The great utility of the standard deviation score (= Z-score)
There is great utility in using the standard deviation score (SDS),
also called Z-score, i.e. the difference between observed
(y) and predicted (Y) value divided by the residual scatter (RSD)
about the mean predicted value:
SDS = Z-score = (y - Y)/RSD
The great advantage is that the SDS can be used for any index; if the deviations (y - Y) are normally distributed, regardless of whether we are dealing with the hemoglobin concentration, standing height, serum creatinine concentration or FEV1, the Z-score discloses how rare or common the observation is. For example, if the Z-score is smaller than -1.64 then the observation occurs in only 5% of the reference population. A SDS > +1.96 is encountered in only 2½ per cent of all healthy subjects.
In the reference population, the trajectory from the lowest to the highest SDS encompasses 0 to 100% of all subjects. If we depict the cumulative percentage of the population up to a certain SDS (Y-axis) as a function of the standard deviation score (X-axis), an S-shaped curve is obtained: this then depicts graphically the relationship between percentile and SDS in the reference population.
In overt pathology observed values fall outside the lowest (0%) and highest (100%) percentiles of a healthy population. On that account percentiles are not very practical in pathological cases, but the Z-score looses none of its usefulness. If the Z-score of the FEV1 = -3, for example, this signifies that the FEV1 is far below the 2½ percentile in a healthy population. Particularly if the subject presented with respiratory symptoms chances are small that we are dealing with a ‘normal’ FEV1