Module 4 presentation on sampling methods

presentation on sampling methods

1. College of Public Health and Medical sciences Department of Epidemiology Presentation on Sampling By MPH/MSc group 4 January ,2017 Jimma University 1 1/16/2017 MPH/MSc-G-4-2017

2. 1/16/2017 MPH/MSc-G-4-2017 2 S/n o Name Department 1 Tadesse G/ medhin Epidemiology 2 Banchiayehu Alebachew Health service management 3 Mulugeta Mengistu Microbiology 4 Mulu Demle Hospital care & Administration 5 Selamawit Gebeyehu Reproductive Health Group Members

3. Learning Objectives At the end of this session, participants should be able: To describe the logic of sampling To identify and describe common methods of sampling Discuss problems of bias To identify factors considered in determining sample size 3 1/16/2017 MPH/MSc-G-4-2017

4. Outline Introduction Logic of sampling Sampling methods Bias in sampling Ethical considerations Sample size determination 4 1/16/2017 MPH/MSc-G-4-2017

5. Population : aset which includes all measurements of interest to the researcher. Sample : A subset of the population Parameter : numerical characteristic of a population Statistic : numerical characteristic of a sample 5 1/16/2017 MPH/MSc-G-4-2017

6. Introduction Reference population/Target population/ Source population .-is the population of interest to which the findings of the study are going to be generalized and from which the study subjects are obtained. Study or Sample population :- The population Included in the sample. Sampling unit :- The unit of selection in the sampling process. Study unit :- The unit in which information is collected. 1/16/2017 6 MPH/MSc-G-4-2017

7. Introduction Sampling frame is the list of units from which the sample is selected Sampling fraction :-The ratio of the number of units in the sample to the number of units in the reference population (n/N). 1/16/2017 7 MPH/MSc-G-4-2017

8. Sampling Sampling i s a process by which we study a small part of population to make judgments about the entire population This is for the intension of generalization to the entire population used to make estimates of the population of interest. 8 1/16/2017 MPH/MSc-G-4-2017

9. Introduction…. It is taking representative subgroup of the reference population with the intention of generalization. For this the sample should reflect all the qualities found in the population. 9 1/16/2017 MPH/MSc-G-4-2017

10. Logic of sampling Practical considerations such as cost and population size Inability of researcher to analyze large quantities of data potentially generated by a census Samples can produce sound results if proper rules are followed for the draw 10 1/16/2017 MPH/MSc-G-4-2017

11. Hierarchy of sampling Study subjects The actual participants in the study Sample Subjects who are selected Sampling Frame The list of potential subjects from which the sample is drawn Source population The Population from whom the study subjects would be obtained Target population The population to whom the results would be applied 11 1/16/2017 MPH/MSc-G-4-2017

12. Advantages of sampling REDUCED COST : ↓demands on resources Eg . material GREATER ACCURACY : lead to better accuracy of collecting data. GREATER SPEED : data collected & summarized quickly. FEASIBILITY : the only feasible method of collecting data. 1/16/2017 12 MPH/MSc-G-4-2017

13. Disadvantages of sampling Sampling error Feeling of discrimination If, legally required to have a record. 1/16/2017 13 MPH/MSc-G-4-2017

14. Types of sampling techniques There are two broad categories of sampling techniques Probability sampling techniques Non probability sampling techniques 14 1/16/2017 MPH/MSc-G-4-2017

15. Probability sampling techniques Is one in which each member of the population has an equal chance of being selected. Types of Probability sampling techniques Simple random sampling Systematic random sampling Stratified random sampling Cluster sampling Multi-stage sampling 15 1/16/2017 MPH/MSc-G-4-2017

16. The method of selection is depend on:- the available sampling frame, how spread out the population is, how costly it is to survey members of the population and how users will analyze the data. 1/16/2017 16 MPH/MSc-G-4-2017

17. Advantages and disadvantages probability sampling Advantages Selection is based on the principle of random selection or chance Reliable estimates can be produced Generalization can be made about the population. Disadvantages More complex, more time-consuming and usually more costly than non-probability sampling 17 1/16/2017 MPH/MSc-G-4-2017

