Sampling

Sampling Issues Sampling Terminology Probability in Sampling Probability Sampling Designs Non-Probability Sampling Designs Sampling Distribution

Sampling Terminology

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 selection is systematic or haphazard, but not random Non-Probability Sampling

Who do you want to generalize to? Groups in Sampling Who do you want to generalize to?

The Theoretical Population Groups in Sampling The Theoretical Population

The Theoretical Population What population can you get access to? Groups in Sampling The Theoretical Population What population can you get access to?

The Theoretical Population Groups in Sampling The Theoretical Population The Study Population

The Theoretical Population How can you get access to them? Groups in Sampling The Theoretical Population The Study Population How can you get access to them?

The Theoretical Population Groups in Sampling The Theoretical Population The Study Population The Sampling Frame

The Theoretical Population Groups in Sampling The Theoretical Population The Study Population The Sampling Frame Who is in your study?

The Theoretical Population Groups in Sampling The Theoretical Population The Study Population The Sampling Frame The Sample

The Theoretical Population Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

The Theoretical Population Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

The Theoretical Population Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

The Theoretical Population Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

Statistical Terms in Sampling Variable

Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility

Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic

Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample

Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample Parameter

Statistical Terms in Sampling Variable 1 2 3 4 5 response Statistic Average = 3.72 sample Parameter Average = 3.75 population

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. A sample is a subset of elements in the population chosen to represent it. Quality of the sample = quality of the inference Would this class be a good representation of all Persian Doctors? Why or why not? This class would not be a good sample of all Persian Dentists, we are more interested in research methodology, so we are different!! This class would not be a good sample of all UNO students. The reason, everyone is a business student and it is therefore biased. It contains no representation from Arts and Sciences, Fine Arts, Engineering, Education, CPACS, or ITT. It might be a good sample to make inferences about the College of Business but not all students at UNO.

The Sampling Distribution sample sample sample

The Sampling Distribution sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5

The Sampling Distribution sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5 Average Average Average

The Sampling Distribution sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5 sample 4 . 2 3 8 6 5 Average Average Average 4 . 2 3 8 6 1 5 ...is the distribution of a statistic across an infinite number of samples The Sampling Distribution...

Random Sampling

Types of Probability Sampling Designs Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Multistage Sampling

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

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

Simple Random Sampling Example: People who subscribe Novin Pezeshki last year People who visit our site draw a simple random sample of n/N

Simple Random Sampling List of Residents

Simple Random Sampling List of Residents Random Subsample

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

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.

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)

Stratified Random Sampling List of Residents

Stratified Random Sampling List of Residents surgical medical Non-clinical Strata

Stratified Random Sampling List of Residents surgical medical Non-clinical Strata Random Subsamples of n/N

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

Systematic Random Sampling Assumes that the population is randomly ordered Advantages - easy; may be more precise than simple random sample Example - Residents study

Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 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 N = 100

Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 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 N = 100 want n = 20

Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 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 N = 100 want n = 20 N/n = 5

Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 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 N = 100 want n = 20 N/n = 5 select a random number from 1-5: chose 4

Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 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 N = 100 want n = 20 N/n = 5 select a random number from 1-5: chose 4 start with #4 and take every 5th unit

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.

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

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.

Multi-Stage Sampling Cluster random sampling can be multi-stage Any combinations of single-stage methods

Multi-Stage Sampling choosing students from medical schools: Select all schools, then sample within schools Sample schools, then measure all students Sample schools, then sample students

Nonrandom Sampling Designs

Types of nonrandom samples Accidental, haphazard, convenience Modal Instance Purposive Expert Quota Snowball Heterogeneity sampling

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

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.

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.

Modal Instance Sampling Sample for the typical case Typical medical students age? Typical socioeconomic class? Problem: may not represent the modal group proportionately

Purposive Sampling Might sample several pre-defined groups (e.g., patients who does not attend at follow up visits) Deliberately sampling an extreme group

Expert Sampling Have a panel of experts make a judgment about the representativeness of your sample Advantage: at least you can say that expert judgment supports the sampling Problem: the “experts” may be wrong

Quota Sampling select people nonrandomly according to some quotas

Snowball Sampling one person recommends another, who recommends another, who recommends another, etc. good way to identify hard-to-reach populations for example, adolescents who abuse recreational drugs

Heterogeneity Sampling make sure you include all sectors - at least several of everything - don't worry about proportions (like in quota sampling) for instance, when brainstorming issues across stakeholder groups

Sampling Random Non Random Haphazard Simple Convenience Systematic Modal Instance Cluster Purposive Multi Stage Expert Stratified Snowball Proportionate Disproportionate Heterogeneity Quota

Any question?