Determining How to Select a Sample

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Determining How to Select a Sample
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Basic Concepts in Sampling

• Population the entire group under study as
  defined by research objectives
• Researchers define populations in specific terms
  such as heads of households located in areas
  served by the company who are responsible for
  making the pest control decision.

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Basic Concepts in Sampling

• Sample a subset of the population that should
  represent the entire group
• Sample unit the basic level of investigation
• Census an accounting of the complete population

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Basic Concepts in Sampling

• Sampling error any error in a survey that occurs
  because a sample is used
• A sample frame a master list of the entire
  population
• Sample frame error the degree to which the
  sample frame fails to account for all of the
  populationa telephone book listing does not
  contain unlisted numbers

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Reasons for Taking a Sample

• Practical considerations such as cost and
  population size
• Inability of researcher to analyze huge amounts
  of data generated by census
• Samples can produce precise results

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Two Basic Sampling Methods

• Probability samples ones in which members of the
  population have a known chance (probability) of
  being selected into the sample
• Non-probability samples instances in which the
  chances (probability) of selecting members from
  the population into the sample are unknown

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Probability Sampling Methods

• Simple random sampling
• Systematic sampling
• Cluster sampling
• Stratified sampling

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Probability Sampling Methods
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Probability SamplingSimple Random Sampling

• Simple random sampling the probability of being
  selected into the sample is known and equal for
  all members of the population
• E.g., Blind Draw Method
• Random Numbers Method (see MRI 12.1, p. 335)

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Probability SamplingSimple Random Sampling

• Advantage
• Known and equal chance of selection
• Disadvantages
• Complete accounting of population needed
• Cumbersome to provide unique designations to
  every population member

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Probability SamplingSystematic Sampling

• Systematic sampling way to select a random
  sample from a directory or list that is much more
  efficient than simple random sampling
• Skip intervalpopulation list size/sample size

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Probability SamplingSystematic Sampling

• Advantages
• Approximate known and equal chance of
  selectionit is a probability sample plan
• Efficiencydo not need to designate every
  population member
• Less expensivefaster than SRS
• Disadvantage
• Small loss in sampling precision

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Probability SamplingCluster Sampling

• Cluster sampling method in which the population
  is divided into groups, any of which can be
  considered a representative sample
• Area sampling

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Probability SamplingCluster Sampling

• Advantage
• Economic efficiencyfaster and less expensive
  than SRS
• Disadvantage
• Cluster specification errorthe more homogeneous
  the clusters, the more precise the sample results

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Cluster Sampling

• In cluster sampling the population is divided
  into subgroups, called clusters.
• Each cluster should represent the population.
• Area sampling is a form of cluster sampling the
  geographic area is divided into clusters.

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Cluster Sampling

• One cluster may be selected to represent the
  entire area with the one-step area sample.
• Several clusters may be selected using the
  two-step area sample.

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A Two-Step Cluster Sample

• A two-step cluster sample (sampling several
  clusters) is preferable to a one-step (selecting
  only one cluster) sample unless the clusters are
  homogeneous.

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Stratified Sampling

• When the researcher knows the answers to the
  research question are likely to vary by subgroups

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Stratified Sampling

• Research Question To what extent do you value
  your college degree? Answers are on a five point
  scale 1 Not valued at all and 5 Very highly
  valued
• We would expect the answers to vary depending on
  classification. Freshmen are likely to value
  less than seniors. We would expect the mean
  scores to be higher as classification goes up.

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Stratified Sampling

• Research Question To what extent do you value
  your college degree?
• We would also expect there to be more agreement
  (less variance) as classification goes up. That
  is, seniors should pretty much agree that there
  is value. Freshmen will have less agreement.

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Stratified Sampling
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Probability SamplingStratified Sampling

• Stratified sampling method in which the
  population is separated into different strata and
  a sample is taken from each stratum
• Proportionate stratified sample
• Disproportionate stratified sample

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Probability SamplingStratified Sampling

• Advantage
• More accurate overall sample of skewed
  populationsee next slide for WHY
• Disadvantage
• More complex sampling plan requiring different
  sample size for each stratum

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Stratified Sampling

• Why is stratified sampling more accurate when
  there are skewed populations?
• The less variance in a group, the less sample
  size it takes to produce a precise answer.
• Why? If 99 of the population (low variance)
  agreed on the choice of Brand A, it would be easy
  to make a precise estimate that the population
  preferred Brand A even with a small sample size.

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Stratified Sampling

• But, if 33 chose Brand A, and 23 chose B, and
  so on (high variance) it would be difficult to
  make a precise estimate of the populations
  preferred brandit would take a larger sample
  size

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Stratified Sampling

• Stratified sampling allows the researcher to
  allocate more sample size to strata with less
  variance and less sample size to strata with less
  variance. Thus, for the same sample size, more
  precision is achieved.
• This is normally accomplished by disproportionate
  sampling. Seniors would be sampled LESS than
  their proportionate share of the population and
  freshmen would be sampled more.

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Stratified Sampling

• Note that we would expect this question to be
  answered differently depending on student
  classification. Not only are the means
  different, variance is less as classification
  goes upSeniors tend to agree more than Freshmen!
  

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Nonprobability Sampling

• With nonprobability sampling methods selection is
  not based on fairness, equity, or equal chance.
• Convenience sampling
• Judgment sampling
• Referral sampling
• Quota sampling

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Nonprobability Sampling
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Nonprobability Sampling

• May not be representative but they are still used
  very often. Why?
• Decision makers want fast, relatively inexpensive
  answers nonprobability samples are faster and
  less costly than probability samples.

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Nonprobability Sampling

• May not be representative but they are still used
  very often. Why?
• Decision makers can make a decision based upon
  what 100 or 200 or 300 people saythey dont feel
  they need a probability sample.

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Nonprobability Sampling

• Convenience samples samples drawn at the
  convenience of the interviewer
• Error occurs in the form of members of the
  population who are infrequent or nonusers of that
  location

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Nonprobability Sampling

• Judgment samples samples that require a
  judgment or an educated guess as to who should
  represent the population
• Subjectivity enters in here, and certain members
  will have a smaller chance of selection than
  others

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Nonprobability Sampling

• Referral samples (snowball samples) samples
  which require respondents to provide the names of
  additional respondents
• Members of the population who are less known,
  disliked, or whose opinions conflict with the
  respondent have a low probability of being
  selected

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Nonprobability Sampling

• Quota samples samples that use a specific quota
  of certain types of individuals to be interviewed
• Often used to ensure that convenience samples
  will have desired proportion of different
  respondent classes

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Online Sampling Techniques

• Random online intercept sampling relies on a
  random selection of Web site visitors
• Invitation online sampling is when potential
  respondents are alerted that they may fill out a
  questionnaire that is hosted at a specific Web
  site

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Online Sampling Techniques

• Online panel sampling refers to consumer or
  other respondent panels that are set up by
  marketing research companies for the explicit
  purpose of conducting surveys with representative
  samples
• Other online sampling approaches

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Developing a Sample Plan

• Sample plan definite sequence of steps that the
  researcher goes through in order to draw and
  ultimately arrive at the final sample

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Developing a Sample Plan

• Define the relevant population.
• Obtain a listing of the population.
• The incidence rate is the percentage of people on
  a list who qualify as members of the population
• Design the sample plan (size and method).

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Developing a Sample Plan

• Draw the sample.
• Substitution methods
• Drop-down substitution
• Oversampling
• Resampling

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Developing a Sample Plan

• Validate the sample.
• Sample validation is a process in which the
  researcher inspects some characteristic(s) of the
  sample to judge how well it represents the
  population.
• Resample, if necessary.