Mathematics 363

Introduction to Statistical Methods

Fall 2016

Exam Overview

Topics for Exam 1

• Displaying data visually – bar charts, segmented bar charts, histograms, boxplots, empirical cumulative distribution function, empirical survival function, time plots, scatterplots, explanatory and response variables
• Displaying data in tables – marginal distributions

• Summarizing one dimensional data numerically – mean, variance, standard deviation, five number summary, quantiles, standardized variables
• Summarizing two dimensional data numerically – covariance, correlation, linear regression, fit, residuals, extrapolation, non-linear transformations

• Producing data – observational study, natural and randomize controlled experiments
• Principles of experimental design – issues with control, factors, levels, simple and stratified random samples

• Axioms of probability – axioms, simple consequences of the axioms, conditional probability, law of total probability, Bayes formula, independence

• Random variables – distribution functions, mass function for discrete random variables, density function for continuous random variables, their properties and their relationships

• Simulating random variables – discrete random variables using sampling from a distribution, continuous random variables using the probability transform

• Expected values – laws of the unconscious statistician, computing means and variances from the mass or density function.

• Families of random variables – review but do not focus on memorizing formulas

Topics for Exam 2

• Law of large numbers and Monte Carlo integration
• Central limit theorem for sums and sample means arising from a simple random sample, estimation of probabilities using the z-score
• Delta method – normal approximation for single and multivariable functions of sample means

• Method of moments estimation
• Maximum likelihood estimation
• Interval estimation – confidence intervals

• Issue associated with hypothesis testing – null and alternative hypotheses, type I and type II errors, significance level and power.
• Likelihood ratios – Neyman-Pearson framework
• Composite hypotheses – power function, p-value
• One and two sample proportion tests
• One and two sample z procedures

• t-procedures – one sample, matched pairs, two sample t-tests

Additional Topics for Final Exams

• Chi-square procedures – G-test, determining degrees of freedom
• One way analysis of variance – F statistics, numerator and denominator degrees of freedom, confidence intervals

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