Common P-Value Misconception

A Common P-Value Misconception is a common widespread statistical interpretation misconception that incorrectly equates p-value with the probability of type I error or the probability that the null hypothesis is true.

• AKA: P-Value Fallacy, P-Value Misinterpretation Error, Statistical Significance Fallacy, Inverse Probability Fallacy.
• Context:
  • It can typically manifest through Incorrect Probability Statements claiming p-value represents hypothesis truth probability.
  • It can typically lead to Overconfident Research Conclusions by misunderstanding statistical evidence strength.
  • It can typically arise from Statistical Education Gaps in distinguishing conditional probability directions.
  • It can often result in Publication Bias through misinterpretation of statistical significance thresholds.
  • It can often cause Replication Crisis Contribution through improper evidence evaluation.
  • It can often perpetuate Statistical Malpractice in research publications.
  • ...
  • It can range from being a Minor P-Value Misconception to being a Major P-Value Misconception, depending on its research impact severity.
  • It can range from being a Novice P-Value Misconception to being an Expert P-Value Misconception, depending on its practitioner experience level.
  • It can range from being an Isolated P-Value Misconception to being a Systematic P-Value Misconception, depending on its occurrence pattern.
  • It can range from being a Verbal P-Value Misconception to being a Computational P-Value Misconception, depending on its manifestation form.
  • ...
  • It can undermine Research Validity through incorrect statistical inference.
  • It can distort Scientific Communication through misleading result interpretation.
  • It can influence Policy Decisions based on misunderstood evidence strength.
  • It can affect Grant Funding Decisions through inflated significance claims.
  • ...
• Example(s):
  • Direct Probability Misconceptions, such as:
    • 3% Error Probability Misconception claiming p=0.03 means 3% chance of false positive.
    • 97% Truth Probability Misconception claiming p=0.03 means 97% chance alternative hypothesis is true.
    • 5% Null Truth Misconception claiming p=0.05 means 5% chance null hypothesis is true.
  • Threshold Interpretation Misconceptions, such as:
    • Binary Significance Misconception treating p=0.049 as fundamentally different from p=0.051.
    • Proof Threshold Misconception claiming p<0.05 proves research hypothesis.
    • No Effect Misconception claiming p>0.05 proves null hypothesis is true.
  • Replication Misconceptions, such as:
    • 95% Replication Misconception believing p=0.05 means 95% chance of study replication.
    • Power Confusion Misconception conflating p-value with statistical power.
    • Sample Size Independence Misconception ignoring p-value dependence on sample size.
  • ...
• Counter-Example(s):
  • Correct P-Value Interpretation, which recognizes p-value as conditional probability under null hypothesis.
  • Bayesian Posterior Probability, which directly estimates hypothesis probability given data.
  • Likelihood Ratio, which compares evidence strength between hypotheses.
  • Confidence Interval Interpretation, which provides parameter range estimates rather than hypothesis tests.
• See: Statistical Misconception, P-Value, Type I Hypothesis Testing Error, Statistical Hypothesis Testing Task, Null Hypothesis, Statistical Significance Measure, Conditional Probability, Research Methodology Error.

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