Quantitative methods: statistics and applied mathematics for economics
Quantitative methods tests statistical description, sampling and inference, regression basics, index numbers and financial mathematics, always as tools applied to economic and financial data.
Descriptive statistics
Mean, median, mode; variance with divisor n (population) or n−1 (sample); standard deviation; coefficient of variation (σ/x̄) to compare dispersion across units; quartiles and skewness (in right-skewed income data, mean > median).
Sampling and inference
Central limit theorem: x̄ is approximately normal for large n, with standard error σ/√n. Confidence interval: x̄ ± z·σ/√n. Sample size: n = (zσ/e)². Hypothesis testing: H0/H1, significance α, test statistic, p-value - a small p-value means the data are unlikely under H0, not that H0 has a given probability of being true.
Regression and financial mathematics
OLS: b = Cov(x,y)/Var(x), a = ȳ − b·x̄; R² is the share of explained variance, not causality. Discounting, NPV (accept if positive), IRR (rate at which NPV = 0), compound growth g = (V_final/V_initial)^(1/n) − 1. Indices: Laspeyres uses base-period quantities, Paasche current quantities, so Laspeyres tends to overstate inflation.
Worked example
A sample of n = 100 gives x̄ = 12.5 and σ = 3. SE = 3/10 = 0.3; the 95% CI is 12.5 ± 1.96 × 0.3 = [11.91, 13.09]. For a margin of error of 0.5 at 95%, n = (1.96 × 3 / 0.5)² = 138.3, hence 139 observations.
Traps
Using σ instead of σ/√n; dividing by n rather than n−1 for sample variance; treating R² as proof of causation; phrasing the CI as a probability about μ; using simple instead of compound growth.