Sampling

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Sampling
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Benefits of sampling and census
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Sampling and inference
Population
Sample
Census
Statistical Inference
Statistics
Parameter

• Errors in marketing research studies result from
  discrepancies between
• The True Value (What you need)
• The population value
• The sample value (What you get)

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Sources of Error in interpreting the Results
from a study
Total Error
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Sample Size and Total Error

• A schematic representation of the plausible
  effect of increasing sample size on the
  magnitude of the total error in shown below.
• As the sample size increases, random sampling
  error decreases and non-sampling error increases.
  
• Total error may increase with increasing sample
  size.

Increasing Sample Size
RSE
NSE
RSE
NSE
RSE
NSE
NSE
Census
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The Distinction Between Precision and Accuracy

• Precision
• The magnitude of random (sampling) error
• Accuracy
• The magnitude of total error
• Smaller the total error, greater the accuracy
• A carefully selected sample may indeed yield
  lower total error than a census. As such, the
  former can yield more accurate results than the
  latter. The same argument applies to a carefully
  selected small sample versus a not-so-carefully
  selected large sample.

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Decisions in Selecting a Sample
Define Universe
Develop Sampling Frame
Specify Sampling Unit and Element
Specify Sampling Method
Determine Sample Size
Specify Sampling Plan
Select the Sample
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Decisions in Selecting a Sample (contd)
Define Universe

• Sampling units (gray iron foundries)
• Elements (purchasing agents)
• Extent (purchased any of our product)
• Time (in the past 6 months)

Develop Sampling Frame

• Using Dun Bradstreet, Standard Poors,
  Thomas Register,
• Yellow Pages, Customer lists, Periodical
  subscription lists
• or other purchased lists
• Using a sequential frame building process

Specify Sampling Unit and Element
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Decisions in Selecting a Sample (contd)
Specify Sampling Method

• Detailing selection criteria
• E.g., probability vs. non-probability
• Simple random vs. stratified
• Proportionate vs. disproportionate
  stratified, etc.

Determine Sample Size

• Using classical, Bayesian or judgmental
  approaches

Specify Sampling Plan

• By detailing operational procedures for
  selection of the sampling units

Select the Sample
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Criteria for Classifying Sampling Techniques

• Probability Vs. non-probability procedures.
• Equal Vs. unequal selection probabilities for
  various elements.
• Element Vs. cluster sampling.
• Unstratified Vs. stratified selection.
• Random Vs. systematic selection of sampling
  units.
• Fixed Vs. sequential procedures.

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Probability Vs. Non-Probability Sampling
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Criteria for Classifying Sampling Techniques
Some Common Sampling Techniques

• Probability
• Simple random
• Cluster
• Systematic
• Stratified

• Non - Probability
• Convenience
• Purposive
• Quota
• Snowball

Proportionate
Disproportionate
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Non-Probability Sampling Procedures
Convenience Sampling

• Sample selection is determined by convenience
  and availability of respondents (sampling
  elements)
• Examples. Church groups, PTA, student, groups,
  etc.
• Pros
• Availability
• Speed, cost
• Greater respondent cooperation
• Oft affords good control of some sources of
  nonsampling error.
• Cons
• No objective measure of reliability available
• Projectability of results questionable

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Non-Probability Sampling Procedures
Purposive Sampling 1

• Researcher uses his judgment to select
  representative sample elements.
• Ex.
• Selecting Columbus, Ohio as the ABC CITY during
  the national elections selecting innovative
  respondents for a study exploring new product
  ideas choosing certain typical stores to study
  the effect of a new point of purchase display
  etc.

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Non-Probability Sampling Procedures
Purposive Sampling 2

• Pros
• Control of nonsampling errors
• Lower cost
• Possibly a fairly representative sample
• Cons
• Reliability cannot be measured
• No statistical basis for projecting study results
  to the entire population

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Non-Probability Sampling Procedures
Quota Sampling

• Established to insure a representative sample
• e.g., Quata based on sex and race
• Black
  White
• 20
  180 200
• Precautions in Establishing Quotas
• Control characteristic used to establish quotas
  must be selected carefully.
• Current data must be available on various breaks
  on the control characteristics.
• Investigator should be in a position to determine
  respondents control characteristics during the
  interview.
• Excessive investigator latitude in filling quotas
  may yield may a questionable sample.

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Non-Probability Sampling Procedures
Quota Sampling

• Pros
• 1. Data is available on subgroups the
  investigator considers relevant.
• 2.Ggenerally the sample is more representative
  than with other non-probability procedures.
• 3. Compared to a stratified sample( the
  probability counterpart of quota sample) the cost
  is lower.
• Cons
• 1. Reliability cannot be assessed statistically.
• 2. Projectability of results is questionable.
• 3. Only a limited number of control
  characteristics may be used.
• 4. Selection of a limited of most relevant
  characteristics is oft difficult
• 5. The need to fill quotas may introduce
  selection bias.

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Non-Probability Sampling Procedures
Snowball Sampling

• The procedure consists of building up a sample of
  a special population by using an initial set of
  members as informants.
• E.g., sampling rare population such as deaf
  persons, families with 3 teenage boys living at
  home, owners of 1957 T-Birds, etc.
• Pros
• 1. speed and low cost in sampling rare
  populations
• 2. can build banks of respondents for future use.
• Cons.
• 1. all the problems associated with
  non-probability sampling procedures dealing with
  reliability and projectability of results.
• 2. referrals by informants may be restricted to
  acquaintances and friends, resulting in greater
  homogeneity in the selected sample than in the
  corresponding population.

