An Introduction to Statistical Methods and Analysis TENTATIVE Course Syllabus--Fall 2007 An introduction to the concepts, techniques, and reasoning central to the understanding of data, this lecture course focuses on the fundamental ideas of statistical analysis used to gain insight into diverse areas of human interest. The use, abuse and misuse of statistics will be the central focus of the course. Topics of exploration will include experimental study design, sampling design, data analysis (visual devices, measures of center, measures of spread, normal distributions, correlation and regression), sampling distributions and the Central Limit Theorem, estimation (confidence intervals) and hypothesis testing (z-test, t-test, chi-square, ANOVA). Applications will be drawn from current events, business, psychology, politics, medicine and other areas of the life and social sciences. Statistical software will be introduced and used extensively in this course, but no prior experience is assumed. An invaluable course for students planning graduate study in the natural or social sciences. Open to any interested student—no college level mathematical knowledge required. Goal of Course: To learn the fundamentals of statistical analyses including data analysis, study design, and basic inference. Class Meeting: Lectures: Mondays/Thursdays, 11:05-12:30, Science Building 103 Group Conferences: Tuesdays, 9:00-9:50 or 10:00-10:50, Library E1 Attendance at lectures and group conferences is mandatory. Group conference will be held weekly. Students will be assigned to one of the two group conferences during the first week of class. Instructor: Daniel King (You can call me anything reasonable, but I usually respond best to the name 'Dan') Phone: (914) 395-2424 (office phone with voice mail) (646) 408-0715 (cell phone—please use it responsibly) E-mail: email@example.com Office: 121 Alice Ilchman Science Building (first floor) Required Text: Moore, David S., The Basic Practice of Statistics, Fourth Edition. W. H. Freeman & Company Publishers, 2007. ISBN: 0-7167-7478-X This mandatory text is available for purchase from the campus bookstore, but you are welcome to purchase it through any vendor you choose. However, purchase of the 4th edition is crucial—make sure to check the ISBN number of the book you plan to buy and compare it to the one given above. This is the main textbook and source of information for the course. We will cover Chapters 1-11, 14-23, and 25-27. Additional reading of essays, journal articles, newspaper clips is also required. These supplemental documents will be provided to students in class. Reserve Texts: Notx, William, Fligner, Michael, and Sorice, Rebecca L., Student Study Guide for Moore's The Basic Practice of Statistics, Fourth Edition. W.H. Freeman & Company Publishers, 2006. This valuable study guide has been placed on reserve at the main desk of the Raushenbush Library. Each section of this study guide begins with an overview of the corresponding section in the main text. Most valuable is the guided assistance provided on selected problems from the text. The authors help students in the process of setting up and thinking about the problems. After using the guided assistance, students can examine the complete solutions which explain exactly how the answer was reached and why it was done that way. Course Readings: For each lecture meeting there will be an assigned reading from the course textbook or from a supplemental handout. These readings will form the basis of the course lectures. In advance of each lecture, students are strongly encouraged to complete the associated reading. See ‘Course Topics and Readings’ below for the schedule of readings. The ability to read mathematics successfully (for deep understanding and long term retention) is a skill that requires significant effort to develop. It is also a skill that is often not developed in traditional high school courses. In this course you will have much opportunity and will be given sufficient guidance in developing your mathematical reading skills. Please consult the ‘Suggestions for Effective Reading of Mathematics’ at the end of this syllabus. Course Exams: There will be three, 90-minute exams during the term. The coverage and tentative dates for these exams are as follows: Exam 1: Thursday, Oct 11—Data Analysis Exam 2: Thursday, Nov 15—Study Design, Basics of Inference Exam 3: Monday, Dec 17—Inference in Practice Calculators: In this course we will focus less on tedious computations and more on the understanding and proper interpretation of statistical calculations. Nevertheless, a calculator with statistical capabilities is a valuable learning tool. Access to a calculator with statistical functionality is required for this course. The Texas Instruments TI-83 or TI-86 is recommended for this course but any calculator with statistical functionality is acceptable. The college owns a few of these calculators that can be borrowed by students. You may already own a calculator that performs some statistical calculations. See me if you need help using your calculator’s statistical functions or need advice on purchasing a calculator for use in this course (and beyond). Computers: We will be using the Microsoft Excel spreadsheet program in this course to do some of our more complicated statistical calculations. Access to Excel and instruction on its use will be provided in group conference. No prior computer experience is required. Conference Work: Group conferences will be held weekly. Time in group conference will be spent in two ways: 1) reinforcing ideas presented in lecture through hands- on activities conducted in workshop mode and 2) designing and executing a small-scale research project in which students working in small teams will be responsible for choosing a topic, designing an appropriate study, collecting data, analyzing data and submitting a formal report of the results. On the last day of lecture students will submit their final written report and give a brief oral presentation of their findings in class. Additional Help: I encourage students who are having difficulty with the course material to meet with me for individualized help. Students are also encouraged to develop and maintain an