COLLEGE OF SCIENCE. School of Mathematical Sciences. NEW (or REVISED) COURSE: COS-STAT-751 Nonparametric Statistics. request date: *Approval

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1 ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences NEW (or REVISED) COURSE: COS-STAT-751 Nonparametric Statistics 1.0 Course Designations and Approvals Required course approvals: Academic Unit Curriculum Committee College Curriculum Committee Approval request date: Approval granted date: Optional designations: General Education: Writing Intensive: Honors Is designation desired? No No No *Approval request date: **Approval granted date: 2.0 Course information: Course title: Nonparametric Statistics Credit hours: 3 Prerequisite(s): COS-STAT-701 or Equivalent Co-requisite(s): Course proposed by: Robert Parody Effective date: Contact hours Maximum students/section Classroom 3 25 Lab Studio Other (specify) 2.a Course Conversion Designation*** (Please check which applies to this course). *For more information on Course Conversion Designations please see page four. Semester Equivalent (SE) Please indicate which quarter course it is equivalent to: Nonparametric Statistics Semester Replacement (SR) Please indicate the quarter course(s) this course is replacing: New July 27, 2010

2 2.b Semester(s) offered (check) Fall Spring Summer (online) Other All courses must be offered at least once every 2 years. If course will be offered on a biannual basis, please indicate here: 2.c Student Requirements Students required to take this course: (by program and year, as appropriate) None Students who might elect to take the course: This is an elective for graduate students in Advanced Certificate and MS programs in Applied Statistics. Graduate students in other programs who interested in nonparametric statistics will also elect to take this class. In the sections that follow, please use sub-numbering as appropriate (eg. 3.1, 3.2, etc.) 3.0 Goals of the course (including rationale for the course, when appropriate): To provide the students with alternative techniques to test statistical hypotheses when the assumptions needed for the usual parametric based statistical techniques are not valid. 4.0 Course description (as it will appear in the RIT Catalog, including pre- and corequisites, and quarters offered). Please use the following format: COS-STAT-751 Nonparametric Statistics The emphasis of this course is how to analyze certain designs when the normality assumption cannot be made, with an emphasis on applications. This includes certain analyses of ranked data and ordinal data. The course provides a review of hypothesis testing and confidence-interval construction. Topics include: sign and Wilcoxon signedrank tests, Mann-Whitney and Friedman tests, runs tests, chi-square tests, rank correlation, rank order tests; and Kolmogorov-Smirnov statistics. 5.0 Possible resources (texts, references, computer packages, etc.) Practical Nonparametric Statistics, Conover Minitab SAS 6.0 Topics (outline): 1. Random Variables and Distributions a. Axioms & Properties of Probability b. Conditional Probability c. Continuous distributions d. Continuous random variables e. Correlation and covariance f. Counting Techniques 2

3 g. Discrete distributions h. Discrete random variables i. Independence j. Measures of Location k. Measures of Variability l. Normal approximations m. Order statistics n. Probability Plots o. Quantiles p. Random Variables q. Sample Spaces and Events 2. Hypothesis Tests a. A.R.E. b. Alpha risk c. Alternative hypothesis d. Critical region e. Level of significance f. Null hypothesis g. Power h. Pvalues i. Sample size 3. Estimates and Confidence Intervals a. 100(1-α )% confidence b. Confidence bounds c. Least squares estimators d. Level of confidence e. Maximum likelihood estimators f. Properties of estimators 4. One Sample NonParametric Tests a. Binomial test b. Confidence interval for p c. Confidence interval for x p (quantile) d. Kolmorgorov distribution test e. Quantile test f. Sign test for median g. Wilcoxon test 5. Paired Samples NonParametric Tests a. Fisher's exact test b. Kendall's tau 3