18. Types………….. 1. Simple random sampling Each unit in the sampling frame has the same chance of being included in the sample as other unit SRS is drawn by the use of random number table , lottery method and random number generated by computer 18 1/16/2017 MPH/MSc-G-4-2017

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20. Simple random sampling Lottery method You could print off the list of N clients, tear then into separate strips, put the strips in a hat, mix them up real good, close your eyes and pull out the first n. Here's a simple procedure that's especially useful if you have the names of the clients already on the computer. Many computer programs can generate a series of random numbers. Let's assume you can copy and paste the list of client names into a column in an EXCEL spreadsheet. Then, in the column right next to it paste the function =RAND () which is EXCEL's way of putting a random number between 0 and 1 in the cells. Then, sort both columns -- the list of names and the random number -- by the random numbers. 1/16/2017 20 MPH/MSc-G-4-2017

21. Cont’d……. Advantage It is simple, easy to apply when the population is small. Disadvantage It is difficult to use this method for the large population in the absence of sampling frame. 21 1/16/2017 MPH/MSc-G-4-2017

22. 2. Systematic random sampling It is Some times called interval sampling since there is a gap or interval between each selected units in the sample. Using this procedure each element in the population has a known and equal probability of selection. 22 1/16/2017 MPH/MSc-G-4-2017

23. …Cont’d Steps in systematic random sampling Number the units on your frame from 1 to N (where N is the total population size). Determine the sampling interval (K) by dividing the number of units in the population (N) by the desired sample size (n). Select a number between one and K at random. This number is called the random start and would be the first number included in your sample Select every K th unit after that first number 23 1/16/2017 MPH/MSc-G-4-2017

24. …Cont’d Systematic sampling should not be used when a cyclic repetition is inherent in the sampling frame. Example To select a sample of 100 from a population of 400, you would need a sampling interval of 400 ÷100 = 4. Therefore, K= 4. You will need to select one unit out of every four units to end up with a total of 100 units in your sample. 24 1/16/2017 MPH/MSc-G-4-2017

25. …Cont’d Select a number between 1 and 4 from a table of random numbers. If you choose 3, the third unit on your frame would be the first unit included in your sample; The sample might consist of the following units to make up a sample of 100: 3 (the random start), 7, 11, 15, 19...395, 399 (up to N, which is 400 in this case). 25 1/16/2017 MPH/MSc-G-4-2017

26. Advantages and disadvantages Advantages Spreads the sample more evenly over the population is simpler to select one random start Disadvantages Can not be used when a cyclic repetition is inherent in the sampling frame The random start decides the chance of the rest sample units 26 1/16/2017 MPH/MSc-G-4-2017

27. 3. Stratified sampling It is done when the population is known to have heterogeneity with regard to some factors and those factors are used for stratification Using stratified sampling the population is divided in to homogenous, mutually exclusive groups called strata and then independent samples are selected from each stratum 27 1/16/2017 MPH/MSc-G-4-2017

28. …Cont’d Advantage of stratification is that it can reduce the variability of sample statistics over that of SRS (it reduces the sample size required for analysis) There are equal allocation and proportionate allocation to determine the sample size after the stratification. 28 1/16/2017 MPH/MSc-G-4-2017

29. Stratified random sampling Proportionate allocation- if the same sampling fraction is used for each stratum Non-proportionate allocation- the strata equal in size and a fixed number of units is selected from each stratum 1/16/2017 MPH/MSc-G-4-2017 29

30. Stratified random sampling 1/16/2017 MPH/MSc-G-4-2017 30

31. Example 1. An agency has clients from three ethnic groups and the agency wants to asses clients view of quality of service for the last year Suppose that in a kebele X, there are the following persons: merchant: 90 employee: 18 students: 9 farmer: 63 Total: 180 To take a sample of 40 staffs, stratified according to the above categories 1/16/2017 MPH/MSc-G-4-2017 31

