Normal Approximation for P-Value Method

A Normal Approximation for P-Value Method is a p-value approximation method that uses normal cumulative distribution function via error function to derive probability values from Z-scores in hypothesis tests.

• AKA: Gaussian P-Value Approximation, Z-Score to P-Value Method, Normal CDF P-Value Method, Error Function P-Value Method.
• Context:
  • It can typically convert Z-scores to p-values using normal CDF.
  • It can typically apply error function for numerical computation.
  • It can typically support F1 P-Value Calculation Methods and Macro-F1 P-Value Calculation Methods.
  • It can often handle two-sided tests by doubling tail probability.
  • It can often provide accurate approximations for large sample sizes.
  • It can often enable statistical inference without exact distributions.
  • It can range from being a One-Tailed Normal Approximation for P-Value Method to being a Two-Tailed Normal Approximation for P-Value Method, depending on its alternative hypothesis type.
  • It can range from being a Standard Normal Approximation for P-Value Method to being a Scaled Normal Approximation for P-Value Method, depending on its variance parameter.
  • It can range from being a Continuous Normal Approximation for P-Value Method to being a Continuity-Corrected Normal Approximation for P-Value Method, depending on its discrete adjustment.
  • It can range from being a Exact Normal Approximation for P-Value Method to being a Approximate Normal Approximation for P-Value Method, depending on its computation precision.
  • ...
• Example(s):
  • Z-Score P-Value Conversions, such as:
    • Z=2.0 → p-value=0.0455 (two-tailed).
    • Z=1.96 → p-value=0.05 (critical value).
  • Greater Alternative Tests, such as:
    • P(Z > z_obs) = 1 - CDF(z_obs).
    • One-sided upper tail test.
  • Two-Sided Tests, such as:
    • P(|Z| > |z_obs|) = 2 * min(CDF(z), 1-CDF(z)).
    • Symmetric alternative hypothesis.
  • ...
• Counter-Example(s):
  • Exact Binomial P-Value Method, which uses discrete distribution.
  • t-Distribution P-Value Method, which accounts for small samples.
  • Chi-Square P-Value Method, which uses chi-square distribution.
• See: P-Value Approximation Method, Normal Distribution, Cumulative Distribution Function, Error Function, Z-Score, Central Limit Theorem, F1 P-Value Calculation Method, Macro-F1 P-Value Calculation Method, Statistical Hypothesis Testing, Asymptotic Normality, Gaussian Distribution.

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