It is often said that without water,

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SAMPLING Chapter 10

• It is often said that without water,
• life would be impossible.
• Similarly, without sampling, marketing research
  as we know it would be impossible.
• Feinberg, Kinnear, Taylor (2008, p. 290)

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Probability vs. Nonprobability Sampling

• Probability Sampling
• Each sampling unit has a known probability of
  being included in the sample
• Nonprobability sampling
• When the probability of selecting each sampling
  unit is unknown

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Probability Sampling Procedures

• Simple Random Sampling
• A sampling approach in which each sampling unit
  in a target population has a known and equal
  probability of being included
• Advantage Good generalizability and unbiased
  estimates
• Disadvantage must be able to identify all
  sampling units within a given population often,
  this is not feasible
• Systematic Random Sampling
• Similar to random sampling, but work with a list
  of sampling units that is ordered in some way
  (e.g., alphabetically).
• Select a starting point at random, then survey
  each nth person where the skip interval
  (population size/desired sample size)
• Advantage quicker and easier than SRS
• Disadvantage may be hidden patterns in the data

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Probability Sampling Procedures

• Stratified Random Sampling
• Break up population into meaningful groups (e.g.,
  men, women), then sample within each strata,
  then combine
• Proportionate stratified sampling here you
  sample based on the size of the populations
  (i.e., sample more from the bigger strata e.g.,
  Caucasians)
• Disproportionate stratified sampling sample the
  same number of units from each strata, regardless
  of the stratas size in the pop.
• A variant is optimal allocation here you use
  smaller sample sizes for strata within which
  there is low variability (as the lower
  variability will give you more precision with
  lower N).
• Advantages more representative can compare
  strata
• Disadvantages Can be hard to figure out what to
  base strata on (Gender? Ethnicity? Political
  party?)

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Probability Sampling Procedures

• Cluster Sampling
• Similar to stratified random sampling, but with
  stratified random sampling, the strata are
  thought to possibly differ between strata (men
  vs. women), but be homogeneous within strata.
• In cluster sampling, you divide overall
  population into subpopulations (like SRS), but
  each of those subpopulations (called clusters)
  are assumed to be mini-representations of the
  population (e.g., survey customers at 10 Red
  Robins in WA).
• Area sampling clusters based on geographic region

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Probability Sampling Procedures

• Cluster Sampling
• One-step clustering just select one cluster
  (e.g., one store) problem may not be
  representative of population
• Two-step cluster sampling break into meaningful
  subgroups (Red Robins in big cities vs. Red
  Robins in suburbs), then randomly sample within
  each of those clusters
• Advantages easy to generate sampling frame cost
  efficient representative can compare clusters
• Disadvantages must be careful in selecting the
  basis for clusters also, within clusters, often
  little variability (theyre homogeneous), and
  this lack of variability leads to less precise
  estimates

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Nonprobability Sampling Procedures

• Convenience Sample
• Survey people based on convenience (e.g., college
  students)
• Advantage is fast and easy
• Disadvantage may not be representative
• Judgment Sampling
• Use your judgment about who is best to survey
• Advantage Can be better than convenience if
  judgment is right
• Disadvantage but if judgment wrong, may not be
  representative/generalizable

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Nonprobability Sampling Procedures

• Quota Sampling
• Sample fixed number of people from each of X
  categories, possibly based on their relative
  prevalence in the population
• Advantage Can ensure that certain groups are
  included
• Disadvantage but b/c you arent using random
  sampling, generalizability may be questionable
• Snowball Sampling
• You contact one person, they contact a friend
  (e.g., one cancer survivor is in contact with
  other survivors, and so recruits them)
• Advantages can make it easier to contact people
  in hard to reach groups
• Disadvantage there may be bias in the way people
  recruit others

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Factors Affecting Choice of Sampling Procedure

• Use some type of random sampling if
• You are collecting quantitative data that you
  want to use to arrive at accurate generalizations
  about population
• You have sufficient resources and time
• You have a good sense for the population
• You are sampling over a broader range (e.g., of
  states, nations)

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Computing the Sample Size Based on Usable Rates

• Several factors can reduce your sample size
• Thus, you may want to plan for more than your
  final sample size (i.e., use a higher number of
  contacts to achieve your final sample size). You
  adjust using the following three factors
• RR reachable rate (e.g., how many people on a
  telephone list will you actually be able to
  reach?)
• OIR overall incidence rate (i.e., of target
  population that will qualify for inclusion e.g.,
  cant use people over 40)
• ECR expected completion rate (i.e., some folks
  wont complete your survey)
• For example ?

