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This webpage says:

Inferential Statistics - Deductive Approach

Descriptive Statistics - Inductive Approach

But I doubt it. If I understand correctly,

  • Inferential Statistics is "given some data, find the probability model that generates the data", so it is a specific-to-general logic process, and therefore it is induction.

  • Descriptive Statistics is "given some data, represent the data in another way", so it is specific-to-specific process of changing data's representation. So it is neither induction or deduction.

Am I wrong?

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up vote 10 down vote accepted

To add to @Peter Flom's answer, it is worth defining the other terms that were used:

Deductive reasoning: Derive conclusions or predictions about specific cases from fundamental rules or theories.

Inductive reasoning: Derive universal rules or theories from observation of many cases.

Inferential statistics use both inductive and deductive reasoning. You are trying to establish rules about the behaviour of a system based on evidence, but you are testing models against probability theories derived deductively (i.e., probability distributions in parametric models or the combinatorics that are the basis of non-parametric models).

Descriptive statistics don't really qualify as "reasoning" in my book. Saying the average of something is x and the standard deviation is s isn't any more of an argument than saying the colour of something is blue. You're describing what you have in front of you, not drawing any conclusions beyond it.

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I don't think either the web-page or your statements are correct. I'd rather stick with more straightforward descriptions:

Inferential statistics: Given a sample, what can we say about the population from which it was drawn?

Descriptive statistics: Given a sample, what can we say about the sample?

Both can be used as part of inductive or deductive reasoning - the type of reasoning is not supplied by the statistics.

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