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FCS 681 Lecture 5

Sampling

What is sampling and Why sample?

  • Selecting part of a larger group
  • Purpose is to make generalizations about the population from the smaller group.
  • Why not study everyone?

--Cost: US Decennial Census, 1990, cost $1.5 billion, 2010, $14 billion

--Quality: When data are collected on a large scale, quality declines

--Timeliness

Advantages of sampling

  • Selecting less than the entire population has advantages:

􀂄 Less expensive

􀂄 Less time

􀂄 Better quality control

Key Sampling Concepts

Copyright ©2002, William M.K. Trochim, All Rights Reserved

Key sampling concepts

  • Distinction between the theoretical population and the actual study population
  • Generalizations can be made only to the actual population

Theoretical Population

The Study or Accessible Population

Theoretical

Study

Sampling Frame

The list or procedure defining the POPULATION (From which the sample will be drawn.)

Examples:

Telephone book

Voters list

Mailing list

Distinguish sampling frame from sample.

Theoretical

Study

Sampling Frame

Selected Sample

Those selected to participate in the study

Not all will necessarily participate

--Non deliverable surveys

--Incomplete surveys

Theoretical

Study

Sampling Frame

Selected Sample

Actual

sample

Subjects who complete the study and data is used in data analysis

Ratio of actual to selected is called response rate

Key Concepts in sampling

  • Random sampling error

--the difference between the sample results and the results of a census conducted using identical procedure.

  • Systematic sampling error

--due to sampling methods or imperfection in execution.

  • Sampling bias

--biased results due to improper sampling (e.g., a sample of a population in which some members of the population are less likely to be included than others)

Sampling bias: an example

  • 1936 Presidential election. Literary Digest poll through telephone incorrectly predicted Alf Landon the winner
  • Problems?

--a biased sample

--response bias: respondents were more likely to express their preference; non-respondents had a different opinion

  • Rule:
  • If you wish to make inferences to the population from which the sample was drawn, a Probability sample must be used.

--each element of the population has a known non-zero probability of selection.

--Randomness is the bases for sample selection

--Tend to give approximate representation of the population

--Allow for prediction of size of error in estimation

Key concepts: sample size

  • The larger the better?
  • The main key is not size, but representativeness
  • Rule of thumb for Quantitative research

--A minimum of 30 per group

--A minimum of 10 per variable for multiple regression

  • In Qualitative research, it doesn't matter as much

-- Not trying to infer generalizability

Types of Samples

Probability

Non-Probability

Convenience

Purposive

Simple Random

Systematic Random

Multi-stage Random

Stratified Random

Cluster Random

Quota

Simple Random Sampling

  • Each element in the population has an equal AND independent probability of selection
  • Equal: every member of a population has an equal chance of being selected.
  • Independent: Selection of one individual has no influence on the selection of the next individual.

Randomly select from a numbered

list

Systematic Random Sampling

  • Each element has an equal (but NOT independent) probability of selection
  • Population size N, desired sample size n, sampling interval r=N/n.
  • Randomly select a start number and select every rth individual
  • Example: N=64, n=8, r=64/8=8. Random start number=3.

Systematic Random Sampling-cont.

  • Has same error rate as simple random sample if the list is in random order
  • Provides the benefits of implicit stratification if the list is grouped

Systematic Random Sampling-Cont.

  • Runs the risk of error if periodicity in the list matches the sampling interval
  • In this example, every 4th element is red, and red never gets sampled. If the random start number had been 4 or 8, ONLY reds would be sampled.

Multi-stage random sampling

  • Each individual in randomly sampled units have an equal chance of being selected.
  • Use simple or systematic sampling to select some sample units (companies, schools, classes, etc.)
  • Use simple or systematic sampling to select individuals from each sampling unit
  • Advantageous with large population

Stratified Random Sampling

  • Divide population into groups that differ in important ways
  • Basis for grouping must be known before sampling
  • Select random sample from within each group

Stratified Random Sampling-cont.

