# Exam

You will take one in-class exam, which serves as an important mid-quarter check of your understanding. The exam will be held during one of our lab sessions. It will be ~~closed-book~~ open-book and without access to the internet.

The exam covers the assigned materials, our classes, and your assignments. Here is a rough overview of things you should be familiar with. The exam will not cover “sample size calculations and clustered data”.

## The causal revolution

**You should understand…**

- …the difference between identifying correlation (math) and identifying causation (philosophy and theory)
- …what it means for a relationship to be causal
- …what it means for an author to engage in a “motte-and-bailey” strategy
- …how a causal model encodes our understanding of a causal relationship
- …how to identify backdoor paths between treatment/exposure and outcome
- …why we close backdoor paths
- …why adjusting for mediators can distort causal effects
- …why adjusting for colliders can distort causal effects
- …why adjusting for potential confounders can distort causal effects, if the confounder was measured post treatment
- …the difference between individual-level causal effects, average treatment effects (ATE), conditional average treatment effect (CATE), average treatment on the treated effects (ATT), and average treatment on the untreated (ATU)
- …what the “fundamental problem of causal inference” is and how we can attempt to address it
- …what a counterfactual is, and how it relates to the potential outcomes framework

**You should be able to…**

- …draw a possible directed acyclic graph (DAG)
- …identify all pathways between treatment/exposure and outcome
- …identify which nodes in the DAG need to be adjusted for (or closed)
- …identify colliders and mediators (which should not be adjusted for)

## Review of regression analysis

**You should understand…**

- …the difference between outcome/response/dependent and explanatory/predictor/independent variables
- …what each of the components in a regression equation stand for, in both “flavors” of notation:
- \(y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon\) for the statistical flavor
- \(y = \alpha + \beta x_1 + \gamma x_2 + \epsilon\) for the econometrics flavor

- …how sliders and switches work as metaphors for regression coefficients
- …what it means to hold variables constant (or to control for variables)
- …how “big data” (or even data on the full population) helps little with causal inference
- …how standard errors can be thought of in terms of repeated draws from a population

**You should be able to…**

- …interpret regression coefficients
- …interpret standard errors, p-values, and confidence intervals
- …interpret other regression diagnostics like \(R^2\)
- …write out the regression equation for a study that uses random assignment and for a study that uses regression analysis without random assignment

## Interactions and transformations

**You should understand…**

- …the main motivation for (and against) using log-transformed and standardized variables
- …the general idea behind and common applications of interactions
- …what “moderation” means (and how it differs from confounding)
- …how additional subgroup analyses reflect multiple hypothesis testing and the implications for statistical significance
- how “slopes”, “marginal effects”, and “partial derivatives” are closely related

**You should be able to…**

- …transform variables
- …interpret the results of regressions that use log-transformed and standardized variables
- …interpret the results of regressions that use interaction terms
- …write out the regression equation for an analysis that uses an interaction
- …use regression results to calculate the expected means and probabilities for subgroups

## Discrete outcomes and regression adjustment

**You should understand…**

- …the benefits and limitations of linear probability models
- …what link and index functions are in the context of generalized linear models
- …the difference between marginal effects at the mean and average marginal effects
- …how Oster’s method uses coefficient stability and the R-squared to bound causal effects

**You should be able to…**

- …interpret the results of a linear probability model
- …interpret marginal effects at the mean and average marginal effects in the context of logistic regression
- …use a rule of thumb to interpret the results of a logit model
- …make predictions about coefficient movements as you close backdoors in a causal model
- …use and interpret the results of Oster’s bounding method

## Fixed effects, value added, and randomized experiments

**You should understand…**

- …how fixed effects work and how they relate to demeaning
- …how fixed effects can “close backdoors” even if you do not have data on these backdoors
- …how value-added estimation relates to fixed effects
- …the “menu” of options you may choose from as you design a randomized trial, including their respective benefits and limitations
- …the benefits of using regression to analyze the results of a randomized trial
- …the motivation behind controlling for covariates even in the context of a randomized trial

**You should be able to…**

- …write the regression equation for a model that includes fixed effects
- …(decide whether to) use fixed effects in your final project
- …interpret the results from value-added models, and describe their benefits and limitations
- …read and interpret the results of academic articles that use a randomized controlled trial
- …decide on and execute analyses for a randomized controlled trial