Statistics and Data
Science 363

Introduction to
Statistical Methods

Spring 2019

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*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