Statistical syllogisms

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Statistical syllogisms

• ...and why generalizations arent always accurate

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What is a statisical syllogism?
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Definition

• type of inductive reasoning based on a
  probability where the strength of the argument is
  reliant on the strength of a generalization
  (major premise)

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WHAT COMPOSES a Statistical Syllogism?
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MAJOR PREMISE

• generalizations which state probabilities that
  form the basis of succeeding assumptions

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Minor Premise

• statement that links the subject/s of the
  conclusion with the major premise

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CONCLUSION

• The assumption made based on the major premise.

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• Major Premise
• 82.5 of IMed students are from PSHS.

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Minor premise

• Jon is an IMed student.

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• Conclusion
• Jon is a most probably a graduate of PSHS.

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• Major Premise
• 17.5 of IMed students are members of the Med.
  Choir.

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• Minor Premise
• Flo is an IMed student.

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• Conclusion
• It is very likely that Flo is not a member of
  the Med. Choir.

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• Evaluating the strength of this type of argument
  is a matter of degree.

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• The reliability of the argument must be
  evaluated using three questions.

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Are there enough cases to support a universal
statement or one that is merely general?
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Have the observed cases been found in every
variety of times, places and circumstances?
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Has a thorough search been made for conflicting
cases?
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criteria for evaluating the strength of a
generalization
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The closer the number of the sample to the
required number, the more reliable the
generalization is.

• Ex. Most apples are red.
• (If 100 apples exist in the world, the sample
  must approach 50 in order to be considered
  reliable.)

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The greater the variety of the members of the
sample, the more reliable the generalization is.

• Ex. 75 of Asians are shorter than 511.
• (The statement would be more reliable if the
  sample included a greater variety of Asians
  instead of just one nationality.)

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The more thorough the search for conflicting
cases, the more reliable the generalization.

• Ex. 90 of men like chocolates.
• (If the number of conflicting cases increases in
  the sample taken, the generalization is made less
  reliable.)

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Fallaciesinvolving statisticalsyllogism
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accident

• application of a general rule when circumstances
  suggest an exception.

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Converse accident

• application of an exception to the rule when the
  generalization should apply.