Evidential Measure

An Evidential Measure is a quantitative statistical inference support measure that quantifies the strength or weight of evidence for or against a hypothesis, claim, or model based on observed data.

• AKA: Evidence Measure, Statistical Evidence Measure, Evidential Weight, Evidence Strength Measure.
• Context:
  • It can typically quantify Information Content supporting statistical inference.
  • It can typically guide Decision Making Processes through evidence assessment.
  • It can typically compare Competing Hypothesises through relative evidence.
  • It can often integrate Multiple Data Sources into unified evidence.
  • It can often calibrate Uncertainty Quantification in probabilistic reasoning.
  • It can often inform Model Selection through evidence comparison.
  • ...
  • It can range from being a Weak Evidential Measure to being a Strong Evidential Measure, depending on its evidence magnitude.
  • It can range from being a Simple Evidential Measure to being a Composite Evidential Measure, depending on its structural complexity.
  • It can range from being a Frequentist Evidential Measure to being a Bayesian Evidential Measure, depending on its statistical paradigm.
  • It can range from being a Discrete Evidential Measure to being a Continuous Evidential Measure, depending on its value domain.
  • ...
  • It can support Evidence-Based Practice across scientific disciplines.
  • It can facilitate Meta-Analysis through evidence synthesis.
  • It can enable Sequential Analysis through evidence accumulation.
  • It can inform Regulatory Decisions through evidence standards.
  • ...
• Example(s):
  • Probability-Based Evidential Measures, such as:
    • P-Value measuring evidence against null hypothesis.
    • Posterior Probability quantifying updated belief.
    • False Discovery Rate controlling multiple testing evidence.
  • Likelihood-Based Evidential Measures, such as:
    • Likelihood Ratio comparing hypothesis support.
    • Bayes Factor quantifying relative evidence.
    • AIC Weight measuring model evidence.
  • Information-Theoretic Evidential Measures, such as:
    • Kullback-Leibler Divergence measuring information gain.
    • Mutual Information quantifying variable dependence.
    • Fisher Information measuring parameter information.
  • Effect-Based Evidential Measures, such as:
    • Cohen's d standardizing effect magnitude.
    • Odds Ratio quantifying association strength.
    • R-Squared measuring variance explanation.
  • ...
• Counter-Example(s):
  • Descriptive Statistic, which summarizes data without evidence assessment.
  • Test Statistic, which transforms data without direct evidence interpretation.
  • Point Estimate, which provides value without evidence strength.
  • Raw Data, which lacks evidence quantification.
• See: Statistical Evidence, Statistical Inference, Hypothesis Testing, Model Selection, Decision Theory, Information Theory, Bayesian Inference.

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