4 c. Mantel-Haenszel test d. McNemar test e. Sign test f. Spearman's rho g. Wilcoxon test 6. Two Samples Nonparametric Tests a. Contingency table test b. Klotz test c. Mann-Whitney test d. Randomization test e. Smirnov distribution test 7. Several Samples NonParametric Tests a. Contingency table test b. Friedman test (rcbd) c. Kruskal-Wallis test d. Median test e. Page test (rcbd, ordered categories) 7.0 Intended course learning outcomes and associated assessment methods of those outcomes (please include as many Course Learning Outcomes as appropriate, one outcome and assessment method per row). Assessment Method Course Learning Outcome Exams Homeworks Labs Project s Level 1: Knowledge Define population mean, variance, standard deviation, and quantile. Write formulas and methods to compute, from a sample, estimates of the population mean, variance, standard deviation, quartiles and other summary statistics. Define discrete and continuous distribution functions for random variables. Define random variable, sample space, independence, joint distribution, covariance, correlation, discrete uniform distribution, quantile, expected value, quartiles, median, and order statistics. Define nominal, ordinal, interval and ratio measurement scales and provide examples of each. Enumerate basic principles of hypothesis testing 4

5 including one-tailed and two-tailed critical regions, level of significance, power, asymptotic relative efficiency, and pvalue. Enumerate and compute by hand measures of rank correlation for bivariate data including Spearman s rho and Kendall s tau. Level 2: Comprehension Explain the major distinctions between parametric and nonparametric statistical methods Describe data analysis situations when nonparametric methods are appropriate. Name and describe procedures for parametric and nonparametric one-sample hypothesis tests of location; e.g., one-sample t-test and sign test. Name and describe procedures for parametric and nonparametric two-sample hypothesis tests of differences of location; e.g., two-sample t- test and Mann-Whitney test. Name and describe procedures for parametric and nonparametric k-sample hypothesis tests of location; e.g., one-way ANOVA and Kruskal- Wallis test. Name and describe the goodness-of-fit test for a probability distribution. Level 4: Analysis For a given set of data, calculate sample mean, median, quartiles, quantiles, variance, standard deviation, and range. Construct a sample CDF and estimate quantiles.. Construct and interpret dotplots, histograms, boxplots, and scatterplots of data. State the hypotheses, define the test statistic, define the critical region, perform the necessary calculations (by hand and/or with Minitab), and state conclusions for common nonparmetric tests. Level 4: Analysis For a given sets of data that are suitable for nonparametric analysis, identify one or more appropriate nonparametric methods and apply the appropriate hypothesis test. Level 5: Synthesis Identify the parametric analog when they exist for the nonparametric procedures. 5

6 Compare the A.R.E. for the parametric and nonparametric procedures. Identify the conditions operational, social, technical when nonparametric and parametric methods would be preferred Search on the web for software to do nonparametric analysis. 8.0 Program outcomes and/or goals supported by this course Relationship to Program Outcomes (1 = slightly, 2=moderately, 3=significantly) Program Outcomes and/or Goals for CQAS 8.1 Advanced Certificate in Lean Six Sigma Demonstrates an solid understanding of statistical thinking and Lean Six Sigma methodology in solving real-world problems Leads Lean Six Sigma improvement projects. Level of Support Advanced Certificate and Masters of Science in Applied Statistics Demonstrates solid understanding of statistical thinking and applied statistics methodology in solving real-world problems Designs studies that are efficient and valid Analyzes data using appropriate statistical methods Communicates the results of statistical analysis with effective reports and presentations. Note: Students obtaining the Advanced Certificate in Applied Statistics will not be expected to perform at the same level as students obtaining a Master of Science degree. 6

7 9.0 General Education Learning Outcome Supported by the Course, if appropriate Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes Creativity, Innovation and Artistic Literacy Demonstrate creative/innovative approaches to course-based assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created Assessment Method 10.0 Other relevant information (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) 7

8 *Optional course designation; approval request date: This is the date that the college curriculum committee forwards this course to the appropriate optional course designation curriculum committee for review. The chair of the college curriculum committee is responsible to fill in this date. **Optional course designation; approval granted date: This is the date the optional course designation curriculum committee approves a course for the requested optional course designation. The chair of the appropriate optional course designation curriculum committee is responsible to fill in this date. ***Course Conversion Designations Please use the following definitions to complete table 2.a on page one. Semester Equivalent (SE) Closely corresponds to an existing quarter course (e.g., a 4 quarter credit hour (qch) course which becomes a 3 semester credit hour (sch) course.) The semester course may develop material in greater depth or length. Semester Replacement (SR) A semester course (or courses) taking the place of a previous quarter course(s) by rearranging or combining material from a previous quarter course(s) (e.g. a two semester sequence that replaces a three quarter sequence). New (N) - No corresponding quarter course(s). 8