  • For a given sample size, reduces error compared to simple random sampling IF the groups are different from each other
  • Probabilities of selection may be different for different groups, as long as they are known
  • Oversampling small groups improves inter-group comparisons

Random Cluster Sampling-Simple

  • Population is divided into groups (states, counties, census tracts, etc.)
  • Some of the groups are randomly selected
  • For given sample size, a cluster sample has more error than a simple random sample
  • Cost savings of clustering may permit larger sample
  • Error is smaller if the clusters are similar to each other

Random Cluster Sampling-Simple

  • Cluster sampling has very high error if the clusters are different from each other
  • Cluster sampling is NOT desirable if the clusters are different
  • It IS random sampling: you randomly choose the clusters
  • But you will tend to omit some kinds of subjects

Random Cluster Sampling-
Stratified

  • Reduce the error in cluster sampling by creating strata of clusters
  • Sample one or more clusters from each stratum
  • The cost-savings of clustering with the error reduction of stratification

Strata

Stratification vs. Clustering

Stratification

  • Divide population into groups different from each other: sexes, races, ages
  • Sample randomly from each group
  • Less error compared to simple random
  • More expensive to obtain stratification information before sampling

Clustering

  • Divide population into comparable groups: schools, cities
  • Randomly sample some of the groups
  • More error compared to simple random
  • Reduces costs to sample only some areas or organizations

  • Combines elements of stratification and clustering

• First you define the clusters.

  • Then you group the clusters into strata of clusters, putting similar clusters together in a stratum.

• Then you randomly pick one (or more) cluster from each of the strata of clusters

• Then you sample the subjects within the sampled clusters (either all the subjects, or a simple random sample of them)

Stratified Cluster Sampling

Random Cluster Sampling—

Stratified

Strata

Strata

The Problem of Non-Response

  • You can randomly select people
  • But you cannot make people respond
  • Non-response destroys the generalizeability of the sample. You are generalizing to people who are willing to respond to surveys
  • If response is 90% or so, not so bad. But if it is 50%, this is a serious problem

The Problem of Non-Response-cont.

  • Multiple call-backs (or contacts) are essential for trying to reduce non-response bias
  • Samples without call-backs have high bias: cannot really be considered random samples
  • Response rates have been falling
  • It is very difficult to get above a 60% response rate
  • You do the best you can, and try to estimate the effect of the error by getting as much information as possible about the predictors of non-response.

Non-probability Samples

  • Quota
  • Judgment or Purposive
  • Convenience

Quota Sampling

  • Classify population members by some relevant variables (e.g. sex)
  • Determine the proportion of sample desired with relevant characteristics (e.g., 100 women, 100 men)
  • Fix a quota of subjects with desired characteristics for each data collector
  • No call-backs or other features to eliminate convenience factors in sample selection

Quota Vs Stratified Sampling

  • In Stratified Sampling, selection of subject is random. Call-backs are used to get that particular subject.
  • Note: Stratified sampling without call-backs may not, in practice, be much different from quota sampling.
  • In Quota Sampling, interviewer selects first available subject who meets criteria: is a convenience sample.

Judgment or Purposive Samples

  • Subjects selected for a good reason tied to purposes of research or researcher’s judgment
  • Usually Small samples, not large enough for power of probability sampling.
  • Nature of research requires small sample
  • Choose subjects with appropriate variability in what you are studying
  • Hard-to-get populations that cannot be found through screening general population

Convenience Sample

  • Subjects selected because it is easy to access them.
  • No reason tied to purposes of research.
  • Students in your class, people on campus, friends, friends’ friends
  • No external validity

Something keep in mind for random sampling

  • Heterogeneity: need larger sample to study more diverse population
  • Desired precision: need larger sample to get smaller error
  • Sampling design: smaller if stratified, larger if cluster
  • Nature of analysis: complex multivariate statistics need larger samples

Sampling in your research

  • Often a non-random selection of basic sampling frame (city, organization etc.)
  • Fit between sampling frame and research goals must be evaluated
  • Sampling frame as a concept is relevant to all kinds of research
  • Non-probability sampling means you cannot generalize beyond the sample
  • Probability sampling means you can generalize to the population defined by the sampling frame

Key Sampling Concepts

Copyright ©2002, William M.K.

Trochim

, All Rights Reserved

Types of Samples

Probability

Non-Probability

Convenience

Purposive

Simple Random

Systematic Random

Multi-stage Random

Stratified Random

Cluster Random

Quota

Simple Random Sampling

•Each element in the population

has an equal AND independent

probability of selection

•Equal: every member of a

population has an equal chance of

being selected.

•Independent: Selection of one

individual has no influence on the

selection of the next individual.

Randomly select

from a numbered

list

Systematic Random Sampling

•Each element has an equal (but NOT independent) probability of selection

•Population size N, desired sample

size n, sampling interval r=N/n.

•Randomly select a start number

and select every rthindividual

•Example: N=64, n=8, r=64/8=8.

Random start number=3.

