Statistical inference and Aristotle's Rhetoric

Area of Science:

• Philosophy of Science
• Statistical Inference
• Epistemology

Background:

• Formal logic requires complete information, unlike real-world reasoning.
• Statistical tests often lack logically justifiable conclusions.
• Aristotle's enthymemes rely on examples, analogies, and signs for truth-seeking.

Discussion:

• This paper defends statistical inference using principles of everyday reasoning.
• Statistical tests function like enthymemes: using examples, model analogies, and effect size as signs against chance.
• Few theories of statistical inference, except a weak version of Fisher's, acknowledge this.

Key Insights:

• Statistical inference is analogous to Aristotelian reasoning from examples, analogies, and signs.
• The size of an effect serves as a sign to reject the null hypothesis.
• Aristotle's reasoning about improbable outcomes anticipates Fisher's statistical approach.

Outlook:

• Statistical inference can be understood as a classical form of reasoning.
• This perspective offers a new framework for understanding and validating statistical methods.
• Further exploration into the Aristotelian roots of scientific reasoning is warranted.