Probability Distributions — When & Why They Matter

Normal Distribution

• Use when: Continuous data, symmetric, bell‑shaped.
• Key properties: Mean = median = mode; defined by μ and σ.
• Common uses: Z‑tests, t‑tests (approx), regression residuals.

t‑Distribution

• Use when: Small samples (n < 30), unknown population SD.
• Key properties: Heavier tails; defined by degrees of freedom.
• Common uses: One‑sample, paired, and two‑sample t‑tests.

Chi‑Square (χ²) Distribution

• Use when: Categorical data; variance tests.
• Key properties: Right‑skewed; defined by degrees of freedom.
• Common uses: χ² test of independence, goodness‑of‑fit.

F‑Distribution

• Use when: Comparing variances; ANOVA.
• Key properties: Ratio of two variances; right‑skewed.
• Common uses: One‑way ANOVA, regression model comparison.

Binomial Distribution

• Use when: Fixed number of trials, two outcomes, constant probability.
• Common uses: Proportions, risk differences, exact tests.