Transcript MGM403 Marketing Research

Chapter 17
Sample Size Determination
*Adapted from Andrei Strijnev
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Basic Considerations in Determining
Sample Size
Precision – the degree of error in a study,
or the size of the estimating interval
How precise should the estimate be?
More – less error, smaller estimation interval
Less – more error, greater estimation interval
Confidence – the degree to which one can
feel confident that an estimate
approximates the true value
 These two terms are highly correlated
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The Importance of Sample Size
Too small sample size leads to
undesirably large sampling error.
Too large sample size wastes time and
money.
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Methods of Determining Sample Size
Ad Hoc Methods
Based on budget constraint
Use of expert guidance
Use previous sample sizes
Statistical Method
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Sample Size Determination: The Intuition
More accurate information required =>
larger sample size needed
More diversified population => larger
sample size needed
The marginal gain in information accuracy
is diminishing with the increase of sample
size
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Sample Size Determination:
The Equation
The relationship between sampling error and sample size:
s
sx =
n
sx = sampling error for variable x
s
= estimated standard deviation for variable x
in the population
n = sample size
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Sampling Error & Sample Size
3.5
3
2.5
Sampling 2
Error 1.5
1
0.5
0
0
500
1000
1500
2000
Sample Size
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Sampling Error & Confidence Interval
Marketing researchers usually use
confidence intervals to describe
sampling error.
Meaning of confidence interval
If the estimate of a variable is 1000
and it has a 95% confidence interval
of 100, then…
 with 95% probability the true value
of that variable is between 900 and
1100.
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Sample Size Determination:
Measures of Interest in Most Surveys
Sample Mean, Examples include:
Mean rating on an attitudes measurement scale
Mean income, age
Mean number of purchases, monthly expenditure
Sample Proportion, Examples include:
Proportion of households owning  2 cars
Proportion of households spending more than
$400/month on food
Probability of purchase
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The Confidence Interval Approach
to Sample Size: Estimates of Means
If a 95% confidence interval of  I95% is
desired,
2
(1.96s)
n=
2
( I 95% )
.
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Example
A marketing manager of a frozen foods firm
wants to estimate the average dollars that
families in a certain city spend on frozen
foods per year.
He wants the estimate to have a 95%
confidence interval of $10.
He estimates that the standard deviation of
annual family expenditures is about $100.
What is the desired sample size for this study?
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In this problem, I95%=10, s=100. Applying
2
(1.96s)
n=
2
( I 95% )
,
we obtain that n=(1.96*100)2/102=385.
Thus, 385 families must be chosen for this study.
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How to Estimate Standard Deviation (s)
1.Subjective judgment
2.Use pilot study
3.If min and max values in population is known,
choose s = (max value - min value) / 6.
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The Confidence Interval Approach
to Sample Size: Estimates of Proportions
If a 95% confidence interval of I95% is
desired,
2
(1.96)
n=
p (1  p )
2
( I 95% )
,
where p is the estimated proportion in
the population.
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Example
A sporting goods marketer wants to estimate
the proportion of tennis players among
college students.
He wants the estimate to have a 95%
confidence interval of 0.02.
A pilot study of 50 students showed that 20
of them played tennis.
What is the required sample size for the final
study?
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In this problem, I95%=0.02, p=20/50=0.4.
Applying
2
(1.96)
n=
p (1  p ) ,
2
( I 95% )
we obtain that n=[(1.962)/0.022]*0.4*(1-0.4)=2305.
Thus, 2305 students must be sampled.
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How to Estimate p
1.Subjective judgment
2.Use pilot study
3.Set p=50%
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More Examples
PETsMART wants to determine the
average number of cats in each U.S.
household. It wants the estimate to have
a 95% confidence interval of  0.5 cat. You
recall once reading an article that says the
households with the most cats was
headed by an 85 year old woman who
owned 35 cats. What is the desired
sample size for this study?
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More Examples
PETsMART wants to determine the
proportion of U.S. households who have
dogs. It wants its estimate to have a 95%
confidence interval of  0.04. What is the
desired sample size for this study?
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Punch-Lines
The intuition of sample size determination
Determine sample size for estimating
means and proportions
Three ways of estimating s and p
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