Statistical Hypothesis Testing Decision Error

A Statistical Hypothesis Testing Decision Error is a inference classification decision error that occurs when a statistical hypothesis test reaches an incorrect conclusion about the truth or falsity of a null hypothesis.

• AKA: Statistical Testing Error, Hypothesis Test Error, Statistical Decision Error, Inference Error.
• Context:
  • It can typically manifest as Type I Error (rejecting true null) or Type II Error (failing to reject false null).
  • It can typically arise from Random Sampling Variation even with correct statistical procedures.
  • It can typically be controlled through Error Rate Selection and Sample Size Determination.
  • It can often result from Test Assumption Violation in real-world data applications.
  • It can often increase with Multiple Testing without appropriate error correction.
  • It can often trade off between error types through significance threshold adjustment.
  • ...
  • It can range from being a Conservative Hypothesis Testing Decision Error to being a Liberal Hypothesis Testing Decision Error, depending on its threshold stringency.
  • It can range from being a Single-Test Hypothesis Testing Decision Error to being a Multiple-Test Hypothesis Testing Decision Error, depending on its testing context.
  • It can range from being a Parametric Hypothesis Testing Decision Error to being a Non-Parametric Hypothesis Testing Decision Error, depending on its test methodology.
  • It can range from being a Frequentist Hypothesis Testing Decision Error to being a Bayesian Hypothesis Testing Decision Error, depending on its statistical framework.
  • ...
  • It can impact Research Validity through incorrect scientific conclusions.
  • It can influence Clinical Decision Making through misidentified treatment effects.
  • It can affect Quality Control Processes through incorrect defect detection.
  • It can contribute to Replication Failure in scientific research.
  • ...
• Example(s):
  • Type I (False Positive) Error), such as:
    • Ineffective Drug Approval Error concluding drug works when it doesn't.
    • False Discrimination Finding Error detecting bias where none exists.
    • Spurious Correlation Error finding relationship in random noise.
  • Type II (False Negative) Error), such as:
    • Missed Treatment Effect Error failing to detect real therapeutic benefit.
    • Undetected Quality Problem Error missing actual manufacturing defect.
    • Overlooked Association Error not finding true variable relationship.
  • Multiple Testing Errors, such as:
    • Family-Wise Error with at least one false positive among multiple tests.
    • False Discovery Error with incorrect discoveries in large-scale testing.
    • Data Dredging Error from extensive hypothesis searching.
  • ...
• Counter-Example(s):
  • Correct Statistical Decision, where test conclusion matches true state.
  • Computational Error, which involves calculation mistakes rather than decision errors.
  • Measurement Error, which affects data quality rather than inference decision.
  • Model Specification Error, which involves incorrect model rather than test decision.
• See: Statistical Hypothesis Testing Task, Type I Hypothesis Testing Error, Type II Error, Statistical Power, Error Rate, Multiple Testing Problem, Statistical Decision Theory.

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