Type I Hypothesis Testing Error

A Type I Hypothesis Testing Error is a statistical decision error that occurs when a true null hypothesis is incorrectly rejected in a hypothesis testing procedure.

• AKA: Type I Error, Type 1 Error, Alpha Error, False Rejection Error, Type I Statistical Hypothesis Testing Error, False Positive Error (in diagnostic contexts).
• Context:
  • It can typically occur when a test statistic falls in the rejection region despite the null hypothesis being true.
  • It can typically be controlled by setting an appropriate significance level (α) that defines maximum acceptable Type I error probability.
  • It can typically be calculated as the probability P(reject H₀ | H₀ is true), denoted by α.
  • It can typically correspond to a False Positive Classification in binary classification contexts.
  • It can often increase when performing multiple hypothesis tests without multiple testing correction.
  • It can often be considered more serious than Type II Hypothesis Testing Error in safety-critical applications.
  • It can often trade off with Type II Hypothesis Testing Error risk in hypothesis test design.
  • It can often result from random sampling variation even with properly conducted tests.
  • It can often lead to false discovery and incorrect scientific conclusions.
  • It can often be reduced through stringent significance levels or replication studies.
  • It can range from being a Conservative Type I Error to being a Liberal Type I Error, depending on its significance threshold.
  • It can range from being a Single Test Type I Error to being a Multiple Test Type I Error, depending on its testing context.
  • It can range from being a Random Type I Error to being a Systematic Type I Error, depending on its error source.
  • It can range from being a Controlled Type I Error to being an Uncontrolled Type I Error, depending on its error management.
  • It can range from being a Marginal Type I Error to being a Family-Wise Type I Error, depending on its error scope.
  • It can be managed through Family-Wise Error Rate control in multiple comparisons.
  • It can be controlled using Bonferroni Correction, Holm-Bonferroni Method, or False Discovery Rate procedures.
  • It can impact research reproducibility and scientific credibility.
  • It can be visualized in hypothesis testing diagrams showing rejection regions and acceptance regions.
  • ...
• Example(s):
  • Medical Testing Type I Errors, such as:
    • Disease Screening False Positive where healthy patient diagnosed as diseased (α = 0.05).
    • COVID-19 Test False Positive indicating infection in uninfected person.
    • Cancer Screening False Alarm triggering unnecessary invasive procedures.
    • Drug Efficacy False Positive where ineffective treatment appears effective.
    • Genetic Test False Positive incorrectly identifying disease risk.
  • Quality Control Type I Errors, such as:
    • Manufacturing Process False Alarm unnecessarily stopping production line.
    • Product Quality False Rejection discarding acceptable products.
    • Software Bug False Detection reporting non-existent errors.
    • Network Intrusion False Alert triggering unnecessary security response.
  • Research Type I Errors, such as:
    • P-Hacking Result from selective reporting of significant results.
    • Publication Bias Outcome where only significant results get published.
    • Multiple Testing False Discovery from uncorrected multiple comparisons.
    • Data Dredging False Positive finding spurious patterns in data.
  • Legal System Type I Errors, such as:
    • False Conviction of innocent defendant (convicting when should acquit).
    • False Patent Rejection denying valid patent application.
    • False Regulatory Violation finding compliance breach where none exists.
  • Financial Type I Errors, such as:
    • False Fraud Detection flagging legitimate transaction as fraudulent.
    • False Market Signal triggering unnecessary trading action.
    • Credit Default False Prediction denying loan to creditworthy applicant.
  • Environmental Type I Errors, such as:
    • False Pollution Alert triggering unnecessary evacuation.
    • Climate Change False Signal detecting trend in random variation.
    • Species Extinction False Alarm declaring species extinct when still present.
  • Machine Learning Type I Errors, such as:
    • Spam Filter False Positive blocking legitimate email.
    • Face Recognition False Match incorrectly identifying person.
    • Anomaly Detection False Alert flagging normal behavior as anomalous.
  • ...
• Counter-Example(s):
  • Type II Hypothesis Testing Error, which fails to reject a false null hypothesis.
  • True Positive Decision, which correctly rejects a false null hypothesis.
  • True Negative Decision, which correctly accepts a true null hypothesis.
  • False Negative Classification, which incorrectly accepts a false null hypothesis.
  • Correct Statistical Decision, which makes the right hypothesis testing choice.
• See: False Positive Classification (equivalent in classification context), Statistical Hypothesis Testing Task, Significance Level, P-Value, Multiple Testing Problem, Family-Wise Error Rate, False Discovery Rate, Statistical Power, Null Hypothesis, Test Statistic, Rejection Region, Statistical Hypothesis Testing Decision Error, Type I Error Probability Measure, Bonferroni Correction, Statistical Decision Theory, Neyman-Pearson Lemma, Hypothesis Test Sensitivity.

---

---

References

2020

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/type_I_and_type_II_errors Retrieved:2020-10-5.
  • In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the non-rejection of a false null hypothesis (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility for non-deterministic algorithms. By selecting a low threshold (cut-off) value and modifying the alpha (p) level, the quality of the hypothesis test can be increased. The knowledge of Type I errors and Type II errors is widely used in medical science, biometrics and computer science.

    Intuitively, type I errors can be thought of as errors of commission, and type II errors as errors of omission. For example, in the context of binary classification, when trying to decide whether an input image X is an image of a dog: an error of commission (type I) is classifying X as a dog when it isn't, whereas an error of omission (type II) is classifying X as not a dog when it is.

2009

• http://www.introductorystatistics.com/escout/main/Glossary.htm
  • QUOTE: type I (hypothesis test) error: The error of incorrectly rejecting a null hypothesis when it is true.

---