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12- Sampling.ppt
- 1. Sampling Sources: -EPIET Introductory course, ThomasGrein, Denis Coulombier, Philippe Sudre, Mike Catchpole -IDEA Brigitte Helynck, Philippe Malfait, Institut de veille sanitaire Modified: Denise Antona, EPIET 2003
- 2. Objectives of presentation •Definition of sampling • Why do we use samples? • Concept of representativeness • Main methods of sampling • Sampling error • Sample size calculation
- 3. Definition of sampling Procedureby which some members of a given population are selected as representatives of the entire population
- 4. Definition of samplingterms • Sampling unit – Subject under observation on which information is collected • Sampling fraction – Ratio between the sample size and the population size • Sampling frame – Any list of all the sampling units in the population • Sampling scheme – Method of selecting sampling units from sampling frame
- 5. Why do weuse samples ? Get information from large populations – At minimal cost – At maximum speed – At increased accuracy – Using enhanced tools
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- 7. What we needto know • Concepts – Representativeness – Sampling methods – Choice of the right design • Calculations – Sampling error – Design effect – Sample size
- 8. Sampling and representativeness Sample TargetPopulation Sampling Population Target Population Sampling Population Sample
- 9. Representativeness • Person • Demographiccharacteristics (age, sex…) • Exposure/susceptibility • Place (Example : urban vs. rural) • Time • Seasonality • Day of the week • Time of the day Ensure representativeness before starting, confirm once completed !!!!!!
- 10. Types of samples •Non-probability samples • Probability samples
- 11. Non probability samples •Quotas • Sample reflects population structure • Time/resources constraints • Convenience samples (purposive units) • Biased • Best or worst scenario Probability of being chosen : unknown
- 12. Probability samples • Randomsampling • Each subject has a known probability of being chosen • Reduces possibility of selection bias • Allows application of statistical theory to results
- 13. Sampling error • Nosample is the exact mirror image of the population • Magnitude of error can be measured in probability samples • Expressed by standard error – of mean, proportion, differences, etc • Function of – amount of variability in measuring factor of interest – sample size
- 14. Methods used inprobability samples • Simple random sampling • Systematic sampling • Stratified sampling • Multistage sampling • Cluster sampling
- 15. Quality of anestimate Precision & validity No precision Random error ! Precision but no validity Systematic error (Bias) !
- 16. Simple random sampling •Principle –Equal chance of drawing each unit • Procedure –Number all units –Randomly draw units
- 17. Simple random sampling •Advantages –Simple –Sampling error easily measured • Disadvantages –Need complete list of units –Does not always achieve best representativeness –Units may be scattered
- 18. Example: evaluate theprevalence of tooth decay among the 1200 children attending a school • List of children attending the school • Children numerated from 1 to 1200 • Sample size = 100 children • Random sampling of 100 numbers between 1 and 1200 How to randomly select? Simple random sampling
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- 20. 57172 42088 7009811333 26902 29959 43909 49607 33883 87680 28923 15659 09839 45817 89405 70743 77950 67344 10609 87119 15859 74577 42791 75889 11607 11596 01796 24498 17009 67119 00614 49529 56149 55678 38169 47228 49931 94303 67448 31286 80719 65101 77729 83949 83358 75230 56624 27549 93809 19505 82000 79068 45552 86776 48980 56684 40950 86216 48161 17646 24164 35513 94057 51834 12182 59744 65695 83710 41125 14291 74773 66391 13382 48076 73151 48724 35670 38453 63154 58116 38629 94576 48859 75654 17152 66516 78796 73099 60728 32063 12431 23898 23683 10853 04038 75246 01881 99056 46747 08846 01331 88163 74462 14551 23094 29831 95387 23917 07421 97869 88092 72201 15243 21100 48125 05243 16181 39641 36970 99522 53501 58431 68149 25405 23463 49168 02048 31522 07698 24181 01161 01527 17046 31460 91507 16050 22921 25930 79579 43488 13211 71120 91715 49881 68127 00501 37484 99278 28751 80855 02035 10910 55309 10713 36439 65660 72554 77021 46279 22705 92034 90892 69853 06175 61221 76825 18239 47687 50612 84077 41387 54107 09190 74305 68196 75634 81415 98504 32168 17822 49946 37545 47201 85224 38461 44528 30953 08633 08049 68698 08759 45611 07556 24587 88753 71626 64864 54986 38964 83534 60557 50031 75829 05622 30237 77795 41870 26300 Table of random numbers
- 21. EPITABLE: random numberlisting
- 22. EPITABLE: random numberlisting
- 23. Systematic sampling • N= 1200, and n = 60 sampling fraction = 1200/60 = 20 • List persons from 1 to 1200 • Randomly select a number between 1 and 20 (ex : 8) 1st person selected = the 8th on the list 2nd person = 8 + 20 = the 28th etc .....
