#### Transcript Marketing Research Aaker, Kumar, Day Ninth Edition Instructor’s Presentation Slides

```Marketing Research
Aaker, Kumar, Day
Ninth Edition
Instructor’s Presentation Slides
1
Chapter Fifteen
Sample Size and Statistical
Theory
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Determining the Sample Size
 Used when a person knows from experience what sample size to
 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 (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
 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
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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
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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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