This is a course in the basic concepts of applied mathematical statistics: parametric models, estimation, confidence intervals, hypothesis testing. We will touch on linear modeling since the followup course MTH 411 rarely gets enough student interest to run.
Prerequisites cover i.a. elementary probability theory (sample space, events, probability), density & distribution functions, conditioning, independence, expectation, samples, parameter estimation, confidence intervals, hypothesis testing, central limit theorem.
The followup course MTH 411 continuation covers regression, correlation, linear models, ANOVA, randomized block designs, non-parametric methods
After you finish this course, you will be able to:
- Explain, derive and prove core results of applied statistics, including but not limited to:
- Point estimators, and their properties -- how are the standard computations for normal and binomial distributions derived, and why do they work; computations such as sample means, proportions.
- Hypothesis testing -- how and why do the standard hypothesis tests work?
- Recognize when the tests and methods you have learned fail to apply.
Exams and grading
Your performance in this course will be measured on your class presence and participation, one semester-long research paper critique project, and a final exam.
The course will build on class participation and discussion. For every 5 missed class meetings without prior approval or documented severe crisis your final grade will be penalized by one full grade step.
The source of your grades in this course will be on a written report. You may either pick a research paper and evaluate its statistical methods, or you may pick a topic in mathematical statistics not covered in the course.
Research paper critique
Your research paper report should
- Comprehensively describe the statistical analysis methods and the data collection methods used by the authors of the paper.
- Critically evaluate the choices made by the authors: data collection designs, analysis methods.
- Recalculate the statistical analyses of the authors, alternatively a comprehensive explanation of why the research paper does not provide enough information to replicate the analyses.
Your statistical report should
- Comprehensively describe the topic, technique or theorem of your topic
- Give context, guidelines, and practical considerations
- Provide an example of it in action.
Each of these tasks is graded on a scale of A/C/D:
D is awarded for a completed report, with no more than 4 minor flaws.
C is awarded for a completed report without any flaws.
A is awarded for a completed report without any flaws that also contains a suggestion and evaluation of alternative choices the paper authors could have made.
The course has a final exam: this final exam is Pass/Fail. Failing the exam will fail the course. There will be an opportunity in the final that allow you to raise your grade by up to two minor grade steps: for instance, raise from a B to a B+ or an A-.
Your final grade, assuming all three tasks as well as the final exam have been passed, is an arithmetic mean of the three tasks, using quality points. The calculation is rounded to an even letter grade: decimal part strictly exceeding 0.6 is rounded up, all other decimal parts are rounded down.
An average grade of E is rounded up to a D.
Textbook: Keener: Theoretical Statistics
An e-book is available free for CUNY CSI students through the library webpage.
- Explore the central limit theorem, and how it fails for the