are called statistic. the sample mean (x) is a statistic. 5/11/2022 16
- 17. Selecting types of sampling techniques Random (= probability) sampling All elements in the population have a nonzero and known chance of being selected Purpose: To avoid bias representativeness Non-random (= deliberate or purposive) sampling Selection (partly) based on the judgement of the interviewer or researcher Purpose: to obtain a workable sample when developing a sampling frame is near impossible or too time consuming representativeness..? 5/11/2022 17
- 18. All elements of the target population have known and positive chance of being selected Examples: ◦ Simple Random Sampling ◦ Systematic RS ◦ Cluster Sampling ◦ Stratified Random sampling Probability Sampling Non-Probability Sampling • NOT All elements of the target population have known and positive chance of being selected Examples: – Convenience sampling – Judgment/Expert Sampling – Quota sampling – Snowballing Types of Sampling Techniques… 5/11/2022 18
- 19. Types of Sampling Techniques Judgment al Non-Probability Sampling Techniques Stratified Quota Probability Sampling techniques Simple Random Convenienc e Snowbal l Systematic Cluster 5/11/2022 19
- 20. Non-probability Sampling Techniques Judgmental we use different strategies to sample Typical cases Heterogeneity Extreme cases Confirming and non-confirming cases Purposive Visiting places near roads, towns, etc Interviewing people available during data collection Observing whichever areas key actors want to show us Advantage(s)=easy, fast and may help us collect data that would not have been collected. 5/11/2022 20
- 21. Non-probability Sampling Techniques Quota: quotas are assigned to different strata groups and interviewers are given quotas to be filled from different strata. ◦ A researcher first identifies categories of people (e.g., male, female) then decides how many to get from each category. Snowball (Network) Sampling – chain sampling ◦ This is a method for identifying and selecting the cases in a network. ◦ It begins with one or a few people or cases and use them to establish contact with others. You start with one or two information-rich key informants and ask them if they know persons who know a lot about your topic of interest. 5/11/2022 21
- 22. Probability Sampling Techniques 1. Simple Random Sampling (SRS) ◦ The simplest and easiest method. ◦ each element of the population has an equal chance of being selected into the sample. ◦ It assumes that an accurate sampling frame exists. ◦ Usually two methods are adopted to pick a sample (lottery method and random table). E.g., simple random sampling for household surveys 1. Population = all households in the country 2. Sampling frame = the list of all households (20 million in Ethiopia?) 3. Sample size = say we have resources to cover only 20,000 households 4. Sampling fraction 20,000/20,000,000 or 0.1% 5. Select randomly 20,000 households from the long list of 20,000,000 households 5/11/2022 22
- 23. Probability Sampling Techniques Systematic Sampling Technique In SYSTEMATIC SAMPLING individuals are chosen at regular intervals (for example every nth) from the sampling frame. ◦ The major advantages of SS are its simplicity and flexibility. ◦ instead of a list of random numbers, the researcher calculates a sampling interval. The sampling interval is the standard distance between elements selected in the sample. 5/11/2022 23
- 24. Probability Sampling Techniques E.g., a systematic sample is to be selected from 1200 students of a school. The sample size to be selected is 100. The sampling fraction is: 100/1200= sample size/study population = 1/12 The sampling interval is therefore 12. The first student in the sample is chosen randomly, for example by blindly picking one out of twelve pieces of paper, numbered 1 to 12. If number 6 is picked -every twelfth student will be included –i.e. 6, 18, 30, 42, etc. 5/11/2022 24
- 25. Probability Sampling Techniques Stratified Sampling A population is subdivided into the appropriate strata and a simple random sample taken using either SRS or SS techniques from each stratum. Particularly useful when we have heterogeneous populations. E.g., low income, middle income, high income areas 5/11/2022 25
- 26. Probability Sampling Techniques The reasons for stratifying To increase a sample’s statistical efficiency (smaller standard errors). To provide adequate data for analyzing the various subpopulation. To enable different research methods and procedures to be used in different strata. Can be multiple stage stratified random sampling E.g., in the household survey we may be interested to have sufficient number of households from each region of Ethiopia; stratify by region! 5/11/2022 26
- 27. Probability Sampling Techniques How to Stratify ◦ Three major decisions must be made in order to stratify the given population into some mutually exclusive groups. (1) What stratification base to use: stratification would be based on the principal variable under study such as income, age, education, sex, location, religion, etc. 5/11/2022 27
- 28. Probability Sampling Techniques (2) How many strata to use: there is no precise answer as to how many strata to use. ◦ The more strata the closer one would be to come to maximizing inter-strata differences and minimizing intra-strata variables. (3) What strata sample size to draw: different approaches could be used: One could adopt a proportionate sampling procedure. Or use disproportionate sampling, which allocates elements on the basis of some bias. 5/11/2022 28
