1. Sampling: Final and Initial Sample-Size Determination
Chapter 13
Sampling: Final and Initial Sample-Size Determination

2. Relationship to Marketing
Figure Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process
Focus of this
Chapter
Relationship to
Previous Chapters
Statistical Approach to Determining Sample Size
Adjusting the Statistically Determined Sample Size
Research Design Components (Chapter 3)
Sampling Design Process (Chapter 12)
Approach to Problem
Field Work
Data Preparation
and Analysis
Report Preparation
and Presentation
Research Design
Problem Definition
Relationship to Marketing
Research Process
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3. Figure 13.2 Final and Initial Sample Size Determination: An Overview
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4. Opening Vignette What Would You Do?
Definitions and Symbols (Table 13.1)
The Sampling Distribution
(Figs 13a.1-13a.3) (Appendix 13a)
Statistical Approach to Determining Sample Size (Fig 13.3)
Confidence Interval Approach
(Fig 13.4) (Table 13.2)
Adjusting the Statistically Determined Sample Size
Means
Proportions
Be a DM! Be an MR! Experiential Learning
What Would You Do?
Application to Contemporary Issues (Fig 13.5)
International Social Media Ethics
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5. Definitions and Symbols
Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population. A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken.
Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter.
Random sampling error: The error when the sample selected is an imperfect representation of the population of interest.
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6. Definitions and Symbols (Cont.)
Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter.
Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence.
Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.
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7. Symbols for Population and Sample Variables
Table 13.1
Symbols for Population and Sample Variables
Variable
Population
Sample
Mean μ
Proportion π p
Variance
Standard deviation σ s
Size N n
Standard error of the mean
Standard error of the proportion
Standardized variate (z)
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8. Figure 13.3 The Confidence Interval Approach and Determining Sample Size
Means
Proportions
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9. The Confidence Interval Approachz .
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10. The Confidence Interval Approach (Cont.)
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11. The Confidence Interval Approach (Cont.)
The confidence interval is given by
We can now set a 95% confidence interval around the sample mean of $182.
The 95% confidence interval is given by
= (3.18) =
Thus the 95% confidence interval ranges from $ to $
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12. Figure 13.4 95% Confidence Interval
0.475
𝑋 𝐿 𝑋
𝑋 𝑈
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13. Sample Size Determination for Means and Proportions
Table 13.2
Sample Size Determination for Means and Proportions
Steps
Means
Proportions
1. Specify the level of precision.
𝐷= 𝑋 −𝜇=±$5.0
𝐷=𝑝−𝜋=±0.05
2. Specify the confidence level (CL).
CL = 95%
3. Determine the z value associated with the CL.
Z value is 1.96
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14. Sample Size Determination for Means and Proportions
Table 13.2 (Cont.)
Sample Size Determination for Means and Proportions
Steps
Means
Proportions
4. Determine the standard deviation of the population
Estimate σ
σ = 55
Estimate π
π = 0.64
5. Determine the sample size using the formula for the standard error
𝑛= 𝜎 2 𝑧 2 𝐷 2
𝑛= (1.96)
=465
𝑛= 𝜋(1−𝜋) 𝑧 2 𝐷 2
𝑛= 0.64(1−0.64) (1.96)
=355
6. If necessary, reestimate the confidence interval by employing s to estimate σ
= 𝑋 ±𝑧 𝑠 𝑋
=𝑝±𝑧 𝑠 𝑝
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15. A sample size of 400 is enough to represent China’s more than 1
A sample size of 400 is enough to represent China’s more than 1.3 billion people or the more than 300 million American people.
The sample size is independent of the population size for large populations.

16. Adjusting the Statistically Determined Sample Size
Incidence rate refers to the rate of occurrence or the percentage of persons eligible to participate in the study.
In general, if there are c qualifying factors with an incidence of Q1, Q2, Q3, ...QC, each expressed as a proportion,
Incidence rate = Q1 x Q2 x Q3....x QC
Initial sample size = Final sample size
Incidence rate x Completion rate
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17. Copyright © 2011 Pearson Education, Inc.

18. International Marketing Research
When conducting marketing research in foreign countries, statistical estimation of sample size can be difficult, because estimates of the population variance might be unavailable.
When statistical estimation of sample size is attempted, the differences in estimates of population variance should be recognized and factored in, if possible.
When the goal is to examine differences across countries or international markets, it is desirable to have the same sample size across countries.
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19. Marketing Research & Social Media
It is feasible to have large, even very large, sample sizes when conducting marketing research in social media.
In many social media projects, the sample size can far exceed that required by statistical considerations.
It is important to address the issues of the appropriateness and representativeness of social media as outlined in Chapter 12.
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20. Ethics in Marketing Research
The researcher has the ethical responsibility to not use large estimates of the population variance simply to increase the cost of the project by inflating the sample size.
When the sample standard deviation varies widely from that which is assumed, the researcher should disclose the larger confidence interval to the client and jointly arrive at a corrective action.
Incorrectly reporting the confidence intervals of survey estimates based on statistical samples is unethical.
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21. Acronym: Size
The statistical considerations involved in determining the sample size can be summarized by the acronym SIZE: S ampling distribution I nterval (confidence) Z value E stimation of population standard deviation
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22. Finding Probabilities Corresponding to Known Values
Figure 13A.1
Finding Probabilities Corresponding to Known Values
Area is
Area between µ and µ + 1 s =
Area between µ and µ + 2 =
Area between µ and µ + 3 =
X Scale
μ-3σ
μ-2σ
μ-1σ μ
μ+1σ
μ+2σ
μ+3σ
(μ=50,σ=5) 35 40 45 50 55 60 65
Z Scale -3 -2 -1 +1 +2 +3
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23. Finding Values Corresponding to Known Probabilities
Figure 13A.2
Finding Values Corresponding to Known Probabilities
Area is 0.500
Area is 0.450
Area is 0.050 X 50
X Scale
Z =
Z Scale
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24. Finding Values Corresponding to Known Probabilities:
Figure 13A.3
Finding Values Corresponding to Known Probabilities:
Confidence Interval
Area is 0.475 X 50
X Scale
Z = -1.96
Z Scale
Area is 0.025
Z = 1.96
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