Derivation of Probability pxu
Source: http://mathworld.wolfram.com/ConfidenceInterval.html, reference AB30
Assuming Normal Distribution of results:
Pxu = ERF(n/SQRT(2))
where
- Pxu = probability result x lies within ± n SD of mean u in figure A
- ERF = error function
- n = specified number of Standard Deviations
- SD = Standard Deviation
Substituting #SD for n and taking absolute value of # SD:
Pxu = ERFC(ABS(#SD)/(SQRT(2)))
where
- Pxu = probability each independent result lies within # SD of either side of mean = either half of area under curve in figure B
- # SD = measured difference between any result and the mean
Taking complement of error function to select area outside of confidence interval:
pxu = ERFC(ABS(#SD)/(SQRT(2)))
where
- pxu = probability any result lies outside # SD of either side of mean = either half of area under curve in figure C
- ERFC = complimentary error function = 1 - ERF
pxu = ERFC(ABS(#SD)/(SQRT(2)))
Top of page |