Wrap-Up

First Half Topics

First Half Topics

See the previous slidedeck for a review of the midterm topics.

Second Half Topics

Regression and Adjustments

Concepts

  • SLR slope as ATE
  • ANOVA vs regression parameterizations
  • Regression adjustments for precision

Skills (examples)

  • Based on a plot, decide whether regression is preferable to ANOVA
  • Identify variables useful for adjustments
  • Formulate linear model with adjustments
  • Distinguish between blocking and adjustments

Non-compliance

Concepts

  • One vs two-sided
  • Compliers and Never-takers
  • \(ITT_Y\), \(ITT_D\), \(CACE\)

Skills (examples)

  • Calculate \(ITT_Y\), \(ITT_D\), and \(CACE\) from summary statistics
  • Interpret \(CACE\) and \(ITT_Y\) in context of a study and which matters

Interference

Concepts

  • SUTVA violation
  • Direct Effect
  • Spillover Effect
  • Multilevel Design

Skills (examples)

  • Formulate different estimands
  • Identify source of inference in a study
  • Use data from a mulitlevel design to estimate direct and spillover effects
  • Propose changes to a study to account for interference

Adaptive Design

Concepts

  • Explore vs Exploit
  • Regret
  • ETC
  • UCB
  • Hoeffding’s Bound

Skills (examples)

  • Calculate regret for a given sequence of actions
  • Implement ETC or UCB in a simple setting

Sequential Analysis

Concepts

  • Likelihood Ratio
  • SPRT
  • Thesholds A and B

Skills (examples)

  • Describe steps of SPRT
  • Write form of the likelihood ratio for a simple setting / model
  • Interpret a plot of the likelihood ratio over time
  • Identify settings where sequential analysis is useful

Crossover Design

Concepts

  • Addresses strong between-subject heterogeneity
  • Each subject serves as their own control

Skills (examples)

  • Write out the schedule of outcomes for a crossover design
  • Identify settings where crossover design is useful
  • Describe how a CAR study could be modified to be a crossover design

Latin Squares

Concepts

  • Two blocking factors
  • All factors have the same number of levels
  • Each level of each factor appears once in each row and column
  • Random assignment amounts to randomly selecting a LS

Skills (examples)

  • Describe how to construct a Latin Square for a given set of blocking factors and treatment conditions
  • Identify settings where a Latin Square design is useful
  • Describe how a CAR study could be modified to be a Latin Square design

Data Set Inventory

In pairs, match data sets to techniques.

10:00

Big Ideas

“To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.”

  • R.A. Fisher

Big ideas I

  1. Potential outcomes allows to us define causal parameters
  2. Two approaches to inference: design-based and model-based
  3. Random Assignment allows for unbiased estimation of causal parameters
  4. Factorial designs allow us to estimate interactions and use data more efficiently

Big ideas II

  1. Blocking allows us to reduce variance and increase power
  2. Sequential analysis allows for continuous monitoring of data and early stopping
  3. Adaptive designs allow us to learn and adjust our approach as we go to minimize regret
  4. Causal complications arise, but there are solutions