Introduction to Sampling

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Introduction to Sampling
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Objectives

• Understand reasons for sampling
• Know kinds of samples
• Characteristics
• Uses
• Strengths and weaknesses
• Mechanics of sample selection
• Determining size
• Process of selection
• Implications of sample for analysis

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Why Sample

• Cost or cost effectiveness
• Tradeoff between quantity and quality of data
• Lack of availability of population

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Terminology

• unit of analysis or element-unit about which
  information is collected and the basis of
  analysis.
• population-all elements or units to which
  explanation, descriptions are meant to apply.
• survey population-elements actually sampled.

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• sampling unit-element picked in samples. May be
  same as unit of analysis, but not necessarily
  (e.g. cluster samples).
• sampling frame-list from which sample picked.
  May be same as survey population, but not
  necessarily (as above)
• observation units-element from which data
  collected. Usually same as sampling units, but
  not necessarily (e.g. data on congress. offices
  collected from sample of AAs).

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• variable-a measure of some characteristic (e.g.
  how much a person makes).
• Statistic-a summary of a variable for a group.
  (e.g. mean or median income for people in the
  sample.) Varies with the sample selected
• parameter-a statistic for a population. Constant.

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• Sample Design-procedures for selecting units from
  the population for the sample.
• Sampling Fraction-percent of the population
  selected for the sample

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Types of Samples

• Almost all samples are combinations of types.
• Probability-Sample selected so that there is a
  known probability of selection for all units in
  the population.
• Non-probability-Probabilities are not known.

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Non-Probability

• Convenience-selection driven by availability of
  units.
• Purposive-selection based on need to observe
  units with specific characteristics.
• Quota-units selected so that predetermined number
  of specified types of units are selected.
• Snowball or referral-respondents nominated by
  other respondents.

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Non-probability Considerations

• Cannot calculate error due to sampling
• Typically less expensive
• May be only practical alternative
• Convenience
• Least costly
• Most susceptible to unrepresentativeness
• Purposive
• Insures that required diversity is present
• Not necessarily related to population

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• Quota
• Requires identifiable characteristic
• Makes sample representative of quota
  characteristic
• Snowball
• Useful to find small populations when there is
  connection between members
• May/likely to introduce factors making sample
  non-representative

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Probability

• Simple random sample-randomly select units in
  population.
• Systematic sample-sample every nth unit from a
  list (periodicity an issue).
• Stratified sample-samples drawn separately within
  separate strata of the population.
• Multistage/Cluster sample-sample clusters of
  units and then sample within clusters.

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Types of Stratified Samples

• Proportionate- percent of sample drawn from each
  strata equals percent of the population in the
  strata.
• Disproportionate-some strata are sampled at a
  higher rate so that a different proportion exists
  in the sample than in the population. Useful for
  obtaining sufficient number of smaller
  strata/groups.

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Reasons to Stratify Sample

• Efficient sample when groups of interest are
  small.
• Reduction in error due to sampling.

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Probability Sample Considerations

• Simple random sample
• requires inventory of units and practical way of
  getting to each one
• predictable error
• not subject to factors making unrepresentative
• Systematic sample
• requires units that are inventoried and ordered
• generally good as or better than SRS
• susceptible to error due to periodicity

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• Stratified Random-
• Similar to quota, except random sample in each
  strata
• Must have characteristic identifiable before
  sample is selected
• Allows for control of representativeness of
  strata
• Allows for efficient representation of small
  strata

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• Multistage cluster
• Good where individuals not identifiable from an
  inventory
• Error can be calculated
• Error will almost always be higher.

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Other Sampling

• Experiments
• Focus Groups
• Threshold (Quality control)

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More Terminology

• sampling distribution-distribution of estimates
  of a parameter over a large number of samples.
• standard deviation-a measure of the degree of
  variability of a set of values calculated by
  calculating the mean and differences between the
  mean and each value, squaring the differences and
  averaging them, and taking the square root.

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• standard error-measurement of the expected error
  due to sampling. It is the standard deviation of
  the values for a parameter obtained from an
  infinite number of samples.
• confidence level-probability of a specified error
  due to sampling.

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• confidence interval-the interval around a
  parameter for a sample in which the population
  parameter will be found with a specified level of
  confidence (z_score).
• sampling bias-the difference in the average
  values of parameters from an infinite number of
  samples and the population parameter.
• Power-ability to correctly determine that a
  relationship in a population exists based on a
  sample.

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Sampling error refers only to error expected from
random selection!!

• Not...
• - Error due to population sample frame
  discrepancy/non-representativeness
• - Error due to non-response
• - Measurement error

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Factors Affecting Sample Size

• The accuracy needed
• Confidence level
• The variability of what is being measured
• The size of subgroups to be analyzed
• Not usually--size of the population

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Sample Size Calculation for Simple Random Sample
and Estimation of Population Proportion
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Implications of Sample Design for Analysis

• Stratified samples require weights.
• Knowledge of population
• Standard error estimation more complicated if not
  simple random sample.
• Stratified samples
• Cluster samples