This course focuses on the theoretical foundation and applications of probability and statistics with an emphasis on statistical analysis and interpretation. Topics include probability and probability distributions, sampling distributions, inferences based on proportion tests, Chi square, contingency tables, odds ratios, analysis of variance and multiple comparisons techniques, and analysis of variance for some commonly used experimental designs. At least one statistical software package will be used. Prerequisites: Intro. to Statistics and Calculus I
In this course, you will learn the mathematics and applications of various statistical methods which include probability, categorical data analysis, and analysis of variance for some commonly used experimental designs. You will also learn to conduct statistical analyses in R (a language and environment for statistical computing and graphics), to interpret, organize, and explain your results and conclusions in written and verbal formats. This course fulfills a requirement in the applied mathematics major. It can also be used for a mathematics minor.
Upon successful completion of this course students should be able to:
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Solve problems using fundamental probability rules and probability functions of discrete and continuous probability distributions.
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Explain the concept of sampling distribution and obtain the approximate sampling distribution of a sample proportion.
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Identify the underlying assumptions and perform various categorical data analyses using both manual and computer methods of statistical analysis to include: proportion-tests, McNemar test and Chi-square tests.
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Construct statistical models for one-way analysis of variance (ANOVA); identify and verify the underlying assumptions of ANOVA, and perform inferential hypothesis testing using both manual and computer methods of statistical analysis to include various multiple comparisons approaches.
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Construct statistical models for other ANOVA designs such as axb factorial design and randomized complete block design, and perform inferential hypothesis testing using both manual and computer methods of statistical analysis.
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Discuss and present statistical analysis, including methods, results, conclusions and justifications based on supporting evidence in both verbal and written formats.
In addition, at the completion of this course, students will be able to demonstrate the following critical thinking learning outcomes:
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Evaluate and synthesize information from multiple contexts and settings to achieve a common understanding of a phenomenon and to effectively characterize and/or implement an action designed to address a question, challenge, or problem.
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Reflect upon, communicate, and objectively evaluate their thinking processes.
Ott, R. L., & Longnecker, M. T. (2015). An introduction to statistical methods and data analysis. Cengage Learning.
@book{ott2015introduction,
title={An introduction to statistical methods and data analysis},
author={Ott, R Lyman and Longnecker, Micheal T},
year={2015},
publisher={Cengage Learning}
}
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Homework problems and/or computer projects will be assigned for each section from the textbook and/or from other sources.
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Computer assignments will require work with R along with written interpretative analysis and conclusions. R output must be labeled and stapled together with your written analysis.
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Assignments are expected to be neat, organized and stapled. Unreadable work is not acceptable and will not be graded.
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All work should be shown and complete sentences used when a conclusion is called for, as opposed to turning in a list of answers.
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It is crucial that you complete all homework problems and reading assignments so that you do not fall behind on the course. Many quiz and exam questions are based on homework.
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Students are expected to submit their assignments at the appointed time.
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20% of the total scores of an assignment will be deducted for each day late when a graded assignment is submitted after the due date. Absence from class does not automatically extend the due date. LATE ASSIGNMENTS WILL NOT BE ACCEPTED after the assignments have been graded and returned to students.
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When homework problems are to be presented in class, students must have their homework completed prior to presentation. No homework will be accepted if handed in after presentation.
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Each student is expected to submit his/her own original solutions, although students may consult one another when completing assignments. COPYING SOLUTIONS from a classmate or other source WILL NOT BE TOLERATED, and suspected cases will be investigated and documented.
Five quizzes, one midterm exam, and one comprehensive R computer final exam will be given in this course. Make-up quizzes/exams will be given only in extreme circumstances, only if I am contacted by e- mail or in person BEFORE (except for emergencies) the quiz/exam is missed. Arrangements will be made for the quiz/exam to be taken at an earlier time, if at all possible. No make-up quizzes/exams can be given after the quiz/exam has been graded and returned to students.
Acceptable work on exams, quizzes and assignments will show solution steps, results, interpretations, conclusions, justifications, and other responses written in detail and presented in a concise, logical, and organized manner. Grading is based on the quality of thinking reflected in solutions as well as correctness of final results. Final grades are computed as follows:
- Quizzes
- Graded Assignments & Presentations
- Attendance and Class Participation 5%
- Midterm Exam 25%
- R Computer Exam 25%
| Chapter/Section | Description |
|---|---|
| 4.1 | Introduction |
| 4.2 | Finding Probability |
| 4.3 | Prob. Laws |
| 4.4 | Conditional Prob. |
| 4.5 | Bayes' Formula |
| 4.6 | Discrete & Cont. Var. |
| 4.7 | Prob. Dist. for Discrete RVs |
| 4.8 | Binomial & Poisson Dist. |
| 4.9 | Prob. Dist. for Cont. RVs |
| 10.2 | Inferences about |
| 10.3 | Inferences about |
| 10.4 | Chi-square Goodness of Fit Test |
| 10.5 | Chi-square Tests for Indpedendence & Homogeneity |
| 10.7 | Odds & Odds Ratios |
| 8.2 | ANOVA |
| 8.3 | ANOVA Model for a CRD |
| 8.4 | ANOVA Assumptions |
| 9.5 | Tukey's W |
| 9.7 | Dunnett's |
| 14.3 | a x b Factorials |
| 15.2 | ANOVA for a One–Way RCBD |