- 29. Probability Sampling Techniques Cluster Sampling: 1. It may be difficult or impossible to take a simple random sample because a complete sampling frame does not exist, or 2. Logistical difficulties may also discourage random sampling techniques E.G.: interviewing people who are scattered over a large area may be too time-consuming). The selection of groups of study units (clusters) instead of the selection of study units individually is called CLUSTER SAMPLING. It is cost effective (High economic efficiency) It involves sampling of groups Clusters are often geographic units (e.g., districts, villages) or organizational units (e.g., clinics, etc). 5/11/2022 29
- 30. Probability Sampling Techniques E.g., sampling for household survey in Mekelle ◦ Probably no complete sampling frame and costly to cover simple random sample ◦ Randomly select from sub-cities (clusters) ◦ Randomly select kebeles from sub-cities (clusters) ◦ Then randomly select households from the selected kebeles 5/11/2022 30
- 31. Determining the sample size Research designs with too small sample size are unethical ◦ because they waste resources as they can only provide anecdotal evidence. If the sample size is too small, the data will be unusable. Research studies that use too large samples i.e., larger than needed, also are unethical because: they waste time and financial resources, 5/11/2022 31
- 32. Determining the sample size human subjects may also undergo unnecessary experimental procedures that could be distressful and painful. Sample size determination hinges on: i) Degree of homogeneity: The size of the population variance is an important parameter. The greater the dispersion in the population the larger the sample must be to provide a given estimation precession. 5/11/2022 32
- 33. Determining the sample size ii) Degree of confidence required: Since a sample can never reflect its population for certain, the researcher must determine how much precision s/he needs. Precision is measured in terms of (i) An interval range (the margin of error). (ii) The degree of confidence (how sure you are) 5/11/2022 33
- 34. Determining the sample size iii) Number of sub groups to be studied: If the research is to make estimates on several subgroups of the population then the sample must be large enough for each of these subgroups to meet the desired quality level. iv) Cost: cost considerations have a major implications. All studies have some budgetary constraint and hence cost dictates the size of the sample. 5/11/2022 34
- 35. Determining the sample size V) Prior information: If similar previous study exists we can use that prior information to determine our sample size. using prior mean and variance estimates or stratifying the population to reduce variation within groups. samples that have met the requirements of the statistical methods from past studies. Researchers use it because they rarely have information on the variance or standard errors. 5/11/2022 35
- 36. Determining the sample size vi) Practicality: Of course the sample size you select must make sense. We want to take enough observations to obtain reasonably precise estimates of the parameters of interest but we also want to do this within a practical resource budget. Therefore the sample size is usually a compromise between what is DESIRABLE and what is FEASIBLE. In general, the smaller the population, the bigger the sampling ratio has to be for a reasonable sample. 5/11/2022 36
- 37. Determining the sample size Hence as a ‘rule of thumb’: For population of 200 or less use Census For small populations (under 1000 a large sampling ratio (about 30%). Hence, a sample size of about 300 is required. For moderately large population (10,000), a smaller sampling ratio (about 10%) is needed – a sample size around 1,000. To sample from very large population (over 10 million), one can achieve accuracy using tiny sampling ratios (.025%) or samples of about 2,500. 5/11/2022 37
- 38. Determining the sample size STRATEGIES FOR DETERMINING SAMPLE SIZE There are several approaches to determining the sample size. These include: ◦ using a census for small populations, ◦ imitating a sample size of similar studies, ◦ using published tables, and ◦ applying formulas to calculate a sample size. 5/11/2022 38
- 39. Determining the sample size Using a Census for Small Populations ◦ to use the entire population as the sample. ◦ attractive for small populations (e.g., 200 or less). Using a Sample Size of a Similar Study ◦ to use the same sample size as those of studies similar to the one you plan. ◦ a review of the literature in your discipline can provide guidance about "typical" sample sizes which are used. Using Published Tables ◦ is to rely on published tables which provide the sample size for a given set of criteria. 5/11/2022 39
- 40. Determining the sample size Continuous data (margin of error=.03) Categorical data (margin of error=.05) Population size Alpha = .10, t=1.65 alpha = .05, t= 1.96 alpha = .01, t= 2.58 alpha = .10, t=1.65 alpha = .05, t= 1.96 Alpha =.01, t=2.58 100 46 55 68 74 80 87 200 59 75 102 116 132 154 300 65 85 123 143 169 207 400 69 92 137 162 196 250 500 72 96 147 176 218 286 600 73 100 155 187 235 316 700 75 102 161 196 249 341 800 76 104 166 203 260 363 900 76 105 170 209 270 382 1,000 77 106 173 213 278 399 1,500 79 110 183 230 306 461 2,000 83 112 189 239 232 499 4,000 83 119 198 254 351 570 6,000 83 119 209 259 362 598 8,000 83 119 209 262 367 613 10,000 83 119 209 264 370 623 5/11/2022 40
- 41. How to Calculate Sample Size for Different Study Designs The fourth strategy is to calculate sample size using different formula suitable to the research design at hand. In the recent era of evidence-based results, statistics has come under increased scrutiny. Evidence is as good as the data the research is based on, which in turn depends on the statistical soundness of the claims it make. It is very important to understand that method of sample size calculation is different for different study designs and one blanket formula for sample size calculation cannot be used for all study designs. 5/11/2022 41
