Here is my tentative syllabus for my radical redesign.  The structure of the course follows roughly the 9 goals put forth in the GAISE report.  Please comment.

Oh also this: I’m getting rid of slides.  I’ll have a marker for board work and a computer to do the analysis and simulations.  But no slides!

• Week 1-1: Intro class.  Go over syllabus.  Discuss the 9 goals put forth in the GAISE report.  Talk about ethics (IRB, informed consent, etc.)
• Week 1-2: Software: Introduction to R.  Syntax.  Getting data in/out of R.  Basic structures (e.g. data.frames, matrices, vectors, etc.), etc. Reproducible documents (i.e. R Markdown)

• Week 2-1: Critical consumers: Assign students to read this paper over the weekend.  Spend a full day of class discussing pros and cons.
• Week 2-2: Collecting data activity.  I am going to make rectangular cards whose length, width, area, labels, and colors have statistical properties that I design.  I’m going to hand them to the class and make them decide what questions we should ask and what we should measure.  We will come back to this data many times throughout the semester.

• Week 3-1: Graphical Displays and Numerical Summaries:
  • Types of data
    • continuous
    • categorical
    • time-to-event data
  • Univariate summaries for continuous data:
    • mean
    • median
    • variance
    • IQR range
    • percentiles
  • Tables for categorical data
  • Univariate dataviz
    • histograms
    • boxplots
    • barplots
    • violin plots
    • maps!
• Week 3-2: Graphical Displays and Numerical Summaries:
  • Bivariate summaries for continuous data
    • correlation
      • pearson
      • spearman
      • kendall contingency
    • simple linear regression
    • two-way tables
      • odds
      • odds ratio
  • Bivariate dataviz
    • scatter plots
    • mosaic plots
    • stacked bar plots
    • side by side boxplots
    • side by side histograms

(Example data: Hospital General Information.csv https://data.medicare.gov/data/hospital-compare)

• Week 4-1: Variability:
  • Intro to probability
  • Describing Distributions (shape, center, variability, outliers)
    • Expectation and Variance
• Week 4-2: Variability
  • Bayes Theorem
  • Specific Distributions
    • normal
    • binomial

• Week 5-1: Variability
  • Sampling Distributions
    • Lot’s of simulations!
    • Emphasize the difference between data distribution and sampling distribution
  • Bootstrapping
• Week 5-2: Variability
  • Central limit theorem (CLT)
    • Lot’s of simulations

• Week 6-1: Randomness
  • Sampling
    • Discuss famous cases where sampling was poorly done (e.g. Dewey defeats Truman)
    • Talk about the Census!
    • Selection bias
    • Discuss sampling strategies (probability vs probability sampling)
      • SRS
      • Stratified
      • Cluster
    • Discuss population vs sample
• Week 6-2: Statistical Models:
  • Simpsons paradox
  • Very simple models (i.e. X ~ N(mu, sigma))
  • Simple Linear Regression (no inference…..yet)

• Week 7-1: Exam 1
• Week 7-2: Statistical Inference
  • What is statistical inference?
  • Ideas of point and interval estimation
    • Explain correct interpretation of confidence intervals!
  • Idea of hypothesis testing
    • Type I and Type II errors
  • Multiple testing problems (FWER and FDR)

• Week 8-1: Statistical Inference
  • Hypothesis testing of one mean.
    • parametric tests (Z and t-test)
    • non-parametric test (sign test, permutation test)
• Week 8-2: Statistical Inference
  • Interval estimation of one mean
    • parametric (Z and t-interval)
    • non-parametric (bootstrap intervals)

• Weel 9-1: Statistical Inference
  • Two dependent samples hypothesis testing
    • parametric (Z and t-test)
    • non-parametric (Wilcoxon signed rank test, permutation test)
  • Interval estimation
    • parametric (Z and t-intervals)
    • non-parametric (bootstrap intervals)
• Week 9-2: Statistical Inference
  • Two independent samples hypothesis testing
    • parametric (Z and t-test, Welch’s test, pooled variance)
    • non-parametric (Wilcoxon Rank Sum/Mann Whitney U, permutation test)
  • Interval Estimation
    • parametric (Z and t-intervals)
    • non-parametric (bootstrap intervals)

• Week 10-1: Statistical Inference
  • Simple Linear Regression
    • parametric (t-tests)
• Week 10-2: Statistical Inference
  • k-sample problems
    • parametric (ANOVA) (It’s just regression with categorical predictors!!!!!)
    • non-parametric (Kruskal-Wallis)

• Week 11-1: Statistical Inference/Statistical Models
  • Multipel Regression
• Week 11-2: Statistical Inference/Statistical Models
  • Multiple Regression

• Week 12-1: Statistical Inference
  • Categorical Data
    • Inference for proportions
      • parametric (using CLT)
      • non-parametric (permutation test)
    • Chi-square tests
      • parametric (using CLT)
      • non-parametric (permutation test)
• Week 12-2: Statistical Inference/Statistical Models
  • Simple Logistic Regression

• Week 13-1: Statistical Models
  • Survival Analysis
    • Motivate with example why we can’t just use mortality rates (in 100 years everyone is dead!)
    • Censoring
    • Truncation
    • K-M Curves (comparing two K-M curves)
• Week 13-2: Statistical Inference
  • Intro to Missing Data
    • Examples where ignoring missing data is bad
    • Why is the data missing?
    • Missingness mechanisms
    • Really simple multiple imputation?

• Week 14-1: Statistical Inference
  • Introduction to Bayesian statistics
    • Motivate Why?
    • Define prior, likelihood, posterior
    • Estimating a proportion example
    • Credible Intervals
• Week 14-2: Statistical Inference
  • Introduction to Bayesian statistics (continued)
    • Bayesian Hypothesis testing
    • Bayes Factor

• Week 15-1: Case study
  • Case study from start to finish.
  • We are going to start with this data set and analyze it from start to finish.
  • We are going to do it “Data Fest Style”: There is no specific question.  We are just looking for interesting stories to tell from the data.
• Week 15-2: Case Study
  • Case study continued

Week 16: Final Exam