Sample Size Determination See also SampleSizeDetermination'doc

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Sample Size Determination(See also
SampleSizeDetermination.doc)

• Peter Jurkat

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Based on Confidence Intervals

• Upper bound of confidence interal for mean
• Term after sign is error term
• To determine sample size
• Select confidence C and allowable error e
• a C 1
• s from historical knowledge or pilot survey
• Determine za/2 from table or
• Solve equation of error term for
• Similarly for proportion

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Finite Population Correction

• When sample could be greater than 5 of the
  population, can often reduce sample size for
  moderate to small populations
• Let N population size
• Finite population correction factor multiplies
  the sample standard deviation by
• Solving the error term equation with this
  correction factor yields

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Sampling for Small Proportions

• Many studies are conducted looking for the
  proportion of unusual events, such as incidence
  of disease and failures in products and service
  these can be as rare as units in hundred
  thousands
• For reliable results it is recommended that
  sample sizes be large enough so that at least
  five incidences are found in each category
• So for incidences of one in a thousand samples
  as least 5 thousand would be needed

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Samples Sizes to Control Both Type I and Type II
Errors

• Type I error is rejecting a true null hypothesis
  probability denoted by a
• Type II error is accepting a false null
  hypothesis probability denoted by b
• Reducing probability of one type raises the
  probability of the other - only way to control
  both is to have large enough sample sizes
• Theory is complex practical steps have been
  developed based on effect sizes

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Effect Size

• In general, effect size is the difference
  between two variables often measured by their
  means here effect size is the difference
  between the sample mean and the hypothesized
  population mean, i.e., the error term e
• Specified by

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Relationship Between n, a, and 1 - b for One
Effect Size
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Statistical PowerProbability of Not Making a
Type II Error