THE INVESTIGATION OF ERRORS IN PATHOLOGY TESTS FOR VITAMIN B12 AND FOLATE DEFICIENCY BY MEANS OF MEDICAL EXPERIMENTS
 INTRODUCTION THE SERUM VITAMIN B12 INVESTIGATION THE METHYLMALONIC ACID INVESTIGATION THE HOMOCYSTEINE INVESTIGATION THE HOLOTRANSCOBALAMIN INVESTIGATION THE FOLATE INVESTIGATION REFERENCES AND LINKS B12 AND FOLATE INFORMATION RESPONSES TO INVESTIGATION
 THE SERUM B12 EXPERIMENT - A THE SERUM B12 EXPERIMENT - B SERUM B12 EVIDENCE SERUM B12 ERRORS
 Summary Analytes and Laboratories Objectives Findings
 Method Analysis - CI Analysis - Pxu Analysis - Pab
 Observations Lab Performance
 Results - Notes Notes for Charts and Tables
 Results - Assay Quality
 Conclusions Assay Quality

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

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