If a normal reference range for a test is given, then the mean and standard deviation can be derived if the statistical limits are known. If a value is given for an analyte determined by one method, then a comparable value by another method can be approximated.
Assumptions:
(1) There are 2 methods for measuring an analyte.
(2) Both methods perform with comparable precision and accuracy.
(3) Both reference ranges have a normal distribution with a reference range +/- 2 standard deviations (95.45%).
Parameters:
(1) lower limit of reference range for method 1
(2) upper limit of reference range for method 1
(3) patient value by method 1
(4) lower limit of reference range for method 2
(5) upper limit of reference range for method 2
upper limit of the reference range =
= (mean) + ((number of standard deviations) * (standard deviation))
lower limit of the reference range =
= (mean) - ((number of standard deviations) * (standard deviation))
mean value for the normal reference range =
= (lower limit) + (((upper limit) - (lower limit)) / 2) =
= ((upper limit) + (lower limit)) / 2
standard deviation =
= (((upper limit) - (lower limit)) / 2) / (number of standard deviations in the reference range) =
= ((upper limit) - (lower limit)) / (2 * (number of standard deviations))
Z-score for patient value by method 1 =
= ((patient value) - (mean)) / (standard deviation)
approximate comparative value by method 2 =
= ((Z score) * (standard deviation for method 2)) + (mean for method 2)
