Plus-Four Adjustment Method

A Plus-Four Adjustment Method is a continuity correction method that adds two pseudo-successes and two pseudo-failures to binomial counts to improve confidence interval coverage in small samples.

• AKA: Agresti-Coull Adjustment Method, Add-Four Method, Plus-Four Continuity Correction, Modified Wald Adjustment Method.
• Context:
  • It can typically transform proportions as p̃ = (x+2)/(n+4) where x is successes and n is trials.
  • It can typically shift extreme proportions toward 0.5 to avoid boundary problems.
  • It can typically improve coverage probability for Wilson score intervals and Wald intervals.
  • It can often be applied to precision calculation as (TP+2)/(TP+FP+4) and recall calculation as (TP+2)/(TP+FN+4).
  • It can often provide conservative estimates that trade slight bias for better coverage.
  • It can often work well for sample sizes as small as n=5 according to Agresti-Coull.
  • It can range from being a Standard Plus-Four Adjustment Method to being a Generalized Plus-Four Adjustment Method, depending on its adjustment constant.
  • It can range from being a Symmetric Plus-Four Adjustment Method to being a Asymmetric Plus-Four Adjustment Method, depending on its success-failure balance.
  • It can range from being a Fixed Plus-Four Adjustment Method to being a Adaptive Plus-Four Adjustment Method, depending on its sample size sensitivity.
  • It can range from being a Single Plus-Four Adjustment Method to being a Iterated Plus-Four Adjustment Method, depending on its application count.
  • ...
• Example(s):
  • Basic Proportion Adjustments, such as:
    • Original: 3 successes in 10 trials → p=0.3.
    • Adjusted: (3+2)/(10+4) = 5/14 = 0.357.
    • Pulls extreme values toward center, stabilizes variance.
  • F1 Component Adjustments, such as:
    • Precision: TP=8, FP=2 → (8+2)/(8+2+4) = 10/14 = 0.714 vs raw 0.8.
    • Recall: TP=8, FN=1 → (8+2)/(8+1+4) = 10/13 = 0.769 vs raw 0.889.
    • F1 from adjusted values: more conservative, better coverage.
  • Coverage Improvement Examples, such as:
    • n=10: Wald CI coverage 78%, Plus-Four Wald coverage 93%.
    • n=20: Wald CI coverage 87%, Plus-Four Wald coverage 94%.
    • n=50: Wald CI coverage 92%, Plus-Four Wald coverage 95%.
  • ...
• Counter-Example(s):
  • Jeffreys Prior Adjustment, which adds 0.5 to all cells.
  • Yates Continuity Correction, which subtracts 0.5 from |O-E|.
  • No Adjustment Method, which uses raw counts.
• See: Continuity Correction Method, Wilson Score Interval, Agresti-Coull Interval, Small Sample Method, Binomial Proportion, Continuity Correction in Performance Measure Method, Coverage Probability, Conservative Estimation, Pseudo-Count Method, Confidence Interval Construction.

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