Revised 8/2018

MTH 246 - Statistics II (3 CR.)

Course Description

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.

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 Analysis
    • 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