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Honors and Advanced Courses
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


AIMS
(long-term goals after the course has been completed)

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


OBJECTIVES
(short-term curriculum goals)

SECTION 1: Introduction to Statistics and Analytics
Students will

  • 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
  • understand and apply the basic concepts of working in a team
  • be familiar with simple visualizations of data
  • be able to use appropriate visualizations to represent data

SECTION 2: Distribution

Students will
  • know the concept of and be able to calculate the standard deviation
  • understand the characteristics of different distributions
  • understand the characteristics of the Normal Distribution
  • understand the characteristics of the Binomial Distribution
  • be able to apply and interpret a Wilks-Shapiro test

SECTION 3: Experimental Design and Sampling
Students will

  • understand and apply sampling methods
  • be able to identify potential bias and sampling error
  • be aware of the need to recognize lurking variables

SECTION 4: Introduction to Six Sigma
Students will

  • 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
Students will

  • understand benefits of sampling distributions
  • derive The Central Limit Theorem
  • discover the t-distribution

SECTION 6: Introduction to Confidence Intervals and Testing
Students will

  • be able to estimate the mean of single sample
  • test a hypothesized population mean with a single sample
  • understand the concept of a p-value and level of significance

SECTION 7: Type I and II Errors and Power
Students will

  • understand Type I and II Errors in statistical inference
  • understand the concept of Power

SECTION 8: Bivariate Data
Students will

  • be able to examine the relationships between numeric data through:
    • correlation
    • transformations to achieve linearity
    • density elipses
    • test of slopes
    • confidence intervals of slopes
    • Non-parametric testing
  • understand the need to explore an entire dataset, rather than just two variables

SECTION 9: Categorical Data
Students will

  • understand contingency tables and associated visualizations
  • Apply and interpret Chi-Squared and Fisher's exact test

SECTION 10: Comparing two samples
Students will

  • understand and apply the sampling distribution for the difference of two samples

SECTION 11: Experimental Design
Students will

  • understand the basic principles of experimental design
  • understand the benefits of different designs
  • be able to design and conduct their own experiments, including factors and levels
  • be aware of potential issues such as confounding and placebo effect
  • study simple experimental design ideas through "Predictably Irrational: The Hidden Forces That Shape Our Decisions" by Dan Ariely

SECTION 12: Six Sigma II
Students will

  • take a project or experimental task through DMAIC