BMGT 311: Chapter 10
Determining the Size of a Sample
Learning Objectives
• To understand the eight axioms underlying sample size determination with a
probability sample

• To ...
Key Points
• Many managers falsely believe that sample size and sample
representativeness are related, but they are not.

...
Important Points about Sampling
• Sampling method (not sample size) is related to representativeness.

• Only a probabilit...
Sample Accuracy
• Sample accuracy: refers to how close a random sample’s statistic is to the
true population’s value it re...
Page 239
Two Types of Error
• Non sampling error: pertains to all sources of error other than sample
selection method and sample si...
Sample Size and Accuracy
• Which is of these is more accurate? 

• A large probability sample or 

• A small probability s...
Page 240
Page 241
Sample Error
• Variability refers to how similar
or dissimilar responses are to a
given question.
Sample Error
The Confidence
Interval Method of
• Confidence interval approach:
applies the concepts of
accuracy, variability, and
confiden...
Central Limit
Theorem
• Since 95% of samples drawn
from a population will fall within
+ or – 1.96 × sample error (this
log...
Example - Page 243
Figuring out the Sample Error - Module 1 Handout
• n Values:

• n = 1,000

• n = 500

• n = 100

• n = 50

• p and q = 50
...
Figuring out the Sample Error - Module 1 Handout
• n Values:

• n = 1,000 Sample Error _____

• n = 500 Sample Error _____...
Sample Size Formula
• Need to know

• Variability: p × q

• Acceptable margin of sample error: e

• Level of confidence: z
Standard Sample Size Formula
Example: Estimating a Sample Size
• What is the required sample size?

• Five years ago, a survey showed that 42% of consu...
Example: Estimating a Sample Size
• Five years ago, a survey
showed that 42% of
consumers were aware of the
company’s bran...
Example: Estimating a Sample Size
• Five years ago, a survey
showed that 42% of
consumers were aware of the
company’s bran...
Chapter 10 Handout Module 2, Figure out n
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...
Example 1: Page 247
Example 2: Page 247
Practical Considerations
• How to estimate variability (p times q) in the population?

• Expect the worst cast (p = 50; q ...
Practical Considerations
• How to determine the amount of acceptable sample error.

• Researchers should work with manager...
Practical Considerations
• How to decide on the level of confidence to use.

• Researchers typically use 95% or 99%.

• Mos...
Other Methods of Sample Size Determination
• Arbitrary “percentage rule of thumb” 

• Conventional sample size

• Statisti...
Sampling from Small
Populations
• With small populations, use the
finite population multiplier to
determine small size.
Example: Page 255
Example: Page 255
More Practice for Test Questions
• Page 258 - Question #13 - Crest Toothpaste Sample Size

• Page 247 - Sample Size Calcul...
Bmgt 311 chapter_10
Bmgt 311 chapter_10
Bmgt 311 chapter_10
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bmgt 311 marketing research chris lovett fall 2014

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Bmgt 311 chapter_10

  1. 1. BMGT 311: Chapter 10 Determining the Size of a Sample
  2. 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
  3. 3. 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.
  4. 4. 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
  5. 5. Sample Accuracy • Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents
  6. 6. Page 239
  7. 7. 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
  8. 8. 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).
  9. 9. Page 240
  10. 10. Page 241
  11. 11. Sample Error • Variability refers to how similar or dissimilar responses are to a given question.
  12. 12. Sample Error
  13. 13. 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.
  14. 14. 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.
  15. 15. Example - Page 243
  16. 16. 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
  17. 17. 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
  18. 18. Sample Size Formula • Need to know • Variability: p × q • Acceptable margin of sample error: e • Level of confidence: z
  19. 19. Standard Sample Size Formula
  20. 20. 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?
  21. 21. 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?
  22. 22. 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
  23. 23. Chapter 10 Handout Module 2, Figure out n
  24. 24. 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
  25. 25. Example 1: Page 247
  26. 26. Example 2: Page 247
  27. 27. 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?
  28. 28. 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.
  29. 29. 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
  30. 30. Other Methods of Sample Size Determination • Arbitrary “percentage rule of thumb” • Conventional sample size • Statistical analysis approach requirements • Cost basis
  31. 31. Sampling from Small Populations • With small populations, use the finite population multiplier to determine small size.
  32. 32. Example: Page 255
  33. 33. Example: Page 255
  34. 34. 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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