Transcript Marketing Research

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Marketing Research
Aaker, Kumar, Day and Leone
Tenth Edition
Instructor’s Presentation Slides
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Chapter Fifteen
Sample Size and Statistical
Theory
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Determining the Sample Size
Ad Hoc Methods
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Used when a person knows from experience what sample size to adopt
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Used when budgetary constraints dictate the size of the sample
Rule of Thumb
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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
Budget Constraints
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Researcher must decide whether sample size dictated by budget constraints allows a worthwhile
study to be conducted
Comparative Studies
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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 (7:30 P.M. on weekdays)
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Sample Characteristics/Statistics
• Sample mean ( X ) is used to estimate the unknown population mean
Example: A sample of symphony season-ticket holders
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Sample Characteristics/Statistics (Contd.)
Sample mean
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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
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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 X
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Sampling Distribution (Contd.)
The effect of increasing sample size on the normal distribution of X
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Interval Estimation
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X
varies from sample to sample
• The difference between the sample mean ( X ) 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 (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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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 is the 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:
Neyman’s solution
where
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Allocating Sample Size to Strata
where
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