Practical Aspects of Sampling

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Practical Aspects of Sampling

• An Overview

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Why Sample?
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Why Sample?

• Samples are taken to obtain information about
  populations.
• Sample estimators are computed to estimate
  parameters of the the population from which the
  sample was drawn.

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Advantages

• Complete enumeration of all sample units in the
  entire universe is often unnecessary to obtain
  reasonably accurate results.

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Advantages

• An examination of the entire population is often
  too costly, too time-consuming, and impractical
  (if not impossible).

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Advantages

• In the case of destructive testing, the sample
  elements or units must be destroyed or must be
  consumed to obtain necessary measurements.

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Precision

• The standard error se is a measure of
  precision. A smaller se, other things remaining
  the same, means more precision
• .....that is, less variance in the sampling.

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Sample Size

• for a mean
• n z2 ?2 / e2
• where
• e, the sampling error, is the difference between
  sample mean and population mean
• e is expressed in units

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Sample Size

• for a proportion -
• n z2 p (1 p) / e2
• where
• e, the sampling error, is the difference between
  sample proportion and population proportion
  e
  is expressed in percentage points

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Sample Size
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Errors

• Sampling (internal) Error
• The fact that a sample was taken, the sample
  statistic is expected to deviate from the
  population parameter.

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Errors

• Non-Sampling (external) Error
• The practical considerations in taking a sample.
  
• recording errors
• processing errors

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Errors

• Bias
• Most insidious to detect ....
• poorly defined universe
• inadequate sampling design
• improperly worded questions
• distorted answers
• convenience sampling

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Errors

• The sampling error refers to the extent to which
  the sample values on some variable of importance
  to the research differ from those of the
  population from which it was drawn.

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Types of RandomSamples
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Simple Random

• with replacement
• without replacement

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Stratified

• When the population is heterogeneous overall, but
  within it there are homogeneous populations
  (strata) the population is stratified.

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Systematic

• Selecting a random sample, as opposed to the
  simple random selection technique.
• Select the K-th item.
• Draw every I-th item.

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Cluster

• Another modified random sample design -- requires
  that the sample unites be grouped in clusters in
  the universe.
• Not grouped by homogeneous strata in the
  population.

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Multistage

• The selection procedure takes place in a
  hierarchy of stages.
• first primary sample unit
• second second sample unit
• third tertiary sample unit
• . . . . .
• last final (or ultimate) sample unit

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Multistage - An Example

• The president of Supermarkets, Inc. decided to
  sample purchases at 150 stores in the US.
• The first stage is to select, on the basis of
  clustering (save travel time), 15 of the 150
  stores.

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Multistage - An Example

• The researcher recommends that cash register
  files be randomly selected at each of the 150
  stores. second stage
• Then select every 20th purchase in a file using a
  random start. final stage

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Comparison of Survey Sampling Designs
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Simple Random

• How to Select
• assign numbers to elements using random numbers
  table

• Strengths/Weaknesses
• basic, simple, often costly
• must assign a number to each element in target
  population

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Stratified

• How to Select
• divide population into groups that are similar
  within and different between variable of interest

• Strengths/Weaknesses
• with proper strata, can produce very accurate
  estimates.
• less costly than simple random sampling
• must stratify target population correctly

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Stratified

• One of the main reasons for using a stratified
  sample is that stratifying has the effect of
  reducing sampling error for a given sample size
  to a level lower than that of an simple random
  sample of the same size.

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Stratified

• This is so because of a very simple principle
  the more homogeneous a population is on the
  variables being studied, the smaller the sample
  size needed to represent it accurately.
• Stratifying makes each sub-sample more
  homogeneous by eliminating the variation on the
  variable that is used for stratifying.

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Systematic

• How to Select
• select every K-th element are from a list after
  a random start

• Strengths/Weaknesses
• produces very accurate estimates when elements in
  population exhibit order
• used when pop. size not known
• simplifies selection process

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Cluster

• How to Select
• randomly choose clusters and sample all elements
  within each cluster

• Strengths/Weaknesses
• with proper clusters, can produce accurate
  estimates
• useful when sample frame not available or travel
  costs high
• must cluster target population correctly

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Convenience

• In Dining Commons at dinner
• In Student Union
• In classes in which you are enrolled
• Data available in Library
• friend knows somebody ...

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References

• Monette, Duane R., et al. Applied Social
  Research New York Holt, Rinehart and Winston,
  1986.
• Levine, David, et al. Statistics for Managers,
  Second Edition. Upper Saddle River, NJ
  Prentice-Hall, 1999.

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Mini-Cases

• Work as a team
• decide best sampling technique

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Sacramento River Bike Trail
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Scenario 1

• You have been hired by the County of Sacramento
  to estimate the percentage of registered voters
  that favor issuing a bond in order to finance the
  construction of a new bike trail along the
  Sacramento River. Given that you want no more
  than a 0.04 error margin, at the 95 confidence
  level, state how you would conduct such a survey
  using a simple random sample

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Scenario 1 (continued)

• When going over your sampling design with the
  county Parks Director, you are asked whether a
  stratified sample would be appropriate? What is
  your reply? Why?
• What about a systematic sample?

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Travel Vouchers

• Fly the Friendly Skis

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Scenario 2

• The State of California has hired you to estimate
  the number of travel vouchers for legislators
  that have been filed incorrectly. The vouchers
  have been filed as they are processed.
• Which sampling technique would you employee?

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Light Rail
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Scenario 3

• Light Rail has hired you to determine whether
  passengers like the convenience of using light
  rail system.
• Which sampling technique would you employee?

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Trucks
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Scenario 4

• Marketers, Inc., has hired you to determine why
  so many young drivers, both male and female,
  prefer owning a pickup truck as compared to an
  automobile.
• Which sampling technique would you employee?

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Questions?
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