The course establishes techniques for determining whether relationships between variables, particularly intervention and outcome variable, exist in the sense that the appearance of an association can't be explained by chance. The course formalizes and extends the set of phenomena that can be numerically represented in a way as to permit these modes of analysis. This is done in the interest of making predictions and judgments, particularly about what hypotheses are and are not supported by a set of data and to what extent the data support them. It introduces general perspectives from the field of Statistics to a broad audience of lower-division students.

Can you really make statistics say anything you want? Yes and no. Some common statistical comparisons are susceptible to coercion, but there are others that can be trusted to tell the truth. We explore their differences, using examples from the social and medical sciences and cutting-edge computing and graphical techniques.

Is it fair to compare As to Bs without also adjusting for other potentially important variables? (Often it isn't, but sometimes it is.) What do graphs contribute to statistical comparisons? (Some merely heighten statistical illusions; others can be uniquely illuminating.) How should we interpret claims to having found "significant" differences? (Often, very differently than how those making the claims would like us to.) The course will engage with these questions as they arise in economics, medicine, and politics, among other fields, as well as in aspects of student life, and it will leverage modern computing tools and an inductive approach to pedagogy to engage them in an unusually conceptual way. By the end of the course, students will be well-versed in new ways to leverage computing and graphics to reveal structure in data as well as traditional principles of using data to draw conclusion.

The course will be divided into 4 segments: 1) dichotomous & categorical Data; 2) quantitative data; 3) observational comparisons of groups; and 4) a capstone.

1. Dichotomous & Categorical Data

   Using statistical data of the simplest kinds, we introduce several themes of the course: presenting meaningful and relevant summaries; connecting numeric and visual descriptions; recognizing and avoiding fallacies and deceptions; chance versus systematic differences between groups; the distinction between active and passive observation; causal inference from experiments.

   Topics:
   • Fisher's test for everyday experiments, as elaborated with Wardrop's "skeptic vs. advocate" scheme
   • Simulation associated with Fisher's test
   • Summarizing categorical variables one or a few at a time, using traditional graphs, such as bar graphs, informatively colored maps, and modem graphs, including spine plots and mosaic plots.
   • Introduction to "Mondrian" software for making these plots and for efficient summary of variables
   • Critical appraisal of use of graphics in the media
   • Measurement validity

   Text: R.L. Wardrop (1995) Statistics: Learning in the Presence of Variation, chapters 1-7,

   Project: conduct, analyze and write up an experiment.

2. Quantitative Data

   Without introducing new concerns to study design or to statistical inference, quantitative data call for more sophisticated plots and summary measures, as well as more judgment in the choice of plots and summaries.

   Topics:

   • Summarizing quantitative data numerically, via measures of location and spread
   • Building intuition for these measures; additional critical appraisal of use of graphics in the media
   • Graphical and permutation-based assessments of bivariate association (Buja & Cook 1999, Buja, J. Comp. Graph. Stat. 2004)
   • Permutation tests for comparison of two groups on a measurement variable

Text: N. Maxwell (2004) Data Matters: conceptual statistics for a random world, Key College Publishing, Emeryville CA; chapters 6-8.

Project: Descriptive analysis project, in small groups, with oral presentation.

3. Observational comparisons of groups

   Non-experimental comparisons occupy a spectrum between highly trustworthy and highly fallible. This course segment treats locating and improving a comparison's position on this spectrum, emphasizing conceptual over technical issues.

   Topics:
   • Simpson's paradox
   • Stratified comparisons
   • Direct standardization
   • Simultaneous graphical comparison of groups along several variables
   • Propensity score stratification and matching (as time permits)

4. Capstone

   The final segment ties the sections of the course together. Case studies are used to show how statistical evidence of various kinds, from various sources, can be assembled into a persuasive whole, despite imperfections of each of the parts. In particular, these case studies will illustrate effective uses of the logic of experimentation and of descriptive analysis.

Course Requirements:

Two projects, involving data collection and data analysis, with write-up; quizzes; and problem sets.

Intended Audience:

This will be a First-Year Seminar intended for freshmen with interests in statistics, computing or mathematics, and making sense of data in the health, public policy, and social science sciences.

Class Format:

3 hours a week in seminar format.

This course is distinguished by its use of hands-on, participatory approaches to learning, by its substantial component of descriptive and graphical statistics, and by its narrow and conceptually-focused treatment of statistical inference. Rather than preparing students in specific techniques they may be likely to encounter in later courses, it offers an introduction to general ideas of statistical inference and to specific methods of exploratory analysis and data display.