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Hypothesis Testing

Hypothesis Testing: Hypothesis Testing is the Courtroom of Science. Intermediate Probability Theory visual proof at NICEFA.

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The Formal Theorem

p < \alpha

Analytical Intuition.

Hypothesis Testing is the Courtroom of Science. We assume the Null (no effect) and see if the data is so extreme it rejects it. P-value is the probability of seeing your data if the Null was true.
CAUTION

Institutional Warning.

Type I Error (False Alarm) vs Type II Error (Missing the truth). Power is the ability to detect the truth.

Academic Inquiries.

01

Why p < 0.05?

An arbitrary historical convention by Fisher; context matters more than a hard cutoff.

Standardized References.

  • Definitive Institutional SourceRoss, S.M. (2014). A First Course in Probability.

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Institutional Citation

Reference this proof in your academic research or publications.

NICEFA Visual Mathematics. (2026). Hypothesis Testing: Visual Proof & Intuition. Retrieved from https://www.nicefa.org/library/probability/hypothesis-testing-theory

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