Statistical syllogisms...and why generalizations aren’t always accurate
What is a statisical syllogism?
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)
WHAT COMPOSES a Statistical Syllogism?
MAJOR PREMISE generalizations which state probabilities that form the basis of succeeding assumptions
Minor Premise statement that links the subject/s of the conclusion with the major premise
CONCLUSION The assumption made based on the major premise.
Major Premise 82.5% of IMed students are from PSHS.
Minor premise Jon is an IMed student.
Conclusion Jon is a most probably a graduate of PSHS.
Major Premise 17.5% of IMed students are members of the Med. Choir.
Minor Premise Flo is an IMed student.
Conclusion It is very likely that Flo is not a member of the Med. Choir.
Evaluating the strength of this type of argument is a matter of degree.
The reliability of the argument must be evaluated using three questions.
Are there enough cases to support a universal statement or one that is merely general?
Have the observed cases been found in every variety of times, places and circumstances?
Has a thorough search been made for conflicting cases?
criteria for evaluating the strength of a generalization
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.)
Ex. 75% of Asians are shorter than 5’11”. (The statement would be more reliable if the sample included a greater variety of Asians instead of just one nationality.) The greater the variety of the members of the sample, the more reliable the generalization is.
Ex. 90% of men like chocolates. (If the number of conflicting cases increases in the sample taken, the generalization is made less reliable.) The more thorough the search for conflicting cases, the more reliable the generalization.
Fallacies involving statistical syllogism
accident application of a general rule when circumstances suggest an exception.
Converse accident application of an exception to the rule when the generalization should apply.