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Computing the Sample Size Based on Usable Rates

• You want a sample size of n 500
• You figure you can reach 95 of the folks on your
  list (RR .95)
• You think 60 will be 40 or younger (OIR .60)
• You predict that 70 will complete your survey
  (ECR .70)
• Based on these numbers, you should contact 1,253
  people

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Some Key Terms

• Sampling
• Selection of a small number of elements from a
  larger defined target group of elements and
  expecting that the information gathered from the
  small group will allow judgments to be made about
  the larger group
• Population
• The identifiable set of elements of interest to
  the researcher and pertinent to the information
  problem
• Defined Target Population
• The complete set of elements identified for
  investigation
• Element
• A person or object (e.g., a firm) from the
  defined target population from which information
  is sought
• Sampling Units
• The target population elements available for
  selection during the sampling process
• Sampling Frame
• The list of all eligible sampling units

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Some Key Terms

• Total Error Sampling Error Nonsampling Error
• Sampling Error
• Any type of bias that is attributable to mistakes
  in either drawing a sample or determining the
  sample size
• Nonsampling Error (controllable)
• A bias that occurs in a research study regardless
  of whether a sample or a census is used (recall
  all the different types of errors we discussed)
• Respondent Errors (non response, response errors)
• Researchers measurement/design errors (survey,
  data analysis)
• Problem definition errors
• Administrative errors (data input errors,
  interview errors, poor sample design)

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Central Limit Theorem

• A theory that states that, regardless of the
  shape of the population from which we sample
  (e.g., positively skewed), as long as our sample
  size is gt 30, the sampling distribution of the
  mean (x-bar) will be normally distributed with
  the following characteristics

The mean of the sampling distribution of the
mean will equal the mean in the population.
The standard error of the sampling distribution
of the mean will equal sample standard deviation
(s) divided by sample size (n). This is a sample
estimate of the true standard error in
population. The larger the sample size, the more
precise we can get about our estimate of the true
mean in the population (e.g., in our confidence
interval).
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variance
Note Dr. Joireman does not put a bar above s
or s2.
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Computing Standard Deviation

• Assume your data are continuous
• (i.e., are not just yes/no data).
• For example, lets say we want to know how much
  people would be willing to pay for a tennis
  racquet.
• We sample 7 folks and wish to generalize to the
  population.
• Results ?

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Example of Computing Standard Deviation (for a
Sample)
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Formulas forVariance and Standard Deviation
Sum of Squared Deviations
POPULATION
SAMPLE
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The Sum of Squared Deviations (SS)

• Both Formulas Give Identical Answers!
• SS NUMERATOR of the Variance
• Examples on board

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Example of Computing Standard Deviation (for a
Sample)
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This is the standard deviation of the sampling
distribution of means. This (4.09) will naturally
be smaller than our sample standard deviation
(10.82) based on our single sample of scores, and
it will become smaller as n increases.
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Confidence Intervals

• A confidence interval is the statistical range of
  
• values within which the true value of the
• target population parameter is expected to lie.

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Computing Confidence Intervals

• 95 Confidence Interval
• We are 95 confident that the mean of the
  population from which we took our sample has a
  mean between these lower and upper limits.
• To compute, we need

Critical Z-value for our desired level of
confidence (see next page for Z-critical values)
Standard error of mean
Mean of our sample
Based on these results, we are 95 confident that
the mean in the population from which we sampled
is between 66.98 and 83.02. Cool beans!
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Common Z-Critical Values

• To be 90 confident, you use a z-critical value
  of 1.65
• To be 95 confident, you use a z-critical value
  of 1.96
• To be 99 confident, you use a z-critical value
  of 2.58

An example Z-critical values for 95
confidence (put ½ of .05 on each side)
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What if my data are Yes/No?Here we want to
estimate the population percentage.

• For example, a CNN poll (9/25/08) asked whether
  readers believed Obama and McCain should continue
  with their plans to debate on Friday (9/26/08).
• Results ?

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Recent Poll on Presidential Debate
Yes 75 (or yes, but debate on economy) No
25 No (wait till bailout is taken care of) N
9782 Lets compute standard error and 95
confidence interval Here, p yes, q (1-p) or
no