Sampling

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Sampling

• Representing populations

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Lets say you wanted to know whether people over
60 used the Internet for medical information

• You could save a bundle on providing medical
  information by putting up a web page with the
  necessary information rather than contacting
  people directly or having them call their doctors
  for it

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But how could you determine whether they would
use it?

• Track them all down and ask them?
• Practically impossible
• Prohibitively expensive
• Not really necessary

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So

• Talk to some of them and estimate what the rest
  would say
• But which ones should be talked to?
• Sampling theory guides us in the choice of people
  to measure as well as estimating what the entire
  population would have answered

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Samples and Sampling

• A sample is a subgroup drawn from a larger
  population that is meant to represent all members
• Sampling refers to the actions taken to draw a
  sample from a population

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Examples of Sampling

• Small portions of food are given away in
  supermarkets in order to get you to buy the
  product (I made it through grad school this way)
• Geologists drill out deep cylinders of rock to
  determine whether to drill for oil
• Farmers pick ears of corn from many parts of the
  field to check for insects
• Short portions of songs are downloaded from the
  Internet by prospective buyers

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Sampling frame

• A list of the units of the population used to
  draw the sample
• A sampling frame must closely reflect population
• (e.g., telephone books, voter registration lists)

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Parameters and statistics

• Parameter
• A true characteristic of a population
• Average age of Lexingtonians
• Statistic
• A numeric summary of a variable in a sample
• Mean age of a sample of Lexingtonians
• Sample statistics are computed in order to
  estimate population parameters.

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Random sample

• The best method for representing the entire
  population with a sample is to use a random
  sample
• In a random sample, each person in the population
  of interest has an equal and known chance of
  being selected
• allows researchers to calculate sampling error

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Nonrandom samples

• In nonrandom samples, the likelihood of inclusion
  of any individual elements from the population
  into the sample is not known
• Means that many of the advantages of statistical
  analyses are lost

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The researcher may choose a nonrandom sample for
several reasons

• Purpose of the study
• explore variable relationships (experiment)
• exploratory research
• Cost versus value
• probability sample may be too expensive
• Low incidence of preferred respondents
• black lawyers
• Willingness to participate
• focus groups
• Time constraints
• Exploratory study

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Types of nonrandom samples

• Convenience sample (also called haphazard or
  accidental sample)
• Volunteer sample
• Purposive sample
• Quota sample
• Network sample

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Convenience sample

• Respondents are included based on availability
• students in introductory courses
• mall intercepts
• movie studio tours

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Volunteer sample

• Respondents choose to participate in the study
• clinical trials
• consumer juries
• extra-credit psych experiments

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Volunteers are different

• higher educational status
• higher occupational status
• greater need for approval
• higher IQ
• lower authoritarianism
• more sociable
• more arousal-seeking
• less conventional
• tend to be first children
• younger

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Purposive sample

• Subjects selected on the basis of specific
  characteristics or qualities
• users of a particular brand
• young mothers with small children
• doctors
• members of a fan club
• target market members

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Quota sample

• respondents are selected nonrandomly according
  on the basis of their known proportion in a
  population (Frey et al., 2000)
• Large/medium/small hospitals
• Caucasian/Black/Asian
• Heavy/medium/light users
• Responses may be weighted according to population
  proportion

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Network sample

• Snowball sample
• ask respondents to recommend additional
  sources/respondents
• cheaper
• helps identify people with certain
  characteristics
• aids in respondent compliance
• identify networks of people

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Random samples

• Simple random sample
• Systematic random sample
• Stratified random sample
• Cluster sample

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Simple random sample (SRS)

• The simple random sample is a case where each
  element has an equal chance of being selected
  into the sample
• Lottery
• Random number table
• Roulette wheel
• Random digit dialing
• Statistics often assume a SRS

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Systematic random sampling

• A random sample that chooses every nth
  person/text from a complete list of a population
  after starting at a random point. (Frey et al.,
  2000)
• For example, if you have a sampling frame of 600
  elements and you need a sample of 100, then you
  would have to pick every 6th name. You randomly
  choose the first name--it turns out to be the 4th
  element. You then choose the 4th, 10th, 16th,
  22nd, etc.

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Stratified random sample

• A sample developed by first splitting the
  population based on some important characteristic
  and sampling randomly from within categories
• e.g. age, gender, race, income
• random samples are taken from within each of the
  subpopulations

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Cluster sampling

• Larger groupings of individual sample elements
  are chosen, then the elements are measured
• Usually geographic areas

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Cluster sampling

• Advantages
• Only part of the population needs to be
  enumerated
• Costs reduced
• Cluster estimates can be compared to population
  numbers

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Cluster sampling

• Disadvantages
• Sampling errors are likely
• Clusters may not be representative of the
  population
• Number and size of clusters is important
• Each subject or unit must be assigned to a
  specific cluster

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Multi-stage sampling

• Sample large groups/clusters, then sample smaller
  units within the groups, and so on
• metropolitan area
• county
• block
• residence
• individual

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Sample Size

• Generally speaking, the larger the better
• But quality is most important
• Though people find it hard to believe, you can
  make some pretty good estimates of very large
  populations from rather small samples
• National polls can be pretty accurate with 600
  respondents

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Sample size

• There is a law of diminishing returns
• additional units add less and less precision
• The first respondent is the most valuable, the
  second is second-most, etc.
• Will often be determined by time and cost
  considerations

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Sampling error

• A number that expresses how much the
  characteristics of a sample probably differ from
  the characteristics of its population (Frey et
  al., 2000)
• Sampling error can be estimated for random
  samples
• this is nonsystematic error variance

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Sampling error

• Two key components of sampling error estimates
  are confidence levels and confidence intervals
• We express the accuracy of our sample statistics
  in terms of a level of confidence that the
  statistics fall within a specified interval from
  the parameter. (Babbie)
• tradeoff between confidence level and confidence
  interval

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Example

• Research finds that 45 of males say that they
  have broken the speed limit by 15 mph in the last
  two months.
• The researcher is 99 confident that the actual
  percent is between 42 and 48.
• That is, if the researcher took 100 samples, she
  would expect that in 99 of them the estimate of
  the of males speeding by 15 mph would fall
  between 42 48.

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So

• We use samples to estimate population parameters
  because our estimates can be pretty close while
  drastically reducing the costs of carrying out
  the research
• Samples are either random or nonrandom
• Random samples allow us to estimate the sampling
  error attached to statistics describing the sample

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• Nonrandom samples are used when random samples
  are too expensive or impractical
• They employ methods other than randomization
  meant to increase their representativeness
• A number of different types of random and
  nonrandom sampling can be used to reduce costs or
  improve sample quality