32. Example the first step is to find the total number of persons(180) and calculate the percentage in each group. merchant = (90 / 180) x 100 = 50 % employee = ( 18 / 180 ) x100 = 10 % students = (9 / 180 ) x 100 = 5 % farmer = (63 / 180) x 100 = 35 % 1/16/2017 MPH/MSc-G-4-2017 32

33. Example This tells us that of our sample of 40 50% should be merchant =20 10% should be employee =4 5% should be students =2 35% should be farmer =14 Total = 40 1/16/2017 MPH/MSc-G-4-2017 33

34. Advantages and disadvantages Advantages Each  subdivision or strata can be treated as a population. Stratification will almost certainly produce a gain in precision in the estimates of the whole population, because a heterogeneous population is split into fairly homogeneous strata. Ensures representativeness of minority population Disadvantages problems if strata not clearly defined. analysis is (or can be) quite complicated. 34 1/16/2017 MPH/MSc-G-4-2017

35. 3. Cluster Sampling It is used where homogenous population is dispersed over a wide geographic area which is costly to travel & access all regions for the study. Cluster sampling divides the population into groups or clusters. Cluster sampling is a sampling technique used when “natural” groupings are evident in statistical population. 35 1/16/2017 MPH/MSc-G-4-2017

36. Cluster …. It is preferable to select a large number of small clusters rather than a small number of large clusters . 1/16/2017 MPH/MSc-G-4-2017 36

37. Cluster sampling 1/16/2017 MPH/MSc-G-4-2017 37

38. Sampling with probability proportional to size(PPS) Probability sampling requires that each member of the survey population has a chance of being included in the sample , but it does not require that this chance be the same for everyone . 1/16/2017 MPH/MSc-G-4-2017 38

39. Requires that a sampling frame of clusters with measures of size be available of developed This information can be used in the sampling selection in order to increase the efficiency. This is known as sampling with probability proportional to size (PPS) . 1/16/2017 MPH/MSc-G-4-2017 39

40. With this method, the bigger the size of the unit, the higher the chance it has of being included in the sample. For this method to achieve increased efficiency, the measure of size needs to be accurate. 1/16/2017 MPH/MSc-G-4-2017 40

41. Steps in PPS 1.List all villages in the project area 2.Calculate the running cumulative population 3.Determine the number of sites which will be visited and the total sample size desired 4.Divide the total population of the project area by the number of sites and get the sampling interval (SI) 5.Choose a number between 1 and the SI at random (RS) 6.Calculate the following series: RS; RS + SI; RS + 2SI;RS + 3SI; ... 1/16/2017 MPH/MSc-G-4-2017 41

42. Example Planned clusters to be included in the study = 40 Cumulative size of the HHs = 17,219 Sampling interval = 17,219/40 = 430 Random start between 1 and 430 = 73 Clusters selected = 001, 005, 008, etc. 1/16/2017 MPH/MSc-G-4-2017 42

43. Cluster No. HH size Cum. size Sampling No. Cluster selected 001 002 003 004 005 006 007 008 009 . . 170 (last) 120 105 132 96 110 102 165 98 115 . . 196 120 225 357 453 563 665 839 937 1,052 . . 17,219 73 503 933 . . 001 005 008 . . 1/16/2017 MPH/MSc-G-4-2017 43

44. Con’t … The candidate clusters will be selected in cluster sampling are large cluster of small sizes 1/16/2017 MPH/MSc-G-4-2017 44

45. Advantages and disadvantages of cluster sampling Advantages reduced field costs applicable where no complete list of units is available (special lists only need be formed for clusters). Disadvantages clusters may not be representative of whole population but may be too alike analysis more complicated than for simple random sampling. 45 1/16/2017 MPH/MSc-G-4-2017

46. 5. Multi Stage Sampling Multi stage sampling is like the cluster sampling, except that it involves picking a sample from with in each chosen cluster rather than including all within the cluster. This type of sampling requires at least two stages: First stage -large groups or clusters identified and selected. Contain more population units than are needed for the final sample. 46 1/16/2017 MPH/MSc-G-4-2017

