The Logic Of Sampling

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Chapter 7

• The Logic Of Sampling

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Chapter Outline

• Introduction
• A Brief History of Sampling
• Nonprobability Sampling
• The Theory and Logic of Probability Sampling

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Chapter Outline

• Populations and Sampling Frames
• Types of Sampling Designs
• Multistage Cluster Sampling
• Probability Sampling in Review

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Political Polls and Survey Sampling

• In the 2004 Presidential election, pollsters
  generally agreed that the election was too close
  to call.
• To gather this information, they interviewed
  fewer than 2,000 people.

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Election Eve Polls - U.S. Presidential
Candidates, 2004
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Election Eve Polls - U.S. Presidential
Candidates, 2004
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Election Eve Polls - U.S. Presidential
Candidates, 2004
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Bush Approval Raw Poll Data
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Question

• One of the most visible uses of survey sampling
  lies in _____________.
• political polling
• probability sampling
• core sampling
• traditional polling

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Answer A

• One of the most visible uses of survey sampling
  lies in political polling.

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Observation and Sampling

• Polls and other forms of social research rest on
  observations.
• The task of researchers is to select the key
  aspects to observe (sample).
• Generalizing from a sample to a larger population
  is called probability sampling and involves
  random selection.

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Nonprobability Sampling

• Technique in which samples are selected in a way
  that is not suggested by probability theory.
• Examples include reliance on available subjects
  as well as purposive (judgmental), quota, and
  snowball sampling.

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Types of Nonprobability Sampling

• Reliance on available subjects
• Only justified if less risky sampling methods are
  not possible.
• Researchers must exercise caution in generalizing
  from their data when this method is used.

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Types of Nonprobability Sampling

• Purposive or judgmental sampling
• Selecting a sample based on knowledge of a
  population, its elements, and the purpose of the
  study.
• Used when field researchers are interested in
  studying cases that dont fit into regular
  patterns of attitudes and behaviors

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Types of Nonprobability Sampling

• Snowball sampling
• Appropriate when members of a population are
  difficult to locate.
• Researcher collects data on members of the target
  population she can locate, then asks them to help
  locate other members of that population.

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Types of Nonprobability Sampling

• Quota sampling
• Begin with a matrix of the population.
• Data is collected from people with the
  characteristics of a given cell.
• Each group is assigned a weight appropriate to
  their portion of the population.
• Data should represent the total population.

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Question

• ______________sampling occurs when units are
  selected on the basis of prespecified
  characteristics.
• snowball
• quota
• purposive
• probability

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Answer B

• Quota sampling occurs when units are selected on
  the basis of prespecified characteristics.

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Informant

• Someone who is well versed in the social
  phenomenon that you wish to study and who is
  willing to tell you what he or she knows about it.

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Probability Sampling

• Used when researchers want precise, statistical
  descriptions of large populations.
• A sample of individuals from a population must
  contain the same variations that exist in the
  population.

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Populations and Sampling Frames

• Findings based on a sample represent the
  aggregation of elements that compose the sampling
  frame.
• Sampling frames do not always include all the
  elements their names imply.
• All elements must have equal representation in
  the frame.

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A Population of 100 Folks

• Sampling aims to reflect the characteristics and
  dynamics of large populations.
• Lets assume our total population only has 100
  members.

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Sample of Convenience Easy but Not Representative
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Types of Sampling Designs

• Simple random sampling (SRS)
• Systematic sampling
• Stratified sampling

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Representativeness

• Representativeness - Quality of a sample having
  the same distribution of characteristics as the
  population from which it was selected.
• EPSEM - Equal probability of selection method. A
  sample design in which each member of a
  population has the same chance of being selected
  into the sample.

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Question

• ______________describes a sample whose aggregate
  characteristics closely approximate the aggregate
  characteristics of the population.
• exclusion
• probability sampling
• EPSEM
• representativeness
• none of these choices

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Answer D

• Representativeness describes a sample whose
  aggregate characteristics closely approximate the
  aggregate characteristics of the population.

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Population

• The theoretically specified aggregation of study
  elements.
• Study population - Aggregation of elements from
  which the sample is actually selected.
• Element - Unit about which information is
  collected and that provides the basis of analysis.

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Random selection

• Each element has an equal chance of selection
  independent of any other event in the selection
  process.

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Sampling unit

• Element or set of elements considered for
  selection in some stage of sampling.

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Parameter

• Summary description of a given variable in a
  population.

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A Population of 10 People with 09
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The Sampling Distribution of Samples of 1

• In this example, the mean amount of money these
  people have is 4.50 (45/10).
• If we picked 10 different samples of 1 person
  each, our estimates of the mean would range all
  across the board.

