p-Value Measure

A p-Value Measure is a statistical measure that calculates the probability of obtaining test results at least as extreme as those observed under the assumption that the null hypothesis is true.

• AKA: P-Value Calculator, P-Value Function, Significance Probability Measure, P-Value Computing Function, Tail Probability Calculator.
• Context:
  • Function Domain: a Test Statistic Value, Sampling Distribution, and Alternative Hypothesis Direction.
  • Function Range: an Observed p-Value between 0 and 1.
  • It can typically compute observed p-values from test statistics using appropriate sampling distributions.
  • It can typically produce an Observed p-Value that quantifies statistical evidence against the null hypothesis.
  • It can typically utilize cumulative distribution functions to calculate tail probabilities.
  • It can often be implemented in statistical software systems and hypothesis testing algorithms.
  • It can often apply different formulas depending on the statistical test type and alternative hypothesis direction.
  • It can often incorporate degrees of freedom for tests involving t-distributions or chi-square distributions.
  • It can range from being a Simple p-Value Measure to being a Complex p-Value Measure, depending on its test complexity.
  • It can range from being an Exact p-Value Measure to being an Approximate p-Value Measure, depending on its calculation method.
  • It can range from being a Parametric p-Value Measure to being a Non-Parametric p-Value Measure, depending on its distributional assumptions.
  • It can range from being a One-Tailed p-Value Measure to being a Two-Tailed p-Value Measure, depending on its hypothesis directionality.
  • It can handle both continuous distributions and discrete distributions through appropriate methods.
  • It can be adjusted for multiple comparisons using correction methods like Bonferroni correction.
  • It can utilize permutation test algorithms for exact p-values when assumptions are violated.
  • It can employ Monte Carlo methods for approximate p-values in complex scenarios.
  • It can incorporate continuity corrections for discrete test statistics.
  • ...
• Example(s):
  • Parametric p-Value Measures, such as:
    • t-Test p-Value Measure calculating P(|T| ≥ |t|) using t-distribution with df degrees of freedom.
    • Z-Test p-Value Measure calculating P(|Z| ≥ |z|) using standard normal distribution.
    • F-Test p-Value Measure calculating P(F ≥ f) using F-distribution for variance comparisons.
    • Chi-Square Test p-Value Measure calculating P(χ² ≥ χ²ₒᵦₛ) for independence testing.
  • Non-Parametric p-Value Measures, such as:
    • Wilcoxon Test p-Value Measure using rank sum distributions.
    • Mann-Whitney U p-Value Measure for independent samples.
    • Kruskal-Wallis p-Value Measure for multiple group comparisons.
    • Permutation Test p-Value Measure using empirical distributions from resampling.
  • Exact p-Value Measures, such as:
    • Fisher's Exact Test p-Value Measure for 2×2 contingency tables.
    • Binomial Test p-Value Measure for proportion testing.
    • McNemar's Test p-Value Measure for paired categorical data.
  • Correlation p-Value Measures, such as:
    • Pearson Correlation p-Value Measure testing H₀: ρ = 0.
    • Spearman Correlation p-Value Measure for rank correlations.
    • Kendall's Tau p-Value Measure for concordance testing.
  • Distribution Test p-Value Measures, such as:
    • Kolmogorov-Smirnov p-Value Measure for distribution comparisons.
    • Shapiro-Wilk p-Value Measure for normality testing.
    • Anderson-Darling p-Value Measure for goodness-of-fit.
  • ...
• Counter-Example(s):
  • Test Statistic Measure, which calculates the standardized statistic rather than its probability.
  • Effect Size Measure, which quantifies magnitude rather than significance probability.
  • Confidence Interval Measure, which provides range estimates rather than single probabilities.
  • Bayes Factor Measure, which computes evidence ratios rather than frequentist probabilities.
  • Likelihood Function, which evaluates parameter likelihood rather than tail probabilities.
  • Posterior Probability Measure, which incorporates prior information unlike p-values.
• See: Observed p-Value, Statistical Significance Measure, Test Statistic, Sampling Distribution, Cumulative Distribution Function, Statistical Hypothesis Testing Task, Extreme Test Statistic Measure, Type I Error Probability Measure, Multiple Testing Problem.

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