SITE HOME PAGE THE VITAMIN B12 AND FOLATE PATHOLOGY INVESTIGATION MEDICAL HOME PAGE
 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 MMA EXPERIMENT MMA EVIDENCE MMA ERRORS
 Summary Analytes and Laboratories Objectives Findings
 Method Series 1 Sample Collection Analysis - CI Analysis - Pxu Analysis - Pab
 Observations Summary Problems Lab Performance
 Results - Notes Notes for Charts and Tables
 Results - Series 1 CHW Qualitative CHW Quantitative MP Qualitative MP Quantitative QHPS Qualitative QHPS Quantitative MP vs WCH MP vs CHW MP vs QHPS
 Conclusions Assay Quality Diagnostic Utility

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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