Editing Reference range (section)

====Probability of random variability====
Reference ranges aid in the evaluation of whether a test result's deviation from the mean is a result of random variability or a result of an underlying disease or condition. If the reference group used to establish the reference range can be assumed to be representative of the individual person in a healthy state, then a test result from that individual that turns out to be lower or higher than the reference range can be interpreted as that there is less than 2.5% probability that this would have occurred by random variability in the absence of disease or other condition, which, in turn, is strongly indicative for considering an underlying disease or condition as a cause.

Such further consideration can be performed, for example, by an [[Differential diagnosis#Specific methods|epidemiology-based differential diagnostic procedure]], where potential candidate conditions are listed that may explain the finding, followed by calculations of how probable they are to have occurred in the first place, in turn followed by a comparison with the probability that the result would have occurred by random variability.

If the establishment of the reference range could have been made assuming a normal distribution, then the probability that the result would be an effect of random variability can be further specified as follows:

The [[standard deviation]], if not given already, can be inversely calculated by the fact that the [[absolute value]] of the difference between the mean and either the upper or lower limit of the reference range is approximately 2 standard deviations (more accurately 1.96), and thus:

:{{math|Standard deviation (s.d.) ≈ {{sfrac|{{mabs | (Mean) - (Upper limit) }} |2}}}}.

The [[standard score]] for the individual's test can subsequently be calculated as:

:{{math|1= Standard score (''z'') = {{sfrac|{{mabs | (Mean) - (individual measurement) }} |s.d.}}}}.

The probability that a value is of a certain distance from the mean can subsequently be calculated from the [[Standard score#prediction intervals|relation between standard score and prediction intervals]]. For example, a standard score of 2.58 corresponds to a prediction interval of 99%,<ref name=Kirkup2002>[https://books.google.com/books?id=rDsec-JnCAwC&pg=PA111 Page 111] in: {{cite book |author=Kirkup, Les |title=Data analysis with Excel: an introduction for physical scientists |publisher=Cambridge University Press |location=Cambridge, UK |year=2002 |isbn=978-0-521-79737-5 }}</ref> corresponding to a probability of 0.5% that a result is at least such far from the mean in the absence of disease.