F1 P-Value Calculation Method

An F1 P-Value Calculation Method is a p-value calculation method that derives statistical significance for F1 scores using Z-scores computed from delta-method standard errors against a null hypothesis.

• AKA: F1 Significance Test Method, F1 Hypothesis Testing Method, F1 Score P-Value Method, F1 Statistical Test.
• Context:
  • It can typically compute Z-scores using Delta-Method F1 Standard Error Estimation Methods.
  • It can typically apply Normal Approximation for P-Value Methods to derive p-values.
  • It can typically test against null hypothesis values like 0.5 or random baseline.
  • It can often support two-sided alternative hypothesis tests or one-sided alternative hypothesis tests.
  • It can often enable statistical inference for model performance evaluation.
  • It can often handle small sample adjustments through t-distribution approximations.
  • It can range from being a Single F1 P-Value Calculation Method to being a Multiple F1 P-Value Calculation Method, depending on its test multiplicity.
  • It can range from being a Exact F1 P-Value Calculation Method to being a Approximate F1 P-Value Calculation Method, depending on its distribution assumption.
  • It can range from being a Conservative F1 P-Value Calculation Method to being a Liberal F1 P-Value Calculation Method, depending on its variance estimation.
  • It can range from being a Parametric F1 P-Value Calculation Method to being a Non-Parametric F1 P-Value Calculation Method, depending on its distributional assumption.
  • ...
• Example(s):
  • F1 vs Random Baseline Tests, such as:
    • F1_obs=0.857, null=0.5, SE=0.028 → Z=(0.857-0.5)/0.028=12.75 → p<0.001 (highly significant).
    • F1_obs=0.55, null=0.5, SE=0.04 → Z=(0.55-0.5)/0.04=1.25 → p=0.211 (not significant).
    • F1_obs=0.75, null=0.333 (random 3-class), SE=0.035 → Z=11.91 → p<0.001.
  • F1 Threshold Significance Tests, such as:
    • Testing if F1=0.82 significantly exceeds minimum threshold of 0.8: Z=(0.82-0.8)/0.015=1.33 → p=0.092 (one-sided).
    • Production readiness test: F1 must significantly exceed 0.85.
  • Temporal F1 Comparisons, such as:
    • Current model F1=0.91 vs previous version null=0.88, testing for significant improvement.
    • Monthly model evaluation against fixed baseline performance.
  • ...
• Counter-Example(s):
  • Bootstrap P-Value Method, which uses resampling distribution.
  • Permutation Test Method, which shuffles labels.
  • Bayesian Posterior Probability Method, which uses prior distributions.
• See: Observed p-Value, Statistical Hypothesis Testing Method, Delta-Method F1 Standard Error Estimation Method, Normal Approximation for P-Value Method, Z-Score for Performance Metric Test Method, Precision P-Value Calculation Method, Recall P-Value Calculation Method, AUC P-Value Calculation Method, Two-Sided Alternative Hypothesis Test, Greater Alternative Hypothesis Test, Null Hypothesis, Statistical Significance, Type I Error.

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