Greek letters are ubiquitous in mathematics and statistics. This appendix provides a reference for the Greek alphabet, including pronunciation and common uses in statistical contexts.
| Letter | Lowercase | Uppercase | Name | Pronunciation | Common Statistical Uses |
|---|---|---|---|---|---|
| 1 | α | Α | Alpha | AL-fah | Significance level (Type I error rate); regression intercept |
| 2 | β | Β | Beta | BAY-tah | Type II error rate; regression coefficients; slope parameters |
| 3 | γ | Γ | Gamma | GAM-ah | Gamma distribution; shape parameter |
| 4 | δ | Δ | Delta | DEL-tah | Change or difference; effect size (Cohen’s d uses Roman d) |
| 5 | ε | Ε | Epsilon | EP-si-lon | Error term in models; small quantity approaching zero |
| 6 | ζ | Ζ | Zeta | ZAY-tah | Rarely used in statistics |
| 7 | η | Η | Eta | AY-tah | Effect size (η²); learning rate |
| 8 | θ | Θ | Theta | THAY-tah | Generic parameter; angle |
| 9 | ι | Ι | Iota | eye-OH-tah | Rarely used in statistics |
| 10 | κ | Κ | Kappa | KAP-ah | Cohen’s kappa (agreement); condition number |
| 11 | λ | Λ | Lambda | LAM-dah | Rate parameter (Poisson, exponential); eigenvalue; Wilks’ lambda |
| 12 | μ | Μ | Mu | MYOO | Population mean |
| 13 | ν | Ν | Nu | NOO | Degrees of freedom |
| 14 | ξ | Ξ | Xi | KSEE or ZIGH | Rarely used; sometimes for random variables |
| 15 | ο | Ο | Omicron | OM-i-kron | Rarely used (resembles Roman O) |
| 16 | π | Π | Pi | PIE | Mathematical constant (≈ 3.14159); product notation (Π) |
| 17 | ρ | Ρ | Rho | ROW | Population correlation coefficient; autocorrelation |
| 18 | σ | Σ | Sigma | SIG-mah | Population standard deviation (σ); summation (Σ) |
| 19 | τ | Τ | Tau | TAW (rhymes with cow) | Kendall’s tau; time constant |
| 20 | υ | Υ | Upsilon | OOP-si-lon | Rarely used in statistics |
| 21 | φ | Φ | Phi | FYE or FEE | Phi coefficient; standard normal PDF (φ); golden ratio |
| 22 | χ | Χ | Chi | KYE (rhymes with sky) | Chi-square distribution and test (χ²) |
| 23 | ψ | Ψ | Psi | SIGH or PSEE | Rarely used; sometimes for angles or wave functions |
| 24 | ω | Ω | Omega | oh-MAY-gah | Effect size (ω²); angular frequency |
The following Greek letters conventionally represent population parameters (true but unknown values):
Greek letters are written in LaTeX (and thus in Quarto documents) using backslash commands:
$\alpha$ → α $\Alpha$ → Α
$\beta$ → β $\Beta$ → Β
$\gamma$ → γ $\Gamma$ → Γ
$\delta$ → δ $\Delta$ → Δ
$\epsilon$ → ε $\mu$ → μ
$\sigma$ → σ $\Sigma$ → Σ
$\chi$ → χ $\lambda$ → λ
$\theta$ → θ $\rho$ → ρR supports Greek letters in plots using the expression() function:
# Axis labels with Greek letters
plot(x, y,
xlab = expression(mu),
ylab = expression(sigma^2))
# More complex expressions
title(expression(paste("Mean = ", mu, ", SD = ", sigma)))
# In ggplot2
library(ggplot2)
ggplot(data, aes(x, y)) +
geom_point() +
labs(x = expression(alpha),
y = expression(beta))A useful convention in statistics:
| Population Parameter | Sample Statistic |
|---|---|
| μ (mu) - population mean | \(\bar{x}\) - sample mean |
| σ (sigma) - population SD | s - sample SD |
| ρ (rho) - population correlation | r - sample correlation |
| β (beta) - population slope | b - sample slope |
| π (pi) - population proportion | p̂ - sample proportion |
\[f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}\]
\[z = \frac{x - \mu}{\sigma}\]
\[Y_i = \beta_0 + \beta_1 X_i + \epsilon_i\]
where \(\epsilon_i \sim N(0, \sigma^2)\)
\[\rho = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y}\]
\[\chi^2 = \sum \frac{(O - E)^2}{E}\]
\[F = \frac{MS_{\text{between}}}{MS_{\text{within}}} = \frac{\sigma^2_{\text{between}}}{\sigma^2_{\text{within}}}\]
Mastering Greek letters is essential for reading and writing statistical notation. The most important letters to memorize are:
With practice, these symbols become as natural as the Roman alphabet, and they provide a universal language for expressing statistical concepts precisely and concisely.