VIEWS: 28 PAGES: 60 POSTED ON: 8/25/2012
Sampling 1 Sampling Issues Sampling Terminology Probability in Sampling Probability Sampling Designs Non-Probability Sampling Designs Sampling Distribution 2 Sampling Terminology 3 Two Major Types of Sampling Methods Probability Sampling uses some form of random selection requires that each unit have a known (often equal) probability of being selected Non-Probability selection is systematic or Sampling haphazard, but not random 4 Groups in Sampling Who do you want to generalize to? 5 Groups in Sampling The Theoretical Population 6 Groups in Sampling The Theoretical Population What population can you get access to? 7 Groups in Sampling The Theoretical Population The Study Population 8 Groups in Sampling The Theoretical Population The Study Population How can you get access to them? 9 Groups in Sampling The Theoretical Population The Study Population The Sampling Frame 10 Groups in Sampling The Theoretical Population The Study Population The Sampling Frame Who is in your study? 11 Groups in Sampling The Theoretical Population The Study Population The Sampling Frame The Sample 12 Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample 13 Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample 14 Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample 15 Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample 16 Statistical Terms in Sampling Variable 17 Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility 18 Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic 19 Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample 20 Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample Parameter 21 Statistical Terms in Sampling Variable 1 2 3 4 5 response Statistic Average = 3.72 sample Parameter Average = 3.75 population 22 Statistical Inference Statistical inference: make generalizations about a population from a sample. A population is the set of all the elements of interest in a study. This class would in be A sample is a subset of elementsnot thea to represent all population chosengood sample of it. Persian Dentists, we are the Quality of the sample = quality of more inference interested in research methodology, so we are different!! Would this class be a good representation of all Persian Doctors? Why or why not? 23 The Sampling Distribution sample sample sample 24 The Sampling Distribution sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 25 The Sampling Distribution sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 Average Average Average 26 The Sampling Distribution sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 Average Average Average 15 10 ...is the distribution The Sampling of a statistic across Distribution... 5 an infinite number 0 of samples 27 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 Random Sampling 28 Types of Probability Sampling Designs Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Multistage Sampling 29 Some Definitions N = the number of cases in the sampling frame n = the number of cases in the sample NCn = the number of combinations (subsets) of n from N f = n/N = the sampling fraction 30 Simple Random Sampling • Objective - select n units out of N such that every NCn has an equal chance • Procedure - use table of random numbers, computer random number generator or mechanical device • can sample with or without replacement • f=n/N is the sampling fraction 31 Simple Random Sampling Example : People who subscribe Novin Pezeshki last year People who visit our site draw a simple random sample of n/N 32 Simple Random Sampling List of Residents 33 Simple Random Sampling List of Residents Random Subsample 34 Stratified Random Sampling • sometimes called "proportional" or "quota" random sampling • Objective - population of N units divided into non-overlapping strata N1, N2, N3, ... Ni such that N1 + N2 + ... + Ni = N, then do simple random sample of n/N in each strata 35 Stratified Sampling The population is first divided into groups called strata. If stratification is evident Example: medical students; preclinical, clerckship, internship Best results when low intra strata variance and high inter strata variance A simple random sample is taken from each stratum. Advantage: If strata are homogeneous, this method is “more precise” than simple random sampling of same sample size As precise but with a smaller total sample size. If there is a dominant strata and it is relatively small, you can enumerate it, and sample the rest. 36 Stratified Sampling - Purposes: • to insure representation of each strata - oversample smaller population groups • sampling problems may differ in each strata • increase precision (lower variance) if strata are homogeneous within (like blocking) 37 Stratified Random Sampling List of Residents 38 Stratified Random Sampling List of Residents surgical medical Non-clinical Strata 39 Stratified Random Sampling List of Residents surgical medical Non-clinical Strata Random Subsamples of n/N 40 Systematic Random Sampling Procedure: number units in population from 1 to N decide on the n that you want or need N/n=k the interval size randomly select a number from 1 to k then take every kth unit 41 Systematic Random Sampling Assumes that the population is randomly ordered Advantages - easy; may be more precise than simple random sample Example - Residents study 42 Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 N = 100 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 43 Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 N = 100 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 want n = 20 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 44 Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 N = 100 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 want n = 20 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 N/n = 5 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 45 Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 N = 100 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 want n = 20 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 N/n = 5 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 select a random number from 1-5: 16 41 66 91 17 42 67 92 chose 4 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 46 Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 N = 100 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 want n = 20 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 N/n = 5 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 select a random number from 1-5: 16 41 66 91 17 42 67 92 chose 4 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 start with #4 and take every 5th unit 23 48 73 98 24 49 74 99 25 50 75 100 47 Cluster Sampling The population is first divided into clusters A cluster is a small-scale version of the population (i.e. heterogeneous group reflecting the variance in the population. Take a simple random sample of the clusters. All elements within each sampled (chosen) cluster form the sample. 48 Cluster Random Sampling Advantages - administratively useful, especially when you have a wide geographic area to cover Example: Randomly sample from city blocks and measure all homes in selected blocks 49 Cluster Sampling vs. Stratified Sampling Stratified sampling seeks to divide the sample into heterogeneous groups so the variance within the strata is low and between the strata is high. Cluster sampling seeks to have each cluster reflect the variance in the population…each cluster is a “mini” population. Each cluster is a mirror of the total population and of each other. 50 Multi-Stage Sampling Cluster random sampling can be multi- stage Any combinations of single-stage methods 51 Multi-Stage Sampling c • hoosing students from medical schools: Select all schools, then sample within schools Sample schools, then measure all students Sample schools, then sample students 52 Nonrandom Sampling Designs 53 Types of nonrandom samples Accidental, haphazard, convenience Modal Instance Purposive Expert Quota Snowball Heterogeneity sampling 54 Accidental or Haphazard Sampling “Man on the street” Medical student in the library available or accessible clients volunteer samples •Problem: we have no evidence for representativeness 55 Convenience Sampling The sample is identified primarily by convenience. It is a nonprobability sampling technique. Items are included in the sample without known probabilities of being selected. Example: A professor conducting research might use student volunteers to constitute a sample. 56 Convenience Sampling Advantage: Relatively easy, fast, often, but not always, cheap Disadvantage: It is impossible to determine how representative of the population the sample is. Try to offset this by collecting large sample size. 57 Quota Sampling select people nonrandomly according to some quotas 61 Sampling Random Non Random Simple Haphazard Systematic Convenience Cluster Modal Instance Multi Stage Purposive Stratified Expert Snowball Proportionate Disproportionate Heterogeneity Quota 64 65