47. Cont’d… Second stage -Population units are picked from with in the selected clusters. (Using any of the possible probability sampling method) for final Sample 47 1/16/2017 MPH/MSc-G-4-2017

48. Cont’d… Advantage It is convenient, economic and efficient Does not require a complete list of members in the target population (this reduce sample preparation cost The list of members is required only for those clusters used in the final stage 48 1/16/2017 MPH/MSc-G-4-2017

49. Cont’d… Disadvantage The same as for cluster sampling Lower accuracy due to higher sampling error 49 1/16/2017 MPH/MSc-G-4-2017

50. B. NON-PROBABILITY SAMPLING TECHNIQUES Non- probability sampling is a sampling technique where the selected units in the sample have an unknown probability of being selected and where some units of the target population may even have no chance at all of being in the sample. 50 1/16/2017 MPH/MSc-G-4-2017

51. Types of non probability sampling techniques Purposive/Judgmental Sampling Quota sampling Convenience /Availability/Accidental/Haphazard Sampling Snowball sampling Self-selection sampling 51 1/16/2017 MPH/MSc-G-4-2017

52. Advantages of Non-probability sampling techniques Quick , Cheaper Used when sampling frame is not available Useful when population is so widely dispersed that cluster sampling would not be efficient Often used in exploratory studies, e.g. for hypothesis generation 52 1/16/2017 MPH/MSc-G-4-2017

53. cont’d… Some researches not interested in working out what proportion of population gives a particular response but rather in obtaining an idea of the range of responses on ideas that people have. It is useful when detailed accuracy is not important 53 1/16/2017 MPH/MSc-G-4-2017

54. Disadvantages of Non-probability sampling techniques Does not involve random selection of sample Samples may not be representative of the source population We can not draw any meaningful inference from the results we obtain. Don’t give actual or well known probabilities for the individuals being selected Some people have a greater, but unknown, chance than others of selection . 54 1/16/2017 MPH/MSc-G-4-2017

55. 1.Convenience/Availability/Accidental or Haphazard sampling Comprises subjects who are simply available in a convenient way to the researcher Members of the population are chosen based on their relative ease of access No randomness and the likelihood of bias is high We can not draw meaningful inference from the results Often a feasible method particularly for students or others with restricted time and resource 55 1/16/2017 MPH/MSc-G-4-2017

56. cont’d… Example -Interviews conducted frequently by TV news program to get a quick reading of public opinion -The typical use of college students in much psychological research is primarily a matter of convenience 56 1/16/2017 MPH/MSc-G-4-2017

57. 2. Quota sampling The population is first segmented in to mutually exclusive subgroups just as in stratified sampling, then Judgment is used to select the subjects or units from each segment based on specified proportion The selection of the sample is non random and samples may be biased because not every one gets a chance of selection 57 1/16/2017 MPH/MSc-G-4-2017

58. Cont’d… Subjects are recruited as they arrive and the researcher will assign them to groups based on variables When the quota for a given group is filled, the researcher will stop recruiting E.g. an interviewer may be told to sample 200 females and 300 males with age 45-60 58 1/16/2017 MPH/MSc-G-4-2017

59. 3. Judgmental sampling or Purposive sampling In purposive sampling, we sample with a certain purpose in mind Targets a particular group of people may be the only option when the desired population for study is rare or very difficult to locate and recruit for a study 59 1/16/2017 MPH/MSc-G-4-2017

60. cont’d… Involves selecting the study group which suits the purpose of your study The power of purposive sampling lies in selecting information rich-cases for in-depth analysis related to the central issue being studied It can be used with both quantitative and qualitative studies 60 1/16/2017 MPH/MSc-G-4-2017

61. 4. Snowball sampling We begin by identifying some one who meets the criteria for inclusion in the study Existing study subjects recruit future subjects from among their acquaintances/ s.b known The sample group appears to grow like a rolling snowball and finally you gain enough data to use for the research 61 1/16/2017 MPH/MSc-G-4-2017

