The Logic of Sampling

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Chapter 7

• The Logic of Sampling

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What is sampling?

• Sampling is the process of systematically
  selecting observations for study

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Why is sampling important in social science?

• From the viewpoint of sampling, whats the
  difference between a chemist studying the atomic
  properties of methane and a political scientist
  studying the political opinions of the American
  electorate?

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Other reasons for sampling

• The population is very large, and resources
  (e.g., time, money, personnel) are insufficient
  to collect information from all members.
• It is impossible to gain access to every member
  of the population.
• Research is in exploratory or pretesting phase.

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Two types of sampling designs

• (Sampling design - a plan describing how a study
  sample will be chosen).
• 1. Nonprobability sampling design a sample that
  does not use mathematical probability theory in
  its design.
• 2. Probability sampling design a sample
  selected in accordance with mathematical
  probability theory, typically involving some
  random-selection mechanism

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1. Nonprobability sampling designs

• (1) Reliance on available subjects
• (2) Snowball sampling
• (3) Purposive or judgment sampling
• (4) Voluntary response sampling
• (5) Quota sampling

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(1) Reliance on available subjects

• The researcher chooses units on the basis that
  they are easily accessible to study
• Also called availability sampling or convenience
  sampling
• Used in pretesting, exploratory research, or
  situations involving limited resources
• Even when justified on the grounds of
  feasibility, researchers should not generalize
  from the data.
• Example Kings County Schools (CA)

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(2) Snowball sampling

• The researcher starts with one person or larger
  unit, then asking that person to name others who
  would be interested in participating, finding
  those people and asking them to suggest others,
  etc.
• Most appropriate when members of a special
  population are difficult to locate, but a few are
  known.
• Used primarily for exploratory purposes, since
  representativeness is questionable.

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(3) Purposive or judgment sampling

• Researcher selects units into the sample on the
  basis of her/his judgment about which ones will
  be the most useful or representative
• Used for pretesting, exploratory research, or
  instances in which certain types of units need to
  be studied for theoretical purposes
• Example Deviant cases sample - study cases that
  dont fit into the more regular pattern to gain
  insight into the pattern.
• Example Sampling radical right and radical left
  political organizations to study the extremes of
  political thought

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(4) Voluntary response sampling

• Researcher uses units who volunteer to be members
  of the sample.
• Sample members respond to an appeal from the
  researcher to become part of the study.
• Examples Kings County Schools (CA)

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(5) Quota sampling

• Researcher selects units into the sample on the
  basis of characteristics of the target population
  (specified in the quota matrix), so that the
  total sample will have the same distribution of
  characteristics as the target population.
• However, units are NOT selected randomly from
  within cells of the quota matrix.

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Example of a simple quota matrix (one variable)
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Example of more complex quota matrix (two
variables)
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(5) Quota sampling - problems

• Since the selection of units within cells of the
  quota matrix is not random, biases may exist in
  the sample.
• If there are errors or omissions in the list of
  target population units, the quota matrix may not
  accurately depict the characteristics of the
  population

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2. Probability sampling designs

• Advantages
• Probability samples avoid conscious or
  unconscious sampling bias.
• Sampling bias - those selected for the sample are
  not representative or typical of the larger
  population, often because of some subjective bias
  of the researchers.
• Probability samples permit quantitative estimates
  of the degree to which a sample is likely to
  represent the population.

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Probability sampling terminology

• Element the unit of analysis, the unit about
  which information is collected and that provides
  the basis for the analysis.
• Population the theoretically specified
  aggregation of elements.
• Study population the collection of elements
  from which the sample is actually selected.

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Population vs. Study population
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Probability sampling terminology

• Sampling frame the list of elements in the
  study population from which the sample is
  actually selected.
• Parameter the summary description of a given
  variable in a population.
• Statistic the summary description of a given
  variable in a sample.

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2. Probability sampling designs

• (1) Simple random sampling
• (2) Systematic sampling with a random start
• (3) Stratified random sampling
• (4) Multistage cluster sampling

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(1) Simple random sampling

• EPSEM ("Equal Probability of Selection Method") -
  each element on the sampling frame has an equal
  chance of selection, and the selection of any one
  element is independent of the selection of any
  other element.
• Examples Kings County (One physical and one
  computer technique).
• Possible problems with physical techniques Draft
  Lottery of 1970

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How to draw a simple random sample

• On the L drive, open
• \faculty\jhonnold\BABBIE BASICS\n90id.sav
• Using (1) Table of random numbers (next slide)

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Table of random numbers

• N90
• n10

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How to draw a simple random sample - SPSS

