Log-normal Distribution
In reality, biological parameters tend to have a log-normal distributions, rather than the arithmetical normal distribution (which is generally referred to as normal distribution without any further specification).
An explanation for this log-normal distribution for biological parameters is: The event where a sample has half the value of the mean or median tends to have almost equal probability to occur as the event where a sample has twice the value of the mean or median. Also, only a log-normal distribution can compensate for the inability of almost all biological parameters to be of negative numbers (at least when measured on absolute scales), with the consequence that there is no definite limit to the size of outliers (extreme values) on the high side, but, on the other hand, they can never be less than zero, resulting in a positive skewness.
As shown in diagram at right, this phenomenon has relatively small effect if the standard deviation (as compared to the mean) is relatively small, as it makes the log-normal distribution appear similar to an arithmetical normal distribution. Thus, the arithmetical normal distribution may be more appropriate to use with small standard deviations for convenience, and the log-normal distribution with large standard deviations.
In a log-normal distribution, the geometric standard deviations and geometric mean more accurately estimate the 95% prediction interval than their arithmetic counterparts.
Read more about this topic: Reference Range, Standard Definition, Establishment Methods
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