T-Score Calculators
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T-Score in Bone Density (DEXA)
T-score = (Patient BMD − Mean BMD of young adults) / SD of young adult BMD
WHO osteoporosis criteria (for postmenopausal women and men ≥ 50): Normal: T-score > −1.0; Osteopenia (low bone mass): T-score −1.0 to −2.5; Osteoporosis: T-score ≤ −2.5. T-score = −2.5 means the patient's BMD is 2.5 SDs below the young adult mean. Each SD decrease in BMD approximately doubles fracture risk. DEXA measures hip (femoral neck preferred) and lumbar spine. T-score < −2.5 qualifies for pharmacological treatment (bisphosphonates, denosumab, teriparatide).
Z-Score in Bone Density
Z-score compares to age-matched peers: T-score = (BMD − young adult mean)/SD; Z-score = (BMD − age-matched mean)/SD. Z-score used for: premenopausal women; men < 50; children. Z-score < −2.0 indicates BMD 'below expected range for age.'
T-Statistic in Statistics
One-sample t-test: t = (x̄ − μ₀) / (s / √n). Two-sample t-test: t = (x̄₁ − x̄₂) / s_pooled × √(1/n₁ + 1/n₂). Degrees of freedom: n−1 (one-sample); n₁+n₂−2 (two-sample). P-value from t-distribution at df. |t| > t_critical → reject H₀.
Glossary
Frequently Asked Questions
A T-score of −2.5 means the patient's bone mineral density (BMD) is 2.5 standard deviations below the mean BMD of a young adult reference population (typically peak bone mass at age 25–30). WHO defines: T-score > −1.0: normal bone density. T-score −1.0 to −2.5: osteopenia (low bone mass, increased fracture risk). T-score ≤ −2.5: osteoporosis (high fracture risk; treatment recommended). Each SD decrease in BMD approximately doubles the risk of hip fracture. T-score is calculated at hip (femoral neck or total hip — used for treatment decisions) and lumbar spine; use the lowest score from either site for clinical classification.
T-score: compares patient's BMD to peak bone mass of young adults (age 25–30); used for postmenopausal women and men ≥ 50; used for WHO osteoporosis diagnosis and treatment decisions. Z-score: compares BMD to age-matched, sex-matched peers; used for premenopausal women, men < 50, and children; Z-score < −2.0 indicates BMD below expected range for age — suggests secondary causes of bone loss (hyperparathyroidism, malabsorption, medications). For an 80-year-old woman with BMD significantly below young adults but average for her age: T-score might be −2.5 (osteoporosis), but Z-score could be normal (+0.1), indicating her BMD matches her peers (i.e., age-related bone loss, not a disease process).
One-sample t-test: t = (x̄ − μ₀) / (s/√n); tests whether a sample mean differs from a hypothesized value μ₀. Two-sample independent t-test: t = (x̄₁ − x̄₂) / (s_p × √(1/n₁ + 1/n₂)), where s_p = pooled standard deviation; tests whether two group means differ. The t-statistic measures how many standard errors the sample mean is from the hypothesized value (or how many SEs separate two sample means). Compare to critical t value from t-distribution at appropriate df (n−1 for one-sample; n₁+n₂−2 for two-sample). If |t_calculated| > t_critical: reject H₀; p < α.
T-test: when population SD is unknown (the usual situation in research) and must be estimated from sample data; used for small samples (n < 30); technically valid for any n when population is normal. Uses t-distribution with df = n−1 (heavier tails than normal, accounting for uncertainty in SD estimation). Z-test: when population SD is known (rare in practice); for testing population proportions with large n; when n is very large (> 30), z ≈ t and both give similar results. In practice: virtually all hypothesis tests on means use t-tests. Z-test arises in textbook problems (known σ) and for large-n proportion tests. The t-distribution approaches the standard normal as df → ∞.