Course+Outline

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All courses have high expectations, but there are different prerequisites and expectations for Honors and Advanced courses. Compared to regular mathematics courses, students in Honors or Advanced courses should expect to encounter topics at a faster pace, which will be investigated in greater depth. Students in an advanced or honors class can expect a greater emphasis on conceptual understanding and abstract thinking with less focus on review and practice. Beyond the expectations of regular mathematics courses, students are expected to be more self-motivated as well as interested in devoting time and energy towards more challenging and thought provoking problems. ====== = = =**COURSE OUTLINE** =  //(long-term goals after the course has been completed)//
 * AIMS**

Students will: 
 * understand the importance and consequences of variation in data
 * be able to explain and interpret data through visualizations
 * understand the crucial role data plays in business and research
 * be able to use statistical inference to make interpretations and predictions
 * be aware of bias in all applications of statistics and analytics
 * understand the application of probability in statistical inference
 * be able to work effectively in teams
 * be able to effectively follow an experimental design process

//(short-term curriculum goals)//
 * OBJECTIVES**

Students will
 * SECTION 1: Introduction to Statistics and Analytics**
 * understand the importance of citing sources correctly
 * become familiar with the basic functions of JMP® software
 * understand different types of variables
 * have a basic understanding of inference and variation
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand and apply the basic concepts of working in a team
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be familiar with simple visualizations of data
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to use appropriate visualizations to represent data

SECTION 2: Distribution
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 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">know the concept of and be able to calculate the standard deviation
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the characteristics of different distributions
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the characteristics of the Normal Distribution
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the characteristics of the Binomial Distribution
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to apply and interpret a Wilks-Shapiro test
 * SECTION 3: Experimental Design and Sampling**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand and apply sampling methods
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to identify potential bias and sampling error
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be aware of the need to recognize lurking variables
 * SECTION 4: Introduction to Six Sigma**
 * understand the significance of variation
 * know about many areas of Six Sigma applications
 * become aware of DMAIC and other core principles
 * apply some Six Sigma principles of decision making as a team
 * SECTION 5: Sampling Distributions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand benefits of sampling distributions
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">derive The Central Limit Theorem
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">discover the //t//-distribution
 * SECTION 6: Introduction to Confidence Intervals and Testing**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to estimate the mean of single sample
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">test a hypothesized population mean with a single sample
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the concept of a p-value and level of significance
 * SECTION 7: Type I and II Errors and Power**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand Type I and II Errors in statistical inference
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the concept of Power
 * SECTION 8: Bivariate Data**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to examine the relationships between numeric data through:
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">correlation
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">transformations to achieve linearity
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">density elipses
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">test of slopes
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">confidence intervals of slopes
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Non-parametric testing
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the need to explore an entire dataset, rather than just two variables
 * SECTION 9: Categorical Data**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand contingency tables and associated visualizations
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Apply and interpret Chi-Squared and Fisher's exact test
 * SECTION 10: Comparing two samples**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand and apply the sampling distribution for the difference of two samples
 * SECTION 11: Experimental Design**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the basic principles of experimental design
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understand the benefits of different designs
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be able to design and conduct their own experiments, including factors and levels
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">be aware of potential issues such as confounding and placebo effect
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">study simple experimental design ideas through <span style="font-family: Arial,Helvetica,sans-serif;">"Predictably Irrational: The Hidden Forces That Shape Our Decisions" by Dan Ariely
 * SECTION 12: Six Sigma II**
 * take a project or experimental task through DMAIC