Marketing Research

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Marketing Research

• Aaker, Kumar, Day
• Ninth Edition
• Instructors Presentation Slides

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Chapter Fifteen
Sample Size and Statistical Theory
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Determining the Sample Size

• Ad Hoc Methods
• Used when a person knows from experience what
  sample size to adopt
• Used when budgetary constraints dictate the size
  of the sample
• Rule of Thumb
• Sample should be large enough, so that when
  divided into groups, each group will have a
  minimum sample size of 100 or more
• If analysis involves comparison between
  subgroups, sample size in each subgroup should be
  20 to 50
• Use disproportionate sampling if one of groups of
  population is relatively small

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Determining the Sample Size (contd.)

• Budget Constraints
• Researcher must decide whether sample size
  dictated by budget constraints allows a
  worthwhile study to be conducted
• Comparative Studies
• Find similar studies and use their sample sizes
  as a guide

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Factors Determining Sample Size

• Number of groups and subgroups within the sample
• Value of information in the study
• Accuracy level required in results
• Cost of sample
• Variability of the population

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Population Characteristics/Parameters

• Population Mean
• Normally unknown
• Determine value as closely as possible by taking
  a sample from population
• Population Variance
• Measure of population dispersion
• Based on degree to which a response differs from
  population average response
• The difference of each value from its mean is
  squared and averaged across all responses

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Population Characteristics/ parameters
The population opinion on symphony starting time
(730 P.M. on weekdays)
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Sample Characteristics/Statistics

• Sample mean ( ) is used to estimate the
  unknown population
• mean
• Example A sample of symphony season-ticket
  holders

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Sample Characteristics/Statistics(contd.)
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Sample Reliability

• X will vary from sample to sample
• As sample size (n) increases, variation in X will
  decrease

standard error of decreases as the
sample size gets larger
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Sampling Distribution
Indicates probability of getting a particular
sample mean
The normal distribution of
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Sampling Distribution (contd.)
The effect of increasing sample size on the
normal distribution of
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Interval Estimation

• varies from sample to sample
• The difference between the sample mean ( )
  and the population mean is the sampling error
• Interval size depends on the confidence level the
  researcher wants for the interval to contain the
  true population mean
• If the population standard deviation is not
  known, it is necessary to estimate it with the
  sample standard deviation

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Interval Estimation
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Interval Estimation (contd.)

• Size of Interval Estimate depends on
• Confidence level
• Population standard deviation
• Sample size

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Sample Size Question

• Size of the sampling error that is desired
• Confidence level
• Expected variance

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Determining the Population Standard Deviation

• Options
• Use a sample standard deviation obtained from a
  previous comparable survey or from a pilot survey
• Estimate the sample standard deviation (s)
  subjectively

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Proportions
Population variance,
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Proportions (contd.)
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Sample Size Formulas
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Coefficient of Variation

• Researcher may require the sample estimate be
  within plus or minus G percentage points of the
  population value
• Therefore,
• D Gm
• The sample size formula may be written as
• C coefficient of variation

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Stratified Sampling

• Useful when
• The population standard deviation differs by
  strata
• The interview cost differs by strata
• Optimal allocation of sampling budget to various
  strata
• Neymans solution

where
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Allocating Sample Size to Strata
where