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Sampling Distributions
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Sampling Distributions
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Sampling Distributions
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Sampling Distributions
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Range of Possible Sample Study Results

• Shifting to a more realistic example, lets
  assume that we want to sample student attitudes
  concerning a proposed conduct code.
• Lets assume 50 of the student body approves
  and 50 disapproves - though the researcher
  doesnt know that.

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Results Produced by Three Hypothetical Studies

• Assuming a large student body, lets suppose we
  selected three different samples, each of
  substantial size.
• We would not expect those samples to perfectly
  reflect attitudes in the whole student body, but
  they should come close.

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Statistic

• Summary description of a variable in a sample.

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Sampling Error

• The degree of error to be expected of a given
  sample design.

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Confidence Level

• The estimated probability that a population
  parameter lies within a given confidence
  interval.
• Thus, we might be 95 confident that between 35
  and 45 of all voters favor Candidate A.
• Confidence interval - The range of values within
  which a population parameter is estimated to lie.

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Sampling Frame

• That list or quasi list of units composing a
  population from which a sample is selected.
• If the sample is to be representative of the
  population, it is essential that the sampling
  frame include all (or nearly all) members of the
  population.

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The Sampling Distribution

• If we were to select a large number of good
  samples, we would expect them to cluster around
  the true value (50), but given enough such
  samples, a few would fall far from the mark.

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Review of Populations and Sampling Frames
Guidelines

• Findings based on a sample represent only the
  aggregation of elements that compose the sampling
  frame.
• Sampling frames do not include all the elements
  their names might imply. Omissions are
  inevitable.
• To be generalized, all elements must have equal
  representation in the frame.

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Question

• A _______________ is the list or quasi list of
  elements from which a probability sample is
  selected.
• confidence level
• confidence interval
• sampling frame
• systematic sample
• none of these choices

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Answer C

• A sampling frame is the list or quasi list of
  elements from which a probability sample is
  selected.

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Simple Random Sampling

• Feasible only with the simplest sampling frame.
• Not the most accurate method available.

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A Simple Random Sample
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Systematic Sampling

• Slightly more accurate than simple random
  sampling.
• Arrangement of elements in the list can result in
  a biased sample.

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Sampling ratio

• Proportion of elements in the population that are
  selected.

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Stratification

• Grouping of units composing a population into
  homogenous groups before sampling.
• This procedure, which may be used in conjunction
  with simple random, systematic, or cluster
  sampling, improves the representativeness of a
  sample, at least in terms of the stratification
  variables.

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Stratified Sampling

• Rather than selecting sample for population at
  large, researcher draws from homogenous subsets
  of the population.
• Results in a greater degree of representativeness
  by decreasing the probable sampling error.

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A Stratified, Systematic Sample with a Random
Start.
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Cluster Sampling

• A multistage sampling in which natural groups are
  sampled initially with the members of each
  selected group being subsampled afterward.

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Multistage Cluster Sampling

• Used when it's not possible or practical to
  create a list of all the elements that compose
  the target population.
• Involves repetition of two basic steps listing
  and sampling.
• Highly efficient but less accurate.

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Probability Proportionate to Size (PPS) Sampling

• Sophisticated form of cluster sampling.
• Used in many large scale survey sampling projects.

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Weighting

• Giving some cases more weight than others.

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Probability Sampling

• Most effective method for selection of study
  elements.
• Avoids researchers biases in element selection.
• Permits estimates of sampling error.

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Quick Quiz
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• 1. Political polling rests on _____________.
• subtle innuendos
• field research
• observations
• none of these choices

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Answer C

• Political polling rests on observations.

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• 2. _____________ sampling is often employed in
  field research whereby each person interviewed
  may be asked to suggest additional people for
  interviewing.
• snowball
• quota
• purposive
• probability

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Answer A

• Snowball sampling is often employed in field
  research whereby each person interviewed may be
  asked to suggest additional people for
  interviewing.

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• 3. ______________ is the general term for samples
  selected in accord with probability theory.
• nonprobability analyses
• correlation coefficients
• probability sampling
• none of these choices

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Answer C

• Probability sampling is the general term for
  samples selected in accord with probability
  theory.

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• 4. A____________ population is that aggregation
  of elements from which a sample is actually
  selected.
• theoretical
• small
• large
• concept
• study

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Answer E

• A study population is that aggregation of
  elements from which a sample is actually selected.

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Question

• 5. Cluster sampling may be used when it is
  impossible to compile an exhaustive list of the
  elements composing the target population.
• True
• False

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Answer True

• Cluster sampling may be used when it is
  impossible to compile an exhaustive list of the
  elements composing the target.