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Probability Sampling Procedures
Simple Random Sampling

• The sample drawn in such a way that every
  possible sample of a given size has an equal
  chance of being selected from the population
• The selection procedure
• 1. define population
• 2. Number each item serially.
• 3. use random number tables to select sample
  elements.
• Pros
• 1. intuitive appeal
• 2. sample statistical manipulations of the data
  possible.
• Cons
• 1. high interview cost
• 2. need complete list of population elements.
• 3. statistically inefficient

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Probability Sampling Procedures
Systematic Sampling

• The procedure consists of selecting every kth
  element after a random start.
• The selection procedure
• 1. define the population and number the elements
• 2. if the population is of size N the desired
  sample of size n, then the sampling (skip)
  interval K N (rounded to the nearest integer)
• 3. select a random number btw 1 and k. that
  defines the first element. Then choose every kth
  element from that point.
• Modifications to the systematic sampling plan to
  avoid some pitfalls
• 1. Randomize population, if possible.
• 2. Change random starting point several times.
• 3. Replicate sample using several smaller
  samplers

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Probability Sampling Procedures
Reliability of Systematic Sampling 1

• If the population elements are arranged randomly
  with respect to the characteristic under study,
  then the reliability of a systematic sample is
  close to that of a corresponding simple random
  sample.
• E.g., Alphabetical listing of respondents.
• If the population elements are ordered with
  respect to the characteristic under study, then a
  systematic sample may yield higher reliability
  than a simple random sample.
• E.g., ordering of retail stores by dollar volume
  of business.
• If the population elements exhibit a cyclical or
  periodic pattern, a systematic sample may yield
  lower reliability than a simple random sample.
• E.g., estimating average daily retail store
  volume using a skip interval of 7 days.

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Probability Sampling Procedures
Reliability of Systematic Sampling 2

• Pros
• 1. simplicity
• 2. speed
• 3. convenience
• 4. increased reliability under certain conditions
• 5. physical listing of population elements not
  essential if selection is done using a spatial or
  time pattern.
• Cons
• 1. statistical problems associated with
  estimating population variance form sample data.
• 2. Problems with populations that exhibit a
  cyclical or periodic pattern.

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Probability Sampling Procedures
Stratified Sampling

• The population is stratified into mutually
  exclusive and exhaustive subgroups and simple
  random samples are drawn from each stratum.
• The selection procedure
• Define the population
• Determine the appropriate basis for
  stratification.
• Establish number of strata and strata boundaries.
• Select a strategy, viz, proportionate or
  disproportionate, for allocating overall sample
  size to various strata. In the proportionate
  stratified sampling plan, the overall sample size
  is allocated to the various strata, in direct
  proportion to the size of the strata in the
  population. The disproportionate plan uses strata
  size as well as strata variabilities for
  allocating sample sizes.
• Select a simple random sample of the size
  specified in 4 above, from each stratum.

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Probability Sampling Procedures
Cluster Sampling 1

• The population is divided into mutually exclusive
  and exhaustive clusters and a simple random
  sample of the clusters is selected.
• The selection procedure
• Define the population
• Specify the appropriate clusters. Each cluster
  should be as heterogeneous as practical.
• Select a random sample of clusters.
• In single stage cluster sampling, every element
  in the selected clusters is studies.
• In two stage cluster sampling, elements are
  further chosen at random from each of the
  selected clusters.
• Area sampling, a special case of cluster
  sampling, consists of dividing the geographic
  area of interest (e.g., a city) into a of
  blocks and then randomly selecting a
  predetermined of blocks. All households in each
  block may be studied or a two stage procedure
  involving further random selection of households
  within each block may be employed.

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Probability Sampling Procedures
Cluster Sampling 2

• Pros
• Lower cost of data collection
• As in area sampling, a physical listing of all
  population elements is not required.
• Cons
• Statistically less efficient than a simple random
  sample
• Selection of elements and analysis of data
  statistically complex.

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Statistical inference from research data
Population
Census
Sample
Description
Description
Parameter(s)
Statistic(s))
Statistical Inference
Estimation/range of error
Test of Significance
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How good are your survey results?- Estimating
the range of Error

• Public opinion polls such as Gallup, Harris, and
  CBS typically report results from a poll followed
  by a qualifying statement.
• The following results are based on a telephone
  survey of a representative sample of 1500
  individuals.
• endorsing______ 45
• opposing ______ 55
• Range of error 3 percentage points, however,
  actual error may be higher due to factors
  associated with practical problems in conducting
  the polls.
• The range of error above corresponds to the 95
  Confidence Interval estimate of the Endorsing
  ______ obtained as follows (making some
  statistical assumptions)

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How good are your survey results?- Estimating
the range of Error

• Range of error for proportion
  error of proportion
• 
  
• P the sample proportion
• N sample size
• Z A multiple corresponding to the selected
  confidence level as follows
• For the above poll, Range of error
  

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How good are your survey results?- Estimating
the range of Error

• Pragmatic interpretation
• There is 95 assurance of being correct in saying
  that the percent in the population
  endorsing________ is within percentage
  points of the poll results i.e., (45 )
• The above only refers to the Random Sampling
  Error. The actual total error may be higher due
  to various Nonsampling Errors.

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Computing sample size

• Formula for the range of error for a proportion
• n sample size
• d the desired precision/range of error
• Z the multiple corresponding to the desired
  confidence level.
• P the proportion being estimated, which is
  assigned the conservative value of .5 unless a
  prior estimate is available.

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Computing sample size

• The desired size for a study designed to estimate
  population proportion (e.g., incidence as in
  the poll)

Note The above table assumes a conservative p of
.5, a simple random sample and a large
population.
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Impact of population size on sample size

• For large populations, (gt20 x sample size) the
  effect on sample size is minimal. For smaller
  populations, a correction factor known as the
  finite population correction (f.p.c.) needs to be
  incorporated into the sample size formula,
  yielding the following