Here is a mathematical formula that acts as a test of clinical significance. This formula helps clinicians determine the clinical value of a research study. When does a patient’s test more likely than not indicate they fall in the normal population? When does he test more likely than not indicate they fall in the abnormal population?

The mean value for the normal population = Xn

The standard deviation for Xn = SDn

The mean value for the abnormal (sick) population = Xa

The standard deviation for Xa = SDa

STEP 1. Calculate the threshold Z value:

Z = (Xa – Xn) / (SDa + SDn)

STEP 2. Calculate the threshold value:

Threshold = Xa – (Z * SDa)

When Xa > Xb, when the patient’s test value is greater than the threshold value, then it is more likely than not that they fall in the abnormal population. When the patient’s test value is less than the threshold value, then it is more likely than not that they fall in the normal population.