62. cont’d… It is often used in hidden population which are difficult for researchers to access e.g. population would be drug abusers The samples are subject to numerous biases. E.g. people who have many friends are more likely to be recruited in to the sample 62 1/16/2017 MPH/MSc-G-4-2017

63. 5. Self/Volunteer selection It is a term used to indicate any situation in which individuals select themselves into a group Common in trials demanding long duration. Respondents themselves decide that they would like to take part in the survey 1/16/2017 63 MPH/MSc-G-4-2017

64. Bias in sampling It occurs during the process of selecting a sample. Failure to include some sample units of the target population into the sample frame. Deliberate exclusion and inclusion explicit of sections of a larger population from sampling frame. 64 1/16/2017 MPH/MSc-G-4-2017

65. Bias … Bias, the opposite of validity, consists of systematic deviations from the true value, always in the same direction. It is possible to eliminate or reduce the non-sampling error (bias) by careful design of the sampling procedure. 65 1/16/2017 MPH/MSc-G-4-2017

66. Some of bias in sampling include Berkison’s bias, Neyman’s bias, Non response bias etc. 66 1/16/2017 MPH/MSc-G-4-2017

67. Non-response bias refers to failure to obtain information on some of the subjects included in the sample to be studied. It results in significant bias when the following situations are fulfilled . When non-respondents constitute a significant proportion of the sample. When non-respondents differ significantly from respondents. 67 1/16/2017 MPH/MSc-G-4-2017

68. Ethical consideration The researcher has an obligation to respect the right, needs, value and desire of study subjects Oral or written permission from study subjects Giving equal chance during sampling for study population to be included in the study Institution review board is considered 68 1/16/2017 MPH/MSc-G-4-2017

69. . Sample Size Determination 69 1/16/2017 MPH/MSc-G-4-2017

70. The number of study subjects selected to represent a given study population. Is a process of choosing a section of the population for observation and study. Important to make inferences based on the findings from the sample. Should be sufficient to represent the characteristics of interest of the study population. Sample Size 70 1/16/2017 MPH/MSc-G-4-2017

71. In estimating a certain characteristic of a population, sample size calculations are important to ensure that estimates are obtained with required precision. The accuracy of the intended results determined by the size of the sample. If the sample is too small, it will be impossible to show that the variation are due to anything more than sampling variation. Cont’d… 71 1/16/2017 MPH/MSc-G-4-2017

72. The objective of the study The study design * Descriptive/Analytic Degree of precision required for generalization. Degree of confidence with which to conclude. Plan for statistical analysis Adjust for population size Adjust for expected response rate Sample size determination depends on 72 1/16/2017 MPH/MSc-G-4-2017

73. Basic questions that should be asked when choosing a sample How large a sample can you collect? What level of budget do you have for the study? What is the prevalence of the condition you are studying? What staff are available to gather the sample? How much time do you have for the research? 73 1/16/2017 MPH/MSc-G-4-2017

74. How many subjects should we study? Too small sample = Reduce waste of time and resources = Results have no practical use Too large sample = Waste of resources = Data quality compromised 74 1/16/2017 MPH/MSc-G-4-2017

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76. PRECISION COST ∆ Sample size = Precision = Cost 76 1/16/2017 MPH/MSc-G-4-2017

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78. Qualitative… More than sample size the richness of the data and analytical capability of the researcher determine the validity and meaningfulness of qualitative data . It is unlikely to be known with precision or certainty at the start of a research project . Sample size will generally be relatively small 78 1/16/2017 MPH/MSc-G-4-2017

79. Quantitative studies Calculations made The bigger the sample ,the better the study becomes Better increase the accuracy and richness of data collection than to increase sample size after a certain point . e.g. –pre-testing of data collection tools -training of data collectors Make extra effort to get a representative sample than large sample 79 1/16/2017 MPH/MSc-G-4-2017