Systematic Random Sampling -cont.

•Has same error rate as simple

random sample if the list is in

random order

•Provides the benefits of implicit

stratification if the list is grouped

Systematic Random Sampling -Cont.

•Runs the risk of error if

periodicity in the list matches

the sampling interval

•In this example, every 4

th

element is red, and red never

gets sampled. If the random

start number had been 4 or 8,

ONLY reds would be

sampled.

Stratified Random Sampling

•Divide population into

groups that differ in

important ways

•Basis for grouping must

be known before

sampling

•Select random sample

from within each group

Stratified Random Sampling -cont.

•For a given sample size, reduces error

compared to simple random sampling IF

the groups are different from each other

•Probabilities of selection may be

different for different groups, as long as

they are known

•Oversampling small groups improves

inter-group comparisons

Random Cluster Sampling -Simple

•Population is divided into groups

(states, counties, census tracts, etc.)

•Some of the groups are randomly

selected

•For given sample size, a cluster

sample has more error than a simple

random sample

•Cost savings of clustering may

permit larger sample

•Error is smaller if the clusters are

similarto each other

Random Cluster Sampling -Simple

•Cluster sampling has very

high error if the clusters are

different from each other

•Cluster sampling is NOT

desirable if the clusters are

different

•It IS random sampling: you

randomly choose the clusters

•But you will tend to omit

some kinds of subjects

Random Cluster Sampling -

Stratified

•Reduce the error in cluster

sampling by creating strata

of clusters

•Sample one or more

clusters from each stratum

•The cost-savings of

clustering with the error

reduction of stratification

Strata

Stratification vs. Clustering

Stratification

•Divide population into

groups different from each

other: sexes, races, ages

•Sample randomly from

each group

•Less error compared to

simple random

•More expensive to obtain

stratification information

before sampling

Clustering

•Divide population into

comparable groups:

schools, cities

•Randomly sample some of

the groups

•More error compared to

simple random

•Reduces costs to sample

only some areas or

organizations

Stratified Cluster Sampling

Strata

Random Cluster Sampling —

Stratified

The Problem of Non -Response

•You can randomly select people

•But you cannot make people respond

•Non-response destroys the generalizeabilityof

the sample. You are generalizing to people who

are willing to respond to surveys

•If response is 90% or so, not so bad. But if it is

50%, this is a serious problem

The Problem of Non -Response-cont.

•Multiple call-backs (or contacts) are essential for

trying to reduce non -response bias

•Samples without call -backs have high bias: cannot

really be considered random samples

•Response rates have been falling

•It is very difficult to get above a 60% response rate

•You do the best you can, and try to estimate the

effect of the error by getting as much information as

possible about the predictors of non -response.

Non-probability Samples

•Quota

•Judgment or Purposive

•Convenience

Quota Sampling

•Classify population members by some relevant

variables (e.g. sex)

•Determine the proportion of sample desired with

relevant characteristics (e.g., 100 women, 100

men)

•Fix a quota of subjects with desired

characteristics for each data collector

•No call-backs or other features to eliminate

convenience factors in sample selection

Quota Vs Stratified Sampling

•In Stratified Sampling,

selection of subject is

random. Call-backs are

used to get that particular

subject.

•Note: Stratified sampling

without call-backs may not,

in practice, be much different

from quota sampling.

•In Quota Sampling,

interviewer selects first

available subject who

meets criteria: is a

convenience sample .

Judgment or Purposive Samples

•Subjects selected for a good reason tied to

purposes of research or researcher ’s judgment

•Usually Smallsamples,not large enough for

power of probability sampling.

–Nature of research requires small sample

–Choose subjects with appropriate variability in what

you are studying

•Hard-to-get populations that cannot be found

through screening general population

Convenience Sample

•Subjects selected because it is easy to access

them.

•No reason tied to purposes of research.

•Students in your class, people on campus,

friends, friends’friends

•No external validity

Something keep in mind for random

sampling

•Heterogeneity: need larger sample to study more

diverse population

•Desired precision: need larger sample to get

smaller error

•Sampling design: smaller if stratified, larger if

cluster

•Nature of analysis: complex multivariate

statistics need larger samples

Sampling in your research

•Often a non-random selection of basic sampling

frame (city, organization etc.)

•Fit between sampling frame and research goals

must be evaluated

•Sampling frame as a concept is relevant to all

kinds of research

•Non-probability sampling means you cannot

generalize beyond the sample

•Probability sampling means you can generalize to

the population defined by the sampling frame