This document discusses determining appropriate sample sizes for research studies. It outlines key points about sample sizes, including that sample size determines accuracy but not representativeness. The confidence interval approach to determining sample size is explained, using a formula that requires estimating variability, acceptable margin of error, and confidence level. Practical considerations like estimating variability and determining an acceptable margin of error are discussed. Other sample size determination methods beyond the confidence interval approach are also outlined. Examples are provided to demonstrate how to use the formula and calculate an appropriate sample size.

1. BMGT 311: Chapter 10
Determining the Size of a Sample
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2. Learning Objectives
• To understand the eight axioms underlying sample size determination with a
probability sample
• To know how to compute sample size using the confidence interval approach
• To become aware of practical considerations in sample size determination
• To be able to describe different methods used to decide sample size,
including knowing whether a particular method is flawed
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3. 3

4. 4

5. Key Points
• Many managers falsely believe that sample size and sample
representativeness are related, but they are not.
• A sample size decision is usually a compromise between what is theoretically
perfect and what is practically feasible.
• Many practitioners have a large sample bias, which is the false belief that
sample size determines a sample’s representativeness.
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6. Important Points about Sampling
• Sampling method (not sample size) is related to representativeness.
• Only a probability sample (random sample) is truly representative of a
population.
• Sample size determines accuracy of findings.
• The only perfect accurate sample is a census - which is for the most part, not
positive in Marketing Research
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7. Sample Accuracy
• Sample accuracy: refers to how close a random sample’s statistic is to the
true population’s value it represents
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8. Page 239
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9. Two Types of Error
• Non sampling error: pertains to all sources of error other than sample
selection method and sample size
• Sampling error: involves sample selection and sample size
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10. Sample Size and Accuracy
• Which is of these is more accurate?
• A large probability sample or
• A small probability sample?
• The larger a probability sample is, the more accurate it is (less sample
error).
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11. Page 240
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12. Page 241
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13. Sample Error
• Variability refers to how similar
or dissimilar responses are to a
given question.
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14. Sample Error
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15. The Confidence
Interval Method of
• Confidence interval approach:
applies the concepts of
accuracy, variability, and
confidence interval to create a
“correct” sample size
• The confidence interval
approach is based upon the
normal curve distribution.
• We can use the normal
distribution because of the
Central Limit Theorem.
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16. Central Limit
Theorem
• Since 95% of samples drawn
from a population will fall within
+ or – 1.96 × sample error (this
logic is based upon our
understanding of the normal
curve), we can make the
following statement . . .
• If we conducted our study over
and over, 1,000 times, we
would expect our result to fall
within a known range. Based
upon this, we say that we are
95% confident that the true
population value falls within this
range.
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17. Example - Page 243
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18. Figuring out the Sample Error - Module 1 Handout
• n Values:
• n = 1,000
• n = 500
• n = 100
• n = 50
• p and q = 50
• Confidence Interval = 95% or 1.96
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19. Figuring out the Sample Error - Module 1 Handout
• n Values:
• n = 1,000 Sample Error _____
• n = 500 Sample Error _____
• n = 100 Sample Error _____
• n = 50 Sample Error _____
• p and q = 50
• Confidence Interval = 95% or 1.96
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20. 20

21. Sample Size Formula
• Need to know
• Variability: p × q
• Acceptable margin of sample error: e
• Level of confidence: z
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22. Standard Sample Size Formula
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23. Example: Estimating a Sample Size
• What is the required sample size?
• Five years ago, a survey showed that 42% of consumers were aware of the
company’s brand (Consumers were either “aware” or “not aware.”)
• After an intense ad campaign, management wants to conduct another survey
and they want to be 95% confident that the survey estimate will be within
±5% of the true percentage of “aware” consumers in the population.
• What is n?
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24. Example: Estimating a Sample Size
• Five years ago, a survey
showed that 42% of
consumers were aware of the
company’s brand (Consumers
were either “aware” or “not
aware.”)
• After an intense ad campaign,
management wants to conduct
another survey and they want
to be 95% confident that the
survey estimate will be within
±5% of the true percentage of
“aware” consumers in the
population.
• Z=1.96 (95% confidence)
• p=42
• q=100-p=58
• e=5
• What is n?
•
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25. Example: Estimating a Sample Size
• Five years ago, a survey
showed that 42% of
consumers were aware of the
company’s brand (Consumers
were either “aware” or “not
aware.”)
• After an intense ad campaign,
management wants to conduct
another survey and they want
to be 95% confident that the
survey estimate will be within
±5% of the true percentage of
“aware” consumers in the
population.
• Z=1.96 (95% confidence)
• p=42
• q=100-p=58
• e=5
• What is n?
• n = 374
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26. Chapter 10 Handout Module 2, Figure out n
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27. First Step = Figure out z and q
Situation Confidence Level Value of z p q (100-p) Allowable Error
1 95% 1.96 65 35 3.5
2 99% 2.58 65 35 3.5
3 95% 1.96 60 40 5
4 99% 2.58 60 40 5
5 95% 1.96 50 50 4
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28. Example 1: Page 247
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29. Example 2: Page 247
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30. Practical Considerations
• How to estimate variability (p times q) in the population?
• Expect the worst cast (p = 50; q = 50)
• Estimate variability
• Previous studies?
• Conduct a pilot study?
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31. Practical Considerations
• How to determine the amount of acceptable sample error.
• Researchers should work with managers to make this decision. How much
error is the manager willing to tolerate?
• See page 251 for practical example
• Researchers should work with managers to take cost into consideration in
this decision.
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32. Practical Considerations
• How to decide on the level of confidence to use.
• Researchers typically use 95% or 99%.
• Most clients would not accept a confidence interval below 95% as a
representative of the overall population
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33. Other Methods of Sample Size Determination
• Arbitrary “percentage rule of thumb”
• Conventional sample size
• Statistical analysis approach requirements
• Cost basis
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34. Sampling from Small
Populations
• With small populations, use the
finite population multiplier to
determine small size.
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35. Example: Page 255
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36. Example: Page 255
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37. More Practice for Test Questions
• Page 258 - Question #13 - Crest Toothpaste Sample Size
• Page 247 - Sample Size Calculations Practice
• Make sure you practice and know all of the equations discussed in class
• Sample Size Margin of Error
• Sample Size Formula
• Small Population Formula
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