Type II Hypothesis Testing Error

A Type II Hypothesis Testing Error is a hypothesis testing error that occurs when a false null hypothesis fails to be rejected.

• AKA: Type II Error, False Negative Error, Beta Error, Missed Detection Error.
• Context:
  • It can typically occur when the test statistic falls in the acceptance region despite the alternative hypothesis being true.
  • It can often be influenced by effect size, sample size, and significance level through statistical power.
  • It can be calculated as the probability P(fail to reject H₀ | H₀ is false), denoted by β.
  • It can be reduced by increasing sample size or using less conservative significance levels.
  • It can range from being a Low Beta Type II Hypothesis Testing Error to being a High Beta Type II Hypothesis Testing Error, depending on its statistical power.
  • It can trade off with Type I Hypothesis Testing Error risk in hypothesis test design.
  • ...
• Example(s):
  • Medical Testing Type II Errors, such as:
    • Disease Screening Miss where actual disease goes undetected.
    • Drug Efficacy Miss where effective treatment appears ineffective.
  • Quality Control Type II Errors, such as:
    • Defect Detection Failure where defective products pass inspection.
    • Process Shift Miss where process degradation goes unnoticed.
  • Research Type II Errors, such as:
    • Underpowered Study Result with insufficient sample size.
    • Small Effect Size Miss below detection threshold.
  • ...
• Counter-Example(s):
  • Type I Hypothesis Testing Error, which incorrectly rejects a true null hypothesis.
  • True Negative, which correctly accepts a true null hypothesis.
  • True Positive, which correctly rejects a false null hypothesis.
• See: Statistical Power, Effect Size, Sample Size Determination, Beta Risk, Null Hypothesis Testing.

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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
  • type II (hypothesis test) error: The error of incorrectly accepting a null hypothesis when it is false.

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Type_I_and_type_II_errors
  • Type II (β): fail to reject the Null Hypothesis when the null hypothesis is false

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