- 42. Cochran’s (1977) sample size determination formula n= Z2pq/d2 Where, n is the desired sample size; Z is standard normal variable at the required confidence level (E.g. Z statistics: 1.96); d is the desired level of precision or level of statistical significance/margin of error the researcher accepts (E.g. 0.05); p is estimated characteristics of target population (variability of population parameters) the researcher assumes; and q is 1-p. 5/11/2022 42
- 43. For example: Let us assume that a researcher wants to estimate proportion of patients having hypertension in pediatric age group in a city. According to previously published studies actual number of hypertensive may not be more than 15 percent. The research wants to calculate this sample size with the precision (5 percent level of significance/margin of error). So if we use the above formula, the sample size is 196. 2 2 2 2 0.15*0.85*(1.96) 196 0.05 pqz n u Cochran’s (1977) Formula 5/11/2022 43
- 44. Cochran’s (1977) Formula Survey studies usually have non-sampling errors due mainly to defective definitions of important variables, failure to and bias of respondents to response, coverage and compiling error of the researchers. Researchers are, therefore, advised to oversample by 10% to 20% of the computed number of samples based on their anticipation of such discrepancies (Naing et al., 2006). 5/11/2022 44
- 45. Kothari’s (2004) Formula According to Kothari (2004) systematic Random Sampling can be considered as improvement over Simple Radom Sampling as systematic sample is spread more evenly over entire population. The statically sample size decision making formula to a population size(N) that is greater than or equal to 10031, as to Kothari is: n= (z 2pq)/d2 fn=n/(1+n/N) if N is less than 10,000 Whereas n=the desire sample size; Z= Standard normal variable at the required level of confidence; P=the proportion in the target population estimated to have characteristic being measured; q=1-p, and d= the level of tactical significance set 5/11/2022 45
- 46. Kothari’s (2004) Formula Finite Population Correction The above sample size formula is valid if the calculated sample size is smaller than or equal to 5% of the population size (n/N ≤0.05) (Daniel, 1999). If this proportion is larger than 5% (n/N>0.05), we need to use the formula with finite population correction (Ibid) as follows. This sample size formula holds true or valid only if we apply the simple random or systematic random sampling methods. 5/11/2022 46
- 47. Yamane’s (1967) Formula Full survey of the data for a given task increases the representative of the population under taken. However, such surveys are in efficient both in- terms of cost and time (Ross et al, 2002). Consequently, taking a representative from the given population is mandatory to accomplish the research study with its time frame and budget. Yamane’s sample size determination (Yemane, 1967) Where, n = the desired sample size; N = total number of population and e = the level of precision or the quality of being care full and accurate which is equal to 0.05 5/11/2022 47
- 48. Exercise It was desired to estimate proportion of diabetic children in a certain school. In a similar study at another school a proportion of 30 % was detected. ◦ Compute the minimal sample size required at a confidence limit of 95% and accepting a difference of up to 4% of the true population. 5/11/2022 48
- 49. Exercise Suppose we wish to evaluate a state-wide extension program in which farmers were encouraged to adopt a new practice. Assume there is a large population but that we do not know the variability in the proportion that will adopt the practice; therefore, assume p=.5 (maximum variability). Furthermore, suppose we desire a 95% confidence level and ±5% precision Calculate the sample size 5/11/2022 49
- 50. Other considerations in determining sample size First, the above approaches to determining sample size have assumed that a simple random sample is the sampling method. Another consideration with sample size is the number needed for the data analysis. ◦ If descriptive statistics are to be used, e.g., mean, frequencies, then nearly any sample size will suffice. ◦ a good size sample, e.g., 200-500, is needed for more rigorous analyses (multiple regression, analysis of covariance, or log- linear analysis, etc). 5/11/2022 50
- 51. Other considerations in determining sample size Finally, the sample size formulas provide the number of responses that need to be obtained. ◦ Many researchers commonly add 10% to the sample size to compensate for persons that the researcher is unable to contact. ◦ The sample size also is often increased by 30% to compensate for non- response. 5/11/2022 51
- 52. Acceptable Response Rate Mangione (1995: 60–61) has provided the following classification of bands of response rate to postal questionnaires (cited in Bryman, 2012:235): ◦ Over 85% is excellent; ◦ 70–85% is very good; ◦ 60–69% is acceptable; ◦ 50–59% is barely acceptable; ◦ below 50% is not acceptable. 5/11/2022 52
- 53. Problems in Sampling Two types of errors: Non sampling errors Sampling errors 1. Non Sampling errors: are biases or errors due to fieldwork problems, interviewer induced bias, clerical problems in managing data, etc. ◦ These would contribute to error in a survey, irrespective of whether a sample is drawn or a census is taken. 2. sampling errors are error which is attributable to sampling, and which therefore, is not present in information gathered in a census. 5/11/2022 53
- 54. Problems in Sampling 1. Non-Sampling Error: refers to ◦ Non-coverage error ◦ Wrong population is being sampled ◦ Non response error ◦ Instrument error ◦ Interviewer’s error 5/11/2022 54