bmgt 311 chapter_10
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bmgt_311_fall_2013_chris_lovettTRANSCRIPT
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BMGT 311: Chapter 10
Determining the Size of a Sample
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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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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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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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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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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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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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Sample Error
• Variability refers to how similar or dissimilar responses are to a given question.
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Sample Error
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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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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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Example - Page 243
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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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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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Sample Size Formula
• Need to know
• Variability: p × q
• Acceptable margin of sample error: e
• Level of confidence: z
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Standard Sample Size Formula
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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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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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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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Chapter 10 Handout Module 2, Figure out n
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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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Example 1: Page 247
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Example 2: Page 247
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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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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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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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Other Methods of Sample Size Determination
• Arbitrary “percentage rule of thumb”
• Conventional sample size
• Statistical analysis approach requirements
• Cost basis
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Sampling from Small Populations
• With small populations, use the finite population multiplier to determine small size.
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Example: Page 255
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Example: Page 255
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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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