====== Statistical syllogism ======

An [[glossary:induction|inductive]] inference that allows to draw a generalised conclusion based on a [[statistics:index|statistical]] proposition.

For example:
> 80 % of all people who come from [[wp>Scandinavia|Scandinavia]] are blond.
> Björn comes from Scandinavia.
> <span conclusio>Therefore there is an 80 % probability that Björn is blond.</span>

Such a conclusion is //valid// as long as the statistical probability with which it holds //true// is not ignored.

===== Description =====

It is possible to draw conclusions that are similar in form to a classical [[glossary:syllogism|syllogism]] on the basis of statistical statements.

These come with different limitations and possibilities than the classic forms. For example, the classical [[logic:formal_fallacies:fallacies_of_distribution:index|fallacies of distribution]] do not necessarily apply, if the distribution is indicated by a statistical dimension. 

Conversely, as with all inductive conclusions, the conclusion is only //true// with a certain probability, which may change at any time due to additional or changed information.

Not least, because [[glossary:induction|inductive]] rather than [[glossary:deduction|deductive]] reasoning is involved, we need to be aware of possible [[logic:induction:index|fallacies of induction]] that may apply.

==== Ecological fallacy ====

The term “[[logic:induction:ecological_fallacy|ecological fallacy]]” refers to an //inadmissible// transfer of a statistical property from a higher aggregation level to a lower one.

The above example avoids this by including the probability with which this is //true// in the conclusion. If that metric was omitted, it would appear as if //every// Scandinavian was //guaranteed// to be blonde, which is of course not a valid conclusion:

> 80 % of all people who come from Scandinavia are blond.
> Björn comes from Scandinavia.
> <s conclusio invalid "invalid conclusion">Therefore: Björn is blond.</s>

For more information, see: <b maniculus "more information under:">[[logic:induction:ecological_fallacy|Ecological fallacy]]</b>.

==== Measure of confidence ====

In many cases, a [[wp>Confidence interval|confidence interval]] or other statistical metric can be used instead of percentages. In some contexts, a qualifying adjective such as “many”, “most” or similar may also be appropriate – although these are of course quite imprecise and can easily lead to discussions as to whether a conclusion based on such vague statements is in fact valid.

===== See also =====

  * [[logic:induction:ecological_fallacy|Ecological fallacy]]
  * [[glossary:syllogism|Syllogism]]

===== More information =====

  * [[wp>Statistical syllogism|Statistical syllogism]] on //Wikipedia//

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