### About

This graduate level course provides an introduction to the basic concepts of probability, common distributions, statistical methods, and data analysis. It is intended for graduate students who have one undergraduate statistics course and who wish to review the fundamentals before taking additional 500 level statistics courses. This course is cohort-based, which means that there is an established start and end date, and that you will interact with other students throughout the course.

Upon completion of this course students will:

- Appreciate and understand the role of statistics in your own field of study.
- Develop an ability to apply appropriate statistical methods to summarize and analyze data for some of the more routine experimental settings.
- Make sense of data and be able to report the results in appropriate table or statistical terms for inclusion in your thesis or paper.
- Perform appropriate statistical techniques using Minitab and interpret the results/outputs.

### Course Topics

This graduate level course covers the following topics:

- An overview of statistics
- Data description: scales of measurement, how to describe data graphically for categorical data (pie chart, bar chart) and graphs for quantitative variables (histogram, stem-and-leaf plot and time plot)
- How to describe data by summary statistics: measures of central tendency and variability
- How to create a box plot
- How to use a statistical package (Minitab)
- How probability and probability distributions are involved in statistics
- How binomial distributions are involved in statistics
- The role that normal distributions play in statistics
- Simple random sampling and sampling distribution of sample mean, central limit theorem, normal approximation to the binomial
- Differentiation between a population and a sample, how to use a statistic to estimate a population parameter, confidence interval and its interpretation, inferences of population proportion, margin of error and sample size computation
- Confidence interval for population mean, Sample size needed for estimating the population mean with a specified confidence level and specified width of the interval
- Hypothesis testing: in terms of how to set up Null and Alternative hypotheses, understanding Type I and Type II errors, performing a statistical test for the population mean
- How to compute power of a test and choosing the sample size for testing population mean
- p-value, how to compute it and how to use it
- Inferences about μ with σ unknown: the t-distribution and the assumptions required to check in order to use it
- How to compare the mean of two populations for independent samples: using pooled variances
*t*-test versus separate variances*t*-test - How to compare the mean of two populations for paired data
- How to compare two population proportions
- Using contingency table and the Chi-square test of independence
- Using an
*F*-test to compare the variances of two populations - Understanding concepts related to linear regression models including, least squares method, correlation, Spearman's rank order correlation, inferences about the parameters in the linear regression model
- Analyzing data using analysis of variance (ANOVA) methods
- Analyzing data using multiple regression methods

### Course Author(s)

Dr. Mosuk Chow is the primary author of these course materials.

### Software

This course will use the statistical software program Minitab. See the Statisitical Software page for more information.

A graphing calculator is recommended for this course, especially for students enrolled or considering the MAS program. Otherwise, a basic calculator that includes factorials and combinations will suffice. Please note that for the final exam using a calculator on a device with internet capabilities (e.g. cell phone) will NOT be permitted.

### Textbook

Ott, R. L. and Longnecker, M. (2016). *An Introduction to Statistical Methods and Data Analysis*, 7th Edition, Cengage Learning.

ISBN 13: 978-1-305-26947-7, ISBN 10: 1-305-26947-0

### Prerequisites

1 undergraduate course in statistics