## MTH 246 - Statistics II at Virginia Highlands Community College

### Course Description

Effective: 2017-08-01

Continues the study of estimation and hypothesis testing with emphasis on advanced regression topics, experimental design, analysis of variance, chi-square tests and non-parametric methods.

Lecture 3 hours. Total 3 hours per week.

3 credits

### General Course Purpose

To serve as a second course in statistics that focuses on multivariate and nonparametric techniques useful to business, science, and social science majors.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 245 or equivalent with a grade of C or better.

### Course Objectives

- Review of Hypothesis Testing
- Conduct hypothesis tests for population means and proportions.
- Conduct a hypothesis test for the equality of two population means where:
- The samples are independent and the population variances are assumed unequal.
- The data consists of matched pairs.
- Conduct a hypothesis test for the presence of correlation.
- Experimental Design
- Define and apply the basic principles of design, including randomization, replication, and treatment/control groups.
- Explain single and double blinding.
- Describe the placebo and experimenter effects and describe how they can be countered using blinding.
- Design experiments using the following methods:
- Completely randomized.
- Randomized block.
- Matched pairs.
- Explain the concept of confounding.
- Correlation and Regression
- Construct and interpret the residual plot related to a simple least-squares regression model.
- Conduct hypothesis tests related to the coefficients of a simple least-squares regression model.
- Construct and Apply a logistic regression model.
- Calculate the coefficient of determination, the adjusted coefficient of determination, and overall P-value for a multiple regression model and use them to construct a best-fit multiple regression equation.
- Categorical Data Anaylsis
- Conduct chi-squared tests for:
- Goodness of fit.
- Independence between rows and columns of a two-way contingency table.
- Homogeneity of population proportions.
- Analysis of Variance (ANOVA)
- Conduct one-way ANOVA to test the equality of two or more population means for both equal and unequal sample sizes and recognize its relationship to the pooled two sample t-test.
- Conduct a multiple comparison test, such as Tukey's HSD, to determine which of the three or more population means differs from the others.
- Conduct two-way ANOVA on sample data categorized with two fixed factors.
- Nonparametric Methods
- Determine the rank of each element of a sorted data set.
- Identify the relationship between a nonparametric test and its corresponding parametric technique.
- Conduct a Wilcoxon signed-ranks test for a single sample.
- Conduct a Wilcoxon signed-ranks test for matched pairs.
- Technology Application
- Construct statistical tables, charts, and graphs using appropriate technology.
- Perform statistical calculations using an appropriate statistical software package.
- Complete statistical project. Students are required to complete some form of semester project in their course that is worth a significant portion of the student's grade. This could be either an individual or group effort, and could be completed in stages through the semester or as a single, stand-alone exercise. As a minimum, the project should require students to manipulate and draw statistical inferences from a large, realistic data set using a statistical software package.

### Major Topics to be Included

- Hypothesis Testing
- Experimental Design
- Correlation and Regression
- Categorical Data Analysis
- Analysis of Variance
- Nonparametric Methods