Introductory Sampling Theory

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Introductory Sampling Theory
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Various types of distributions

• Population
• Sample
• Sampling
• (Normal)

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Population Distribution

• Distribution of the attributes of a population or
  universe.
• May have any shape.
• Skewed left or right
• Flat or peaked

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Sample Distribution

• Distribution of the attributes of a sample drawn
  from a specified population or universe
• Shape will approximate the population or universe
  distribution
• The larger the sample size, the closer the
  approximation, in all likelihood.

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Sampling Distribution

• Distribution of the means (could be other
  statistics) of all possible samples
• Theoretical distribution since all possible
  samples cannot be drawn
• Will always be normal, because of the laws of
  probability

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Normal Distribution

• Symmetrical
• Defined by standard deviations (standard errors)
• Can predict what proportion of cases will fall
  within a specified range of values

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Relation among distributions

• Never know the population characteristics
• Population characteristics are parameters
• Thats why research is done
• Sample distribution shows characteristics
• Can guess at what the population characteristics
  are
• Larger sample size give greater precision and
  confidence

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Variance

• The mean of the squared deviations

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Variance
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Standard Deviation
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Standard error of the mean
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Determining Sample Size
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Factors affecting sample size

• Variability
• Confidence level
• Precision

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2
confidence
n
(variability)
precision
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2
confidence
n
(pq)
precision
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Five types of sampling

• Random (or simple random)
• Stratified random
• Cluster sampling
• Systematic
• Area probability

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Random

• Every subject is known
• Every subject has equal or know probability of
  selection

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Random

• Advantages
• Dont have to know the characteristics of a
  population
• Tends to be completely representative
• Disadvantages
• Complete list is difficult to obtain
• Always a chance of drawing a misleading sample
• Needs a larger sample size

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Stratified random

• Population classified into two or more strata
• Sample drawn from each one
• Cases drawn in proportion to representation in
  population
• Cases can be oversampled, if needed

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Stratified random

• Advantages
• Can be sure no relevant group is omitted
• Greater precision possible with lower sample size
• Disadvantages
• Need to know about the population
• Proportions must be known
• Difficulty in locating cases

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Systematic random

• Selection of every nth name
• Usually quicker

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Cluster

• Done for efficiency
• Population is broken down into smaller groups
• Useful when no sampling frame is available

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Area

• Combines cluster and systematic
• Based on geography