• Change random number seed
• Transform Random number seed (Pick any number
  between 1 and 2,000,000,000)
• Select the sample
• Data Select cases Random sample of cases
  Sample
• Exactly 10 cases from the first 90 cases

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(2) Systematic sampling

• Every kth (e.g., every 4th, every 10th) element
  in the sampling frame is chosen (systematically)
  for inclusion in the sample after a random start
  in the first sampling interval.
• Sampling interval (k) - the standard distance
  between elements selected into the sample
  population size/sample size (e.g.,
  10,000/50020).
• Sampling ratio (1/k) - the proportion of elements
  in the sampling frame that are selected into the
  sample sample size/population size (e.g.,
  500/10,0001/20).

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• After the sampling interval is determined, make a
  random start in the first sampling interval, then
  select every kth element until reaching the end
  of the sampling frame.
• Example of systematic sampling from the Kings
  County site.
• On the L drive, open
• \faculty\jhonnold\BABBIE BASICS\n90id.sav

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(3) Stratified random sampling

• The researcher chooses characteristics of the
  population to represent accurately, without error
  (e.g., age, gender, class standing), divides the
  population into homogeneous groups (strata) on
  the basis of these characteristics, then samples
  randomly from the strata.

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How to draw a stratified random sample

• Decide which population characteristics you want
  to represent accurately.
• Ideally, these will be characteristics that would
  affect the results, if they were not represented
  accurately. You will be limited to
  characteristics on which you have actual
  population data.
• (2) Divide the sampling frame into strata
  (groups) on the basis of these characteristics
• (3) Randomly sample the desired number from each
  group, so that each group is represented in the
  sample in proportion to its representation in the
  population.

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Stratification by age
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Quota vs. stratified sampling
Quota
Stratified
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Examples of stratified random sampling

• Example from Kings County.
• On the L drive, open
• \faculty\jhonnold\BABBIE BASICS\n90sort.sav

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(4) Multistage cluster sampling

• Used when a list of all of the elements in the
  study population does not exist (e.g., the
  American adult population, all college students
  in the U.S.).

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Steps in multistage cluster sampling Two stages
example

• Naturally occurring groups (clusters) of elements
  in the population are listed, and a sample of
  clusters is selected using a probability method
• From the selected clusters, lists of elements are
  developed, and a sample of elements is selected
  from each selected cluster using a probability
  method.

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Advantages/Disadvantages of cluster sampling

• Advantages of cluster sampling
• Convenient for geographically dispersed
  populations (see Area Probability Sampling)
• Reduced travel costs to contact sample elements
• Unavailability of sampling frame prohibits use of
  other methods
• Disadvantages of cluster sampling
• Reduced efficiency in representing the population
  when the cluster elements are similar
• Existence of two or more stages creates increased
  sampling error

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Multistage cluster sampling example
Problem - Select a probability sample of 60
V.C.U. students using a cluster sampling method.
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Area probability sample Example GSS sample of
American adults

• There is no list of American adults, so instead
  we use multistage cluster sampling techniques and
  list all counties in the U.S.
• From the list of counties, we select a subsample
  of counties.
• From this subsample, we list smaller and smaller
  areas, until we reach the block level.
• At the block level, we send our interviewers to
  random households.
• Graphic illustration

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Are probability samples always perfectly
representative?

• NO!
• Sampling error - Entirely by chance, you may draw
  a probability sample whose statistics do not
  accurately represent the parameters of the
  population.
• If the technique has been properly executed and
  the sample is large (e.g., 1,500 in GSS),
  sampling error is likely to be small.
• Probability samples can be used to estimate the
  range within which population parameters should
  fall (Chapter 16).

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Recall advantages of probability sampling

• Probability samples avoid conscious or
  unconscious sampling bias on the part of the
  researchers.
• Probability samples permit quantitative estimates
  of the degree to which a sample is likely to
  represent the population.

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Other sources of error

• Even if a probability sample is unlikely to be
  subject to substantial sampling error, sampling
  error is not the only source of error in
  research.
• Some nonsampling errors in a survey
• Missing data, data entry errors, analysis errors
• Unclear definitions of concepts, defective data
  collection instruments
• Interviewer errors

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Final notes

• Care must be taken in all phases of the research
  project to minimize both sampling and nonsampling
  errors.
• If possible to use, probability samples are
  preferable to nonprobability samples.

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Sampling as practiced by experts

• For example
• Mathematica Policy Research National Opinion
  Research Center (GSS).
• However, the basic techniques are the same.