Statistics
Working
Statistics cheatsheet
Every formula, rule of thumb and decision you need — four A4 pages, built for the exam desk. Page 1 describes data, page 2 is probability & distributions, page 3 is estimation & testing with the critical values, and page 4 is pure theory — definitions, interpretations and classic true/false traps.
Formulas at a glance
Describe
x̄ = Σxᵢ/N · σ² = Σ(xᵢ − x̄)²/N, sample s² ÷ (n − 1) · quartiles by Tukey's hinges · outliers beyond Q₁ − 1.5·IQR / Q₃ + 1.5·IQR · r = Cov/(SDₓ·SDᵧ) · b = Cov/Var(x), a = ȳ − b·x̄, R² = r².
Probability
P(A∪B) = P(A) + P(B) − P(A∩B) · P(A|B) = P(A∩B)/P(B) · Bayes: P(A|B) = P(B|A)P(A)/P(B) · Bin: C(n,k)pᵏ(1−p)ⁿ⁻ᵏ, E = np · Poisson: λᵏ·e−λ/k!, E = Var = λ · z = (x − μ)/σ.
Infer
CI: x̄ ± tn−1,1−α/2·s/√n · T = (x̄ − μ₀)/s·√n · pooled T = (x̄ − ȳ)/sp·√(nm/(n+m)) · χ² = Σ(o − e)²/e, eᵢⱼ = rowᵢ·colⱼ/n · reject H₀ if p < α.