email dialogue with me so that I may provide timely assistance with smaller-scale questions. Students of this course can also access the free services of the Mathematics Resource Center. More information about these services will be discussed in class. Evaluations: At the end of the semester an individual course evaluation and course grade will be given to each student. This evaluation will be based primarily on the results of the three course exams, quality of execution of the research project and class attendance. Worksheets: Completion of worksheets is optional in this course. Students wishing to submit a worksheet should do so on the final day of class. Your worksheet should detail the work completed in class and conference, listing topics studied, research conducted, etc. Forms are available from the Office of Student Records in Westlands. Attendance: Both lecture and conference attendance is absolutely mandatory. Students who miss more than two classes or conferences (without a documented reason) run the risk of reduced course credit. Number of student absences (or occurrences of significant tardiness) at lecture and group conferences missed will be indicated on the course evaluation. If a session is missed, the student is responsible for obtaining class notes and assignments and is expected to be fully prepared for the next class session. Course Topics and Readings The following represents a tentative schedule of our activities during the semester and is subject to revision. The readings listed under each lecture are best read in advance of the lecture. Unit I: Data Analysis Lecture 1 Lecture reading: Moore, BPS: Chapter 1—Picturing Distributions with Graphs Lecture 2 Lecture reading: Moore, BPS: Chapter 2—Describing Distributions with Numbers (Part I) Lecture 3 Lecture reading: Moore, BPS: Chapter 2—Describing Distributions with Numbers (Part II) Lecture 4 Lecture reading: Moore, BPS: Chapter 3—The Normal Distributions Lecture 5 Lecture reading: Moore, BPS: Chapter 27—Statistical Process Control (on CD or on-line) Lecture 6 Lecture reading: Moore, BPS: Chapter 4—Scatterplots and Correlation Lecture 7 Lecture reading: Moore, BPS: Chapter 5—Regression Lecture 8 Lecture reading: Moore, BPS: Chapter 6—Two-Way Tables Lecture 9 Review: Topics in Data Analysis Lecture 10 Exam: Topics in Data Analysis (Tentative Date: Thursday, October 11) Unit II: Study Design and the Basics of Inference Lecture 11 Lecture reading: Moore, BPS: Chapter 8—Producing Data: Sampling Lecture 12 Lecture reading: Moore, BPS: Chapter 9—Producing Data: Experiments Lecture 13 Lecture reading: Moore, BPS: Chapter 10—Introducing Probability Lecture 14 Lecture reading: Moore, BPS: Chapter 11—Sampling Distributions Lecture 15 Lecture reading: Moore, BPS: Chapter 14—Confidence Intervals: The Basics Lecture 16 Lecture reading: Moore, BPS: Chapter 15—Tests of Significance: The Basics Lecture 17 Lecture reading: Moore, BPS: Chapter 16—Inference in Practice Lecture 18 Review: Topics in Study Design, Basics of Inference Lecture 19 Exam: Topics in Study Design, Basics of Inference (Tentative Date: Thursday, Nov. 15) Unit III: Inference in Practice Lecture 20 Lecture reading: Moore, BPS: Chapter 18—Inference about a Population Mean (t-test) Lecture 21 Lecture reading: Moore, BPS: Chapter 19—Two-Sample Problems (Comparing Two Means) Lecture 22 Lecture reading: Moore, BPS: Chapter 20—Inference about a Population Proportion (z-test) Lecture 23 Lecture reading: Moore, BPS: Chapter 21—Comparing Two Proportions Lecture 24 Lecture reading: Moore, BPS: Chapter 23—Two Categorical Variables: The Chi-Square Test Lecture 25 Lecture reading: Moore, BPS: Chapter 25—One-Way Analysis of Variance: Comparing Several Means Moore, BPS: Chapter 26—Nonparametric Tests (on cd or online) Lecture 26 Review: Topics in Inference in Practice Lecture 27 Exam: Topics in Inference in Practice (Tentative Date: Monday, Dec 17) Lecture 28 Student Research Study Presentations Suggestions for Effective Reading of Mathematics 1. When confronted with the task of reading a piece of mathematical text, skim the entire reading first to discern its general outline and to identify its main points and objectives. 2. If necessary, review earlier portions of the textbook (or prior mathematical topics studied) to recall forgotten or unfamiliar vocabulary, techniques or theorems before attempting a thorough reading of the current text. 3. Don’t rush! Read slow! Mathematical writing is typically dense with ideas. Spend as much time as necessary to understand the full intended meaning of each of the author’s arguments and examples. 4. Pay particular attention to the precise statement of new definitions and theorems. 5. Do not immediately skip over a portion of the reading that doesn’t make sense in the hope that its meaning will become more apparent later. Because of the linear nature of mathematical writing in which one topic builds from those that precede it, it is very important to fully understand one topic before proceeding to the next. 6. Try to identify the cause of any misunderstanding of the topics being studied. Consider all reasonable methods to resolve the misunderstanding. Whenever possible discuss difficult portions of the text with a friend, study partner, or study group. 7. If all else fails, make sure to mark any portions of the text that remain perplexing so that you may raise these issues subsequently in class. 8. Occasionally authors will intentionally leave some details of arguments or examples to the reader to complete as an exercises. Authors do this for pedagogical reasons and not laziness! As a useful check on your understanding of the material, always fill-in in the details omitted by the author. 9. Examples in textbooks often come with a moral. Discern the author’s main point in providing the example. Make sure you struggle to understand every aspect of the computation, manipulation, or procedure presented in the example. 10. Always keep pencil and paper handy whenever reading mathematical text. It can be very helpful to highlight important passages, insert marginal notes to yourself (ala Fermat!), and make simple calculations while involved in the reading of the text.
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