80. Sample size calculation Manually Computing by software( epi -info) 80 1/16/2017 MPH/MSc-G-4-2017

81. 1. The single mean The required (minimum) sample size for a large population is given by n=Z 2 2 /w 2 n=sample size - =standard deviation w - required size of standard error(margin of error) 81 1/16/2017 MPH/MSc-G-4-2017

82. 2. Estimating Single proportion Estimates how big the proportion might be (P) Choose the margin of error you will allow Choose the level of confidence The minimum sample size required for a very large population is 82 1/16/2017 MPH/MSc-G-4-2017

83. Finite population correction If N (entire population) is less than 10, 000, the required sample size will be smaller. In such cases calculate the final sample estimate n f by using the following formula. n f = Where n f =desired sample size (with population < 10,000) n=desired sample size (when population > 10,000) N=the estimate of the population size   1/16/2017 MPH/MSc-G-4-2017 83

84. Sample sizes for Analytical studies The primary purpose of an analytical study is to test (one or more) null hypotheses. The determination of the sample sizes requires (type I and type II errors). 1/16/2017 MPH/MSc-G-4-2017 84

85. Comparison between two means (Equal sample sizes) Comparison between two means(Unequal sample sizes) Comparison between two proportions(Equal sample sizes) Comparison between two proportions (Unequal sample sizes) Calculation for hypothesis testing 85 1/16/2017 MPH/MSc-G-4-2017

86. A. Comparison between two means (Equal sample sizes) ∆ = / μ 1 - μ 2 / The means and variances of the two respective groups are ( µ 1 ,  2 1 ) and ( µ 2 ,  2 2 ) . 86 1/16/2017 MPH/MSc-G-4-2017

87. B. Comparison between two means (Unequal sample sizes) λ =n 2 /n 1 87 1/16/2017 MPH/MSc-G-4-2017

88. C. Comparison between two proportions (Equal sample sizes) |p 1 -p 2 | = ∆ with α and power (1-  ) ∆ = P 1 -P 2 Where 88 1/16/2017 MPH/MSc-G-4-2017

89. D. Comparison between two proportions (Unequal sample sizes) Note: This formula is quite general, and applies to :- cross-sectional, case-control and cohort studies. 89 1/16/2017 MPH/MSc-G-4-2017

90. The 10% Rule Note that sample-size estimates should be interpreted as providing merely a minimum estimate of the sample sizes necessary for the study The formula takes into account only the overall crude association between exposure & disease; i.e., no confounders are considered. 10% rule: increase the sample size 10% for each confounder/ variable added 90 1/16/2017 MPH/MSc-G-4-2017

91. Summary Stages in selecting a sample 91 1/16/2017 MPH/MSc-G-4-2017

92. Summary… Sample size calculations depend on a number of assumptions: – the hypothesized difference of interest, Δ – the probability of Type I error (α) – the probability of Type II error (β) – the variance Choice of sample size depends on a balance of reasonable assumptions, time, effort, and expense Sample size estimates might need to be adjusted to compensate for non-response rate, patient dropout or loss to follow-up, lack of compliance, etc. 92 1/16/2017 MPH/MSc-G-4-2017

93. References Prof. Mekonnen Assefa , Fasil Tesema . “Supplementary readings for research under taking,” Jimma university ,April 2000. Martyn Denscome . “The good research Guide for small scale social research projects, Open University Press, Buckingham. Philadelphia. The International Development Research Center Science for Humanity, Canada. Prof. Makonnen Assefa . “Supplementary Readings on Research methodology, Jimma University,2004. Douglas G. Altman “Practical statistics for medical research” Getu Degu and Fasil T. biostatisics lecture note for health science students, Gondar university . Daniel W., foundation for biostatical analysis in health science. Health Services Research Methods: A Guide to Best Practice . John Brazeir , Ray Fitzpatrick , Bamby , and Deborah Ashby ( 1998)   93 1/16/2017 MPH/MSc-G-4-2017

94. 1/16/2017 MPH/MSc-G-4-2017 94 THANK YOU