Biostatistics Formula Sheet

Complete formula reference for exams and research. Search by name or keyword.

Diagnostic Test Accuracy

SensitivityTP / (TP + FN)

Proportion of true positives correctly identified. A highly sensitive test has few false negatives — good for ruling OUT disease (SnNout).

TPTrue positives (sick people correctly testing positive)
FNFalse negatives (sick people incorrectly testing negative)
Example: HIV test sensitivity of 99.5% means 1 in 200 HIV-positive individuals will test falsely negative.
SpecificityTN / (TN + FP)

Proportion of true negatives correctly identified. A highly specific test has few false positives — good for ruling IN disease (SpPin).

TNTrue negatives
FPFalse positives
Sensitivity and specificity are properties of the test itself — they do not change with disease prevalence.
Positive Predictive Value (PPV)TP / (TP + FP)

Probability that a positive test result is truly positive. Varies with disease prevalence — higher prevalence → higher PPV.

TPTrue positives
FPFalse positives
Negative Predictive Value (NPV)TN / (TN + FN)

Probability that a negative test result is truly negative. Higher prevalence → lower NPV.

TNTrue negatives
FNFalse negatives
Likelihood Ratio (+)Sensitivity / (1 − Specificity)

How much more likely a positive test is in a person with the disease vs without. LR+ > 10 is very strong evidence.

Rule of thumb: LR+ >10 rules in, LR− <0.1 rules out disease with certainty.
Likelihood Ratio (−)(1 − Sensitivity) / Specificity

How much less likely a negative test is in a person with disease. LR− < 0.1 strongly rules out disease.

Epidemiology & Risk Measures

Odds Ratio (OR)(a × d) / (b × c)

Association measure for case-control studies. OR >1 = increased odds; <1 = decreased odds; 1 = no association.

a, b, c, dCells of 2×2 table: a=exposed cases, b=exposed controls, c=unexposed cases, d=unexposed controls
Relative Risk (RR)[a/(a+b)] / [c/(c+d)]

Ratio of risk in exposed vs unexposed groups. Used in cohort studies and RCTs. RR = 1 means no association.

OR approximates RR when the outcome is rare (<10% in unexposed group).
Absolute Risk Reduction (ARR)CER − EER

The actual reduction in risk with treatment. More clinically meaningful than RR alone.

CERControl event rate (risk without treatment)
EERExperimental event rate (risk with treatment)
Number Needed to Treat (NNT)1 / ARR

How many patients must be treated for one to benefit. NNT = 1 is perfect; lower is better. NNH uses the same formula for harms.

Example: If ARR = 5%, NNT = 20 (treat 20 patients to prevent 1 event).
Attributable Risk (AR)Risk(exposed) − Risk(unexposed)

The excess risk in exposed group attributable to the exposure. Also called risk difference.

Population Attributable Fraction (PAF)(RR − 1) × Pe / [1 + Pe(RR−1)]

Proportion of disease in the total population attributable to the exposure. Used in public health to estimate disease burden.

PePrevalence of exposure in the population
RRRelative risk

Confidence Intervals & Hypothesis Testing

95% CI for Meanx̄ ± 1.96 × SE

Range within which the true population mean lies with 95% confidence. Use t-critical value (not 1.96) when n < 30 and σ unknown.

SEStandard error = s / √n
1.96z-value for 95% CI; use 2.576 for 99% CI
95% CI for Proportionp̂ ± 1.96 √[p̂(1−p̂)/n]

Valid when np̂ ≥ 5 and n(1−p̂) ≥ 5. Use exact binomial (Clopper-Pearson) for small samples.

p̂Sample proportion
nSample size
One-Sample t-statistict = (x̄ − μ₀) / (s/√n)

Tests if sample mean differs from a hypothesised value. df = n − 1.

x̄Sample mean
μ₀Hypothesised population mean
sSample standard deviation
Chi-Square Statisticχ² = Σ(O−E)²/E

Tests association between categorical variables, or goodness of fit. df = (rows−1)(cols−1) for contingency tables.

OObserved frequency
EExpected frequency = (row total × col total) / grand total
Sample Size (Two-Proportion)n = (z_α + z_β)² × (p₁q₁+p₂q₂) / d²

Estimate required n to detect a difference d between two proportions with given power (1−β) and significance level α.

z_α = 1.96 for α=0.05; z_β = 0.842 for 80% power, 1.282 for 90% power.
Standard Error of Mean (SEM)SE = s / √n

Estimates how much the sample mean would vary if the study were repeated. Smaller with larger n.

sSample standard deviation
nSample size
SEM ≠ SD. SD describes variability in the sample; SEM describes precision of the mean estimate.

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For educational use. Reviewed by Dr. Vishnuvardhan Thotakura (MBBS, MPH, CPH). Last reviewed Sep 2026.