Determining the Size of a Sample

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Determining the Size of a Sample
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Sample Accuracy

• Sample accuracy refers to how close a random
  samples statistic is to the true populations
  value it represents
• Important points
• Sample size is not related to representativeness
• Sample size is related to accuracy

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Sample Size and Accuracy

• The larger a probability sample is, the more
  accurate it is (less sample error).

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A Picture Says 1,000 Words

n 550 - 2000 1,450 4 - 2 2
Probability sample accuracy (error) can be
calculated with a simple formula, and expressed
as a number.
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How to Interpret Sample Accuracy

• From a report
• The sample is accurate 7 at the 95 level of
  confidence
• From a news article
• The accuracy of this survey is 7

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Sample Size Axioms

• To properly understand how to determine sample
  size, it helps to understand the following axioms

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Sample Size Axioms

• The only perfectly accurate sample is a census.
• A probability sample will always have some
  inaccuracy (sample error).
• The larger a probability sample is, the more
  accurate it is (less sample error).

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Sample Size Axioms

• A probability sample can be a very tiny
  percentage of the population size and still be
  very accurate (have little sample error).

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Sample Size Axiom

• The size of the probability sample depends on the
  clients desired accuracy (acceptable sample
  error) balanced against the cost of data
  collection for that sample size.

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The Confidence Interval Method of Determining
Sample Size

• This method is based upon the Confidence Interval
  and the Central Limit Theorem
• Confidence interval range whose endpoints define
  a certain percentage of the response to a question

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The Confidence Interval Method of Determining
Sample Size

• Confidence interval approach applies the
  concepts of accuracy, variability, and confidence
  interval to create a correct sample size
• Two types of error
• Nonsampling 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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The Confidence Interval Method of Determining
Sample Size

• The relationship between sample size and sample
  error

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Review What does sample accuracy mean?

• 95 Accuracy
• Calculate your samples finding, p
• Calculate your samples accuracy, e
• You will be 95 confident that the population
  percentage (p) lies between p e

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Review What does sample accuracy mean?

• Example
• Sample size of 1,000
• Finding 40 of respondents like our brand
• Sample accuracy is 3 (via our formula)
• So 37 - 43 like our brand

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Central Limits Theorem

• The central limits theorem allows us to use the
  logic of the normal curve distribution.
• Since 95 of samples drawn from a population will
  fall or 1.96 x sample error (this logic is
  based upon our understanding of the normal curve)
  we can make the following statement

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The Confidence Interval Method of Determining
Sample Size

• 1.96 x s.d. defines the endpoints of the
  distribution.

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So, what have we learned thus far?

• There is a relationship between
• The level of confidence we wish to have that our
  results would be repeated within some known range
  if we were to conduct the study again, and
• Variability in the population and
• The amount of acceptable sample error (desired
  accuracy) we wish to have and
• The size of the sample!