Basic Sampling

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Basic Sampling
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Basic Sampling

• What is a sample?
• Selection of a subset of elements from a larger
  group of objects
• Why use a sample?
• Saves
• Time
• Money
• Accuracy
• Lessens non-sampling error

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Basic Sampling

• Major definitions
• Sample population entire group of people from
  whom the researcher needs to obtain information
• Sample element -- unit from which information is
  sought (consumers)
• Sampling unit -- elements available for selection
  during the sampling process (consumers who are in
  the US at the time of the study)
• Sampling frame -- list of all sampling units
  available for selection to the sample (list of
  all consumers who are in the US at the time of
  the study)
• Sampling error -- difference between population
  response and sample response
• Non-sampling error all other errors that emerge
  during data collection

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Basic Sampling

• Procedure for selecting a sample
• Define the population who (or what) we want
  data from
• Identify the sampling frame those available to
  get data from
• Select a sampling procedure how we are going to
  obtain the sample
• Determine the sample size (n)
• Draw the sample
• Collect the data

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Basic Sampling

• General Types of Samples
• Non-probability selection of element to be
  included in final sample is based on judgment of
  the researcher
• Probability each element of population has a
  known chance of being selected
• Selection of element is chosen on the basis of
  probability
• Characteristics of probability samples
• Calculation of sampling error ( or - z (sx))
• Make inferences to the population as a whole

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Non-Probability samples

• Convenience
• Sample is defined on the basis of the convenience
  of the researcher
• Judgment
• Hand-picked sample because elements are thought
  to be able to provide special insight to the
  problem at hand
• Snowball
• Respondents are selected on the basis of
  referrals from other sample elements
• Often used in more qualitative/ethnographic type
  studies
• Quota
• Sample chosen such that a specified proportion of
  elements possessing certain characteristics are
  approximately the same as the proportion of
  elements in the universe
• Rule of thumb regarding nonprobability samples
• Best used for exploratory designs or pre-tests

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Advanced Sampling Issues

• Sampling Plans (contd)
• Probability samples
• Simple random sample (SRS)
• Assign a number to each sampling unit
• Use random number table
• Systematic Sample
• Easy alternative to SRS
• Stratified sample
• Divide population into mutually exclusive strata
• Take a SRS from each strata

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Advanced Sampling Issues

• Sampling Plans (contd)
• Probability Samples
• Cluster sample
• Divide population into mutually exclusive
  clusters
• Select a SRS of clusters
• One-stage -- measure all members in the cluster
• Two-stage --measure a SRS within the cluster
• Area sample
• One-stage -- Choose an SRS of blocks in an area
  sample everyone on the block
• Two-stage -- Choose an SRS of blocks in an area
  select an SRS of houses on the block

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Review of Statistics

• Probability Samples note that statistical error
  can be computed when they are used
• Thus, need to know about statistics
• Descriptive statistics
• Estimates of descriptions of a population
• Statistical terms used in sampling
• Mean (m or x) -- Sxi/n
• Variance (s2 or s2) -- S(xi-x)2/n - 1
• Standard Deviation (s or s) Square Root
  (Variance)

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Review of Statistics

• Example MMs represent population of Laczniak
  Yogurt Customers
• Laczniak wants to determine the level of customer
  satisfaction
• Red 1 (Very Dissatisfied)
• Blue 2 (Dissatisfied)
• Brown 3 (Somewhat Dissatisfied)
• Orange 4 (Somewhat Satisfied)
• Yellow 5 (Satisfied)
• Green 6 (Very Satisfied)
• Choose a sample of 20 Customers
• Compute mean (and standard deviation) level of
  satisfaction

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Review of Statistics

• Inferential Statistics
• Terms
• Parameter -- m
• Statistic -- x
• Sample Statistics
• Best estimate of population parameter
• Why? -- Central Limit Theorem

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Review of Statistics

• Central Limit Theorem
• Based on the distribution of the means of
  numerous samples
• Sampling Distribution of Means
• Theorem states
• as sample size (n) approaches infinity (gets
  large), the sampling distribution of means
  becomes normally distributed with mean (m) and
  standard deviation (s/v n)
• Allows the calculation of sampling error ( s /v
  n)
• Thus a confidence interval can be calculated

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Review of Statistics

• Confidence interval -- tells us how close, based
  on n and the sampling procedure, how close the
  sampling mean (x) is to the population mean (m)
• Formula
• x - z (sx) lt (m) lt x z (sx)
• z-values
• 90 -- 1.28
• 95 -- 1.96
• 99 -- 2.58

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Review of Statistics

• Confidence interval -- interpretation
• For the same sampling procedure, 95 out 100
  calculated confidence intervals would include the
  true mean (m)

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Review of Statistics (In-Class 9)

• ABC Company commissioned a study to determine
  customers satisfaction with its offerings.
  Satisfaction was measured on a 1 (Completely
  Dissatisfied) to 8 (Completely Satisfied) scale
  with ten items (which were summed to form a
  satisfaction scale that ranged from 10 - 80). A
  sample of ten customers was randomly chosen.

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Review of Statistics

• The following satisfaction scores emerged
• 32, 71, 64, 50, 48, 63, 38, 41, 47, 52
• Compute the mean, standard deviation of the
  scores
• What is the confidence interval around the
  scores?
• Given the results, what can you conclude?
• Hint compare mean and CI to scale midpoint and
  competitors satisfaction level

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Sample Size

• Sample size and total error
• Larger n increases probability of non-sampling
  error
• Larger n reduces sampling error (s /v n)
• Effect on n on total error?
• Can pre-determine the level of error (by setting
  n)
• Depends mainly on the method of analysis

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Sample Size

• Problem determine the relationship of age
  (younger versus older Cs) and brand usage (low
  versus high) exists
• Use data of consumers to complete the Table

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Sample Size

• Sample size estimation
• With cross-tabulation based research
• Objective is to get a minimum of 25 subjects per
  cell
• Must estimate relationship up front what is
  smallest cell

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Sample Size

• Smallest cell is .10 of total
• So,
• .10 (n) 25
• n 25/.1
• n 250

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Sample Size

• Sample size when research objective is estimate a
  population parameter
• CI x z Sx
• CI x 1.96 (s/ vn)
• n x z2 s2/ h2
• n (1.96)2 s2/ h2
• n (3.84) s2/ h2
• s expected standard deviation
• h absolute precision of the estimate (or with
  of the desired confidence interval)

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Sample Size (Practice Problem)

• Laczniak Yogurt is interested in determining
  customer satisfaction with their brands. They
  measure satisfaction with 10 8-point items (e.g.,
  1 very dissatisfied 8 very satisfied).
• When assessing satisfaction last year, the
  standard deviation of the satisfaction scores was
  7.5. Laczniak management would like to measure
  satisfaction fairly precisely (with or - .50
  scale points).
• What sample size is required?

-_ n3.84s2Lnz ns.847.57.52 e5.84l2S6.2'sshs55
216/.s5sIr es Orin-.for.so TO ???
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Sample Size (Conclusion)

• Unaffected by size of universe
• Affected by
• Choice of Desired Precision of Confidence
  Interval
• Estimate of standard deviation