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- 27. Stratified sampling • Principle: –Classify population into internally homogeneous subgroups (strata) –Draw sample in each strata –Combine results of all strata
- 28. Stratified sampling • Advantages –More precise if variable associated with strata – All subgroups represented, allowing separate conclusions about each of them • Disadvantages – Sampling error difficult to measure – Loss of precision if very small numbers sampled in individual strata
- 29. Example: Stratified sampling •Determine vaccination coverage in a country • One sample drawn in each region • Estimates calculated for each stratum • Each stratum weighted to obtain estimate for country (average)
- 30. Multiple stage sampling Principle •= consecutive samplings • example : sampling unit = household – 1rst stage : drawing areas or blocks – 2nd stage : drawing buildings, houses – 3rd stage : drawing households
- 31. Cluster sampling • Principle –Randomsample of groups (“clusters”) of units –In selected clusters, all units or proportion (sample) of units included
- 32. Example: Cluster sampling Section4 Section 5 Section 3 Section 2 Section 1
- 33. Cluster sampling • Advantages –Simple as complete list of sampling units within population not required – Less travel/resources required • Disadvantages – Imprecise if clusters homogeneous and therefore sample variation greater than population variation (large design effect) – Sampling error difficult to measure
- 34. EPI cluster sampling Toevaluate vaccination coverage: • Without list of persons • Total population of villages • Randomly choose 30 clusters • 30 cluster of 7 children each= 210 children
- 35. Drawing the clusters Youneed : – Map of the region – Distribution of population (by villages or area) – Age distribution (population 12-23 m :3%) 1600 220 3200 400 800 200 1200 200 1600 400 53000 7300 106000 13000 26500 6600 40000 6600 53000 13200 A B C D E F G H I J 12-23 Pop. Village
- 36. Distribution of theclusters A B C D E F G H I J 1600 220 3200 400 800 200 1200 200 1600 400 1600 1820 5020 5420 6220 6420 7620 7820 9420 9820 Total population = 9820 Compute cumulated population
- 37. Distribution of theclusters Then compute sampling fraction : K= = 327 Draw a random number (between 1 and 327) Example: 62 Start from the village including “62” and draw the clusters adding the sampling fraction 9820 30 A B C D E F G H I J 1600 1820 5020 5420 6220 6420 7620 7820 9420 9820 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
- 38. Drawing households andchildren On the spot Go to the center of the village , choose direction (random) Number the houses in this direction Ex: 21 Draw random number (between 1 and 21) to identify the first house to visit From this house progress until finding the 7 children ( itinerary rules fixed beforehand)
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- 40. Selecting a samplingmethod • Population to be studied – Size/geographical distribution – Heterogeneity with respect to variable • Level of precision required • Resources available • Importance of having a precise estimate of the sampling error
- 41. Steps in estimatingsample size • Identify major study variable • Determine type of estimate (%, mean, ratio,...) • Indicate expected frequency of factor of interest • Decide on desired precision of the estimate • Decide on acceptable risk that estimate will fall outside its real population value • Adjust for estimated design effect • Adjust for expected response rate • (Adjust for population size? In case of small size population only)
- 42. Sample size formulain descriptive survey z: alpha risk express in z-score p: expected prevalence q: 1 - p d: absolute precision g: design effect z² * p * q 1.96²*0.15*0.85 n = -------------- ---------------------- = 544 d² 0.03² Cluster sampling z² * p * q 2*1.96²*0.15*0.85 n = g* -------------- ------------------------ = 1088 d² 0.03² Simple random / systematic sampling
- 43. EPITABLE: cluster samplesize calculation
- 44. Place of sampling indescriptive surveys • Define objectives • Define resources available • Identify study population • Identify variables to study • Define precision required • Establish plan of analysis (questionnaire) • Create sampling frame • Select sample • Pilot data collection • Collect data • Analyse data • Communicate results • Use results
- 45. Conclusions • Probability samplesare the best • Beware of … – refusals – absentees – “do not know”
- 46. Conclusions • If indoubt… Call a statistician !!!!