Null Hypothesis Rejection Decision

A Null Hypothesis Rejection Decision is a hypothesis testing statistical inference binary classification decision that concludes there is sufficient evidence to reject the null hypothesis based on comparing a test statistic or p-value to a predetermined significance threshold.

• AKA: Rejecting the Null, Null Rejection, Significant Result Decision, H0 Rejection.
• Context:
  • It can typically occur when P-Value falls below significance level (alpha).
  • It can typically indicate Statistical Evidence against null hypothesis assumption.
  • It can typically lead to acceptance of Alternative Hypothesis by logical implication.
  • It can often result from Extreme Test Statistic in sampling distribution tail.
  • It can often trigger Publication Decision in research dissemination.
  • It can often require Effect Size Consideration for practical significance.
  • ...
  • It can range from being a Weak Null Hypothesis Rejection Decision to being a Strong Null Hypothesis Rejection Decision, depending on its evidence strength.
  • It can range from being a Marginal Null Hypothesis Rejection Decision to being a Decisive Null Hypothesis Rejection Decision, depending on its p-value magnitude.
  • It can range from being a Single-Test Null Hypothesis Rejection Decision to being a Multiple-Test Null Hypothesis Rejection Decision, depending on its testing context.
  • It can range from being a Exploratory Null Hypothesis Rejection Decision to being a Confirmatory Null Hypothesis Rejection Decision, depending on its research phase.
  • ...
  • It can be incorrect when Type I Error occurs (rejecting true null).
  • It can require Multiple Testing Adjustment in simultaneous testing.
  • It can inform Follow-Up Study Design for result confirmation.
  • It can influence Meta-Analysis Inclusion in systematic reviews.
  • ...
• Example(s):
  • Clinical Trial Rejection Decisions, such as:
    • Drug Efficacy Null Rejection concluding treatment differs from placebo (p < 0.05).
    • Safety Threshold Null Rejection finding adverse event rate exceeds baseline (p < 0.01).
    • Dose-Response Null Rejection detecting significant trend across doses (p < 0.001).
  • Quality Control Rejection Decisions, such as:
    • Process Mean Null Rejection detecting shift from target specification (p < 0.05).
    • Variance Homogeneity Null Rejection finding unequal variability (p < 0.10).
    • Defect Rate Null Rejection identifying quality deterioration (p < 0.01).
  • Research Study Rejection Decisions, such as:
    • Correlation Null Rejection finding significant association (r ≠ 0, p < 0.05).
    • Group Difference Null Rejection detecting mean differences (t-test, p < 0.05).
    • Independence Null Rejection establishing variable dependence (χ², p < 0.05).
  • ...
• Counter-Example(s):
  • Failure to Reject Null Hypothesis, which maintains null hypothesis due to insufficient evidence.
  • Type II Error, which fails to reject false null hypothesis.
  • Inconclusive Result, which neither strongly supports nor rejects null.
  • Bayesian Posterior Assessment, which updates belief rather than binary decision.
• See: Statistical Hypothesis Testing Task, Null Hypothesis, P-Value, Significance Level, Alternative Hypothesis, Type I Hypothesis Testing Error, Statistical Decision Theory.

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