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Marketing
Research
Aaker, Kumar, Day
Seventh Edition
Instructor’s Presentation
Slides
Chapter Fifteen
Sample Size and Statistical
Theory
Sample Size and Statistical
Theory
Determining the Sample Size
Use of statistical techniques or ad hoc
methods
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
Marketing Research 7th Edition
© Aaker, Kumar, Day
Rule of Thumb
Sample should be large enough, so that
when it is 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
Marketing Research 7th Edition
© Aaker, Kumar, Day
Rule of Thumb (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
Marketing Research 7th Edition
© Aaker, Kumar, Day
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
Marketing Research 7th Edition
© Aaker, Kumar, Day
Population
Characteristics/parameters
Population Mean
Normally unknown
Determine its 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 it’s mean is squared
and averaged across all responses
Marketing Research 7th Edition
© Aaker, Kumar, Day
Population
Characteristics/parameters
(Contd.)
Sample Characteristics/Statistics
Population mean is not known and must be estimated
from a sample
Sample mean (X) is used to estimate the unknown
population mean
Sample Reliability
X will vary from sample to sample
As sample size (n) increases, variation in X will
decrease
Marketing Research 7th Edition
© Aaker, Kumar, Day
Population
Characteristics/parameters
(Contd.)
Variation of X
Standard error depends on sample size
Assume that variation of X follows
normal distribution
Sampling distribution

Indicates probability of getting a particular
sample mean
Marketing Research 7th Edition
© Aaker, Kumar, Day
Interval Estimation
X varies from sample to sample
The difference between the sample mean (X) and
the population mean is the sampling error
X + sampling error = interval estimate of sample
mean
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
Marketing Research 7th Edition
© Aaker, Kumar, Day
Interval Estimate of the
Population Mean
X + sampling error
sx - population standard deviation
Or
x + z sx / n
N - sample size
Marketing Research 7th Edition
© Aaker, Kumar, Day
Size of Interval Estimate
Confidence level
Population standard deviation
Sample size
Marketing Research 7th Edition
© Aaker, Kumar, Day
Sample - Size Question
Size of the sampling error that is
desired
Confidence level
Sample size n = Z2 s2 /(sampling error)2
Marketing Research 7th Edition
© Aaker, Kumar, Day
Determining the Population
Standard Deviation
Use a sample standard deviation
obtained from a previous comparable
survey or from a pilot survey
Estimate the sample standard deviation
(s) subjectively
Marketing Research 7th Edition
© Aaker, Kumar, Day
Sample Size When
Proportions Are Used
n = z2 p(1 - p)/(sampling error)2
Researcher may require the sample
estimate be within plus or minus G
percentage points of the population
value
D = Gm
Marketing Research 7th Edition
© Aaker, Kumar, Day
Sample Size Formula
N = s2 Z2 /(sampling error)2
N = s2 Z2 / D2
= C2 Z2 / g2
Coefficient of variation: C=(s/m)
Marketing Research 7th Edition
© Aaker, Kumar, Day