Statistics and Data Analysis

Descriptive statistics, hypothesis testing, confidence intervals, and data visualization.

Key Concepts

• •Descriptive statistics: measures of central tendency, dispersion, and shape
• •Sampling distributions: t, chi-squared, and F distributions
• •Hypothesis testing: null and alternative hypotheses, p-values, type I and II errors
• •Confidence intervals: construction and interpretation for means, proportions, and variances
• •Analysis of variance (ANOVA): comparing means across multiple groups
• •Nonparametric methods: sign test, Wilcoxon, Kruskal-Wallis, and rank correlation
• •Maximum likelihood estimation: deriving MLEs and their asymptotic properties
• •Method of moments: equating sample and population moments for parameter estimation
• •Goodness-of-fit tests: chi-squared, Kolmogorov-Smirnov, and Anderson-Darling
• •Data visualization: histograms, QQ plots, residual plots for model diagnostics

Study Tips

• 1.Focus on understanding when to use each test rather than memorizing formulas.
• 2.Practice deriving MLEs for common distributions (exponential, normal, Poisson).
• 3.Learn to interpret p-values and confidence intervals in context.
• 4.Work through ANOVA problems step by step, including the F-test calculation.
• 5.Always check assumptions before applying a statistical test.

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