BiostatisticsTier 1Medical Sciences concept

Z-score interpretation and normal distribution (percentile equivalence)

Core concept

z = (x - mean) / SD - how many SDs a value sits from the reference mean
- Reference is age- and sex-matched (and often ethnicity-matched)
- z is dimensionless - it compares across units and across tests
Normal distribution, area under the curve:

	Comparator	Use
T-score	Young adult peak bone mass	Diagnoses osteoporosis in postmenopausal women and men >=50 (T <= -2.5)
Z-score	Age- and sex-matched peers	Used in premenopausal women, men <50, children; Z <= -2.0 = "below expected range for age" -> hunt for secondary cause

Osteoporosis is never diagnosed on a Z-score alone - "low bone mass for age" is the correct wording
SD is not SEM: SEM = SD / sqrt(n)
- SD describes the spread of individuals; SEM describes the precision of the mean
- 95% CI of a mean = mean +/- 1.96 x SEM
Skewed data (ferritin, CRP, triglycerides, viral load) break the percentile equivalence - log-transform or use non-parametric methods

Z <= -2.0 on DEXA in a young patient -> screen for secondary osteoporosis: coeliac, hyperthyroidism, hypogonadism, hyperparathyroidism, myeloma, glucocorticoids, anorexia
Paediatric growth charts, head circumference and BMI-for-age all use z-scores
Standardised scoring elsewhere: MoCA/ACE-III demographically corrected norms, neuropsychology, semen analysis, echo chamber dimensions indexed to BSA
Reference intervals are constructed as mean +/- 2 SD -> 5% of healthy people fall outside by definition
- Order 20 unrelated tests on a well person and, on average, one comes back abnormal

3 more sections, plus exam facts

Premium unlocks every note across every specialty, and the full exam fact library behind it.