Greek Letters in Statistics: Complete Guide

Statistics and probability theory extensively use Greek letters to represent parameters, distributions, and statistical measures. This guide covers all Greek letters used in descriptive statistics, inferential statistics, probability theory, and statistical modeling.

Core Statistical Parameters

μ (Mu) - Population Mean

• Population Mean: μ is the true mean of entire population
• Expected Value: E[X] = μ for random variable X
• Sample Mean: x̄ estimates μ
• Example: If SAT scores have μ = 1050, that's the population average
• Normal Distribution: N(μ, σ²)

σ (Sigma) - Population Standard Deviation

• Standard Deviation: σ measures spread/dispersion of data
• Variance: σ² is population variance
• Sample Std Dev: s estimates σ
• Example: 68% of data within μ ± σ (normal dist)
• Formula: σ = √[Σ(x-μ)²/N]

Σ (Sigma) - Summation

• Sum: Σx_i = x₁ + x₂ + ... + x_n
• Mean Formula: μ = (Σx_i)/N
• Variance: σ² = Σ(x-μ)²/N

Hypothesis Testing & Significance

α (Alpha) - Significance Level / Type I Error

• Significance Level: α = probability of Type I error
• Common Values: α = 0.05 (5%), α = 0.01 (1%)
• Critical Region: Reject H₀ if p-value < α
• Confidence Level: 1 - α (e.g., 95% when α = 0.05)
• Example: "Significant at α = 0.05 level"

β (Beta) - Type II Error Probability

• Type II Error: β = P(fail to reject H₀ | H₀ is false)
• Power: Power = 1 - β
• Trade-off: Decreasing α often increases β

β Coefficients - Regression Coefficients

• Linear Regression: y = β₀ + β₁x₁ + β₂x₂ + ... + ε
• β₀: Intercept
• β₁, β₂, ...: Slope coefficients
• Example: Price = β₀ + β₁(Size) + β₂(Age)

Correlation & Association

ρ (Rho) - Population Correlation Coefficient

• Pearson's ρ: Measures linear correlation
• Range: -1 ≤ ρ ≤ 1
• ρ = 1: Perfect positive correlation
• ρ = -1: Perfect negative correlation
• ρ = 0: No linear correlation
• Sample Correlation: r estimates ρ

τ (Tau) - Kendall's Tau (Rank Correlation)

• Non-parametric: Rank-based correlation
• Range: -1 ≤ τ ≤ 1
• Use: When data is ordinal or has outliers

Statistical Distributions

χ² (Chi-Squared) Distribution

• Chi-Squared Test: Goodness-of-fit, independence tests
• Test Statistic: χ² = Σ(O-E)²/E
• Degrees of Freedom: ν or df parameter
• Example: χ²(df=5, α=0.05) = 11.07 (critical value)

θ (Theta) - General Parameter

• Unknown Parameter: θ represents any unknown parameter
• Estimation: θ̂ is estimate of θ
• Bayesian: P(θ|data) posterior distribution

λ (Lambda) - Poisson Rate Parameter

• Poisson Distribution: P(X=k) = (λ^k × e^(-λ))/k!
• Mean and Variance: Both equal λ
• Example: If λ = 3 events/hour, find P(2 events)
• Exponential: λ also rate parameter in exponential distribution

ν (Nu) - Degrees of Freedom

• Chi-Squared: χ²(ν) has ν degrees of freedom
• t-Distribution: t(ν) Student's t with ν df
• F-Distribution: F(ν₁, ν₂)

Probability Theory

Ω (Omega) - Sample Space

• Sample Space: Set of all possible outcomes
• Example: Coin flip Ω = {H, T}, Dice Ω = {1,2,3,4,5,6}
• Events: Subsets of Ω

π (Pi) - Proportion / Probability

• Population Proportion: π = successes/total
• Sample Proportion: p̂ estimates π
• Example: If π = 0.6, then 60% have the characteristic

Common Statistical Formulas with Greek Letters

Normal Distribution

Confidence Intervals

Linear Regression

Quick Reference Table

Sample vs Population Notation

Tips for Students

Remembering Greek Letters in Stats

• μ (mu) = Mean: Both start with M
• σ (sigma) = Standard deviation: Both start with S
• ρ (rho) = correlation/Relation: Both start with R
• α (alpha) = Level: First letter (alpha) for significance level

Common Mistakes to Avoid

• Don't confuse μ (population) with x̄ (sample)
• Don't confuse σ (lowercase) with Σ (uppercase summation)
• Remember: Greek = population, Latin = sample
• α is probability of Type I error, not Type II

Related Resources

• Greek Letters in Mathematics
• Greek Letters in Physics
• How to Type Greek Letters
• Complete Greek Alphabet Reference