Table of minimum percentages estimated using Adjusted Wald Method at 99% confidence

wald.go

package main

import (
	"fmt"
	"math"
)

func max(l, r float64) float64 {
	if l > r {
		return l
	}
	return r
}

func adjWald(measuredRate, samplesCollected, samplesRequired float64) float64 {
	zCritical := 2.58 // Magic number from statistics theory
	populationFraction := (samplesRequired - samplesCollected) / (samplesRequired - 1.0)
	rateUncertainty := math.Sqrt(populationFraction*measuredRate*(1-measuredRate)/samplesCollected) * zCritical
	return measuredRate - rateUncertainty
}

func main() {
	for ss := 99.0; ss < 1000.0; ss = ss + 100.0 {
		for pct := 0.01; pct < 1.0; pct = pct * 2 {
			fmt.Printf("%5.0f, %3.0f%%, %6.2f%%\n", ss, pct*100, max(0, adjWald(pct, ss, 1000.0))*100.0)
		}
	}
}

/*

Sample floors computed with Adjusted Wald Method at 99% confidence.

E.g. at Sample Size (SSize) of 199 and error rate (Rate) of 32%,
the Floor (minimum predicted error rate at 99% confidence) is 24.36%.

SSize, Rate,  Floor
   99,   1%,   0.00%
   99,   2%,   0.00%
   99,   4%,   0.00%
   99,   8%,   1.32%
   99,  16%,   6.97%
   99,  32%,  20.51%
   99,  64%,  52.18%
  199,   1%,   0.00%
  199,   2%,   0.00%
  199,   4%,   0.79%
  199,   8%,   3.56%
  199,  16%,  10.00%
  199,  32%,  24.36%
  199,  64%,  56.14%
  299,   1%,   0.00%
  299,   2%,   0.25%
  299,   4%,   1.55%
  299,   8%,   4.61%
  299,  16%,  11.42%
  299,  32%,  26.17%
  299,  64%,  58.00%
  399,   1%,   0.00%
  399,   2%,   0.60%
  399,   4%,   2.04%
  399,   8%,   5.28%
  399,  16%,  12.33%
  399,  32%,  27.33%
  399,  64%,  59.19%
  499,   1%,   0.19%
  499,   2%,   0.85%
  499,   4%,   2.40%
  499,   8%,   5.78%
  499,  16%,  13.00%
  499,  32%,  28.18%
  499,  64%,  60.07%
  599,   1%,   0.34%
  599,   2%,   1.06%
  599,   4%,   2.69%
  599,   8%,   6.19%
  599,  16%,  13.55%
  599,  32%,  28.88%
  599,  64%,  60.79%
  699,   1%,   0.47%
  699,   2%,   1.25%
  699,   4%,   2.95%
  699,   8%,   6.55%
  699,  16%,  14.04%
  699,  32%,  29.50%
  699,  64%,  61.43%
  799,   1%,   0.59%
  799,   2%,   1.43%
  799,   4%,   3.20%
  799,   8%,   6.89%
  799,  16%,  14.50%
  799,  32%,  30.09%
  799,  64%,  62.03%
  899,   1%,   0.73%
  899,   2%,   1.62%
  899,   4%,   3.46%
  899,   8%,   7.26%
  899,  16%,  15.00%
  899,  32%,  30.72%
  899,  64%,  62.69%
  999,   1%,   0.97%
  999,   2%,   1.96%
  999,   4%,   3.95%
  999,   8%,   7.93%
  999,  16%,  15.91%
  999,  32%,  31.88%
  999,  64%,  63.88%
*/