THE VITAMIN B12 AND FOLATE PATHOLOGY INVESTIGATION
THE INVESTIGATION OF ERRORS IN PATHOLOGY TESTS
FOR VITAMIN B12 AND FOLATE DEFICIENCY
BY MEANS OF MEDICAL EXPERIMENTS
THE SERUM VITAMIN B12 INVESTIGATION
THE SERUM B12 EXPERIMENT - B
Summary
Method
Analysis - Pab
Observations
Results - Notes
Results - Assay Quality
Conclusions

Derivation of Probability pab

Source: http://mathworld.wolfram.com/ConfidenceInterval.html, reference AB30

Assuming Normal Distribution of results:

Pxu = ERF(n/SQRT(2))

where

  • Pxu = probability result lies within ± n SD of mean
  • ERF = error function
  • n = specified number of SD
  • SD = Standard Deviation

If, instead of the difference between one result and the mean, we have the difference between any two results then we must use Pab instead of Pxu:

Pab (SQRT(n^2 + n^2)) = ERF(n/SQRT(2)) Taking the RMS value of the two errors

Pab (SQRT(2)n) = ERF(n/SQRT(2)) Simplifying LHS

Pab = ERF(n/2) Subst SQRT(2)n for n in RHS

where

  • Pab = probability that two results lie within n SD of each other, as in figure A

Substituting #SD for n and taking absolute value of # SD:

Pab = ERFC(ABS(#SD/2))

where

  • Pab = probability two results lie within # SD each other = area under curve in figure B
  • # SD = measured difference between two results

Taking complement of error function to select area outside of confidence interval:

pab = ERFC(ABS(#SD/2))

where

  • pab = probability two result lie outside # SD each other = area under curve in figure C
  • ERFC = complimentary error function = 1 - ERF

pab = ERFC(ABS(#SD/2))

Top of page

This web site is owned, designed and maintained by Paul Henry Golding of Nambour, QLD, Australia. © 2007-2016