Introduction to Statistics

General Information

Statistics is the science of analyzing data and arriving at reasonable and intelligent conclusions based upon that analysis. This course will acquaint students with the mathematical concepts of statistical analysis.

PREREQUISITES

MATH 1430: College Algebra

READINGS

Field, A., Miles, J., and Field, Z. (2012). Discovering Statistics Using R. SAGE Publications Ltd.

Groebner, D. F., Shannon, P. W., Fry, P. C., & Smith, K. D. (2011). Business Statistics: A Decision-Making Approach. Prentice Hall/Pearson.

Kerns, G. J. (2016). Introduction to Probability and Statistics using R. [download]

LEARNING OUTCOMES

Students understand the basics of data collection and random sampling.
Students understand how to create, use and interpret tables and charts.
Students understand basic calculations of descriptive statistics.
Students understand the basics of probability.
Students understand the concept of random variables, as well as probability distributions for discrete random variables.
Students understand the basic properties of the normal distribution and sampling distributions in general.
Students construct confidence intervals and calculate sample size selection.
Students learn the methods of hypothesis testing.
Students learn how to conduct regression analysis.

COURSE POLICIES / ADDITIONAL INFORMATION

Attendance is recorded. Unexcused absence lowers the grade accordingly.
It is the students' responsibility to check Canvas and their Webster email regularly.
For every hour spent in class it is expected of the students to invest 3 hours per week outside of class in homework, reviewing material, assignments, etc.

UNIVERSITY POLICIES

Students are required to inform themselves of WUV academic policies.

A full list of these policies is available on the WUV website: http://webster.ac.at/academic-policies

Materials, Assignments and R-Code

Introduction to Probability and Statistics

[Slides][Assignment][RCode][R][LaTeX]

Data Collection

[Slides][Assignment][RCode]

Data Description

[Slides][Assignment][RCode]

Probability

[Slides][Assignment][RCode]

Discrete Probability Distributions

[Slides][Assignment][RCode]

Continuous Probability Distributions

[Slides][Assignment][RCode]

Multivariate Distributions

[Slides][Assignment][RCode]

Sampling Distributions

[Slides][Assignment][RCode]

Interval Estimation

[Slides][Assignment][RCode]

Hypothesis Testing

[Slides][Assignment][RCode]

Analysis of Variance

[Slides][Assignment][RCode]

Simple Linear Regression

[Slides][Assignment][RCode]

Multiple Linear Regression

[Slides][Assignment][RCode]

Binary Dependent Regression Analysis

[Slides][Assignment][RCode]

Categorical Data Analysis

[Slides][Assignment][RCode]

Nonparametric Statistics

[Slides][Assignment][RCode]

Websites

for R [Packages]

for LaTeX

The Not So Short Introduction to LATEX 2ε

LaTeX Math Symbols

LaTeX Project

ShareLaTeX

Weekly Schedule

Week 1

Introduction to Probability and Statistics

· Descriptive and Inferential Statistics

· Populations and Samples

Introduction to R and LaTeX

· Basic R Operations and Concepts

· RSweave

Week 2

Data Collection

· Data Collection Methods

· Data Collection Issues

Data Description

· Types of Data

· Bar Charts

· Pie Charts

Week 3

Data Description

· Histograms

· Line Plots

· Scatter Plots

Probability

· Sample Spaces

· Counting Methods

· Events

Week 4

Probability

· Model Assignment

· Conditional Probability

· Bayes Theorem

Discrete Distributions

· Discrete Uniform Distribution

· Bernoulli Distribution

· Binomial Distribution

Week 5

Discrete Distributions

· Geometric Distribution

· Negative Binomial Distribution

· Hypergeometric Distribution

· Poisson Distribution

Continuous Distributions

· Continuous Uniform Distribution

· Beta Distribution

· Normal Distribution

· Standard Normal Distribution

· Chi-Square Distribution

Week 6

Continuous Distributions

· Gamma Distribution

· Student's t Distribution

· Snedecor's F Distribution

· Exponential Distribution

Multivariate Distributions

· Discrete Joint and Marginal Distribution

· Continuous Joint and Marginal Distribution

· The Bivariate Normal Distribution

Week 7

Multivariate Distributions

· Covariance

· Correlation

Sampling Distribution

· Sampling Error

· Law of Large Numbers & Central Limit Theorem

· Sampling Distribution of the Mean

Week 8

Sampling Distribution

· Sampling Distribution of a Proportion

· Monte Carlo Simulation

· Sampling Techniques

Mid-Term Exam

Week 9

Estimation

· Point Estimate & CI for the Population Mean

· Point Estimate & CI for Proportions

· Sample Size and Margin of Error

Hypothesis Testing

· Null & Alternative Hypotheses

· Hypothesis Tests for Two Population Means

· Hypothesis Tests for Paired Samples

· Hypothesis Tests for Two Population Proportions

Week 10

Hypothesis Testing

· Hypothesis Tests for a Single Population Variance

· Hypothesis Tests for Two Population Variance

· Type I & Type II Errors

Analysis of Variance

· One-Way Analysis of Variance

· Post Hoc Tests

Week 11

Analysis of Variance

· Randomized Complete Block Analysis of Variance

· Two-Factor Analysis of Variance

Simple Linear Regression

· Definition of the Simple Regression Model

· Deriving the Ordinary Least Squares Estimates

· Properties of OLS on Any Sample of Data

Week 12

Simple Linear Regression

· Units of Measurement and Functional Form

· Expected Values and Variances of the OLS Estimators

· Regression through the Origin and Regression on a Constant

Multivariate Linear Regression

· Mechanics and Interpretation of Ordinary Least Squares

· The Expected Value of the OLS Estimators

· The Variance of the OLS Estimators

· The Gauss-Markov Theorem

Week 13

Multivariate Linear Regression

· Effects of Data Scaling on OLS Statistics

· More on Functional Forms

· More on Goodness-of-Fit and Selection of Regressors

· Prediction and Residual Analysis

Binary Dependent Regression Analysis

· Describing Qualitative Information

· A Single Dummy Independent Variable

· Using Dummy Variables for Multiple Categories

· Interactions Involving Dummy Variables

Week 14

Binary Dependent Regression Analysis

· The Linear Probability Model

· Probit

· Logit

Goodness-of-Fit & Contingency Tables

· Chi-Square Goodness-of-Fit Test

· Contingency Analysis

· Loglinear Analysis

Week 15

Nonparametric Statistics

· The Wilcoxon Signed Rank Test for One Population Median

· Nonparametric Tests for Two Population Medians

· Wilcoxon Matched-Pairs Signed Rank Test for Related Samples

· Kruskal-Wallis One-Way Analysis of Variance

Final Exam

Google Sites

Report abuse