I. The Foundations
Here's a concise rewrite, roughly the same length: Causal inference goes beyond mere relationships, aiming to understand "what causes what?". This section delves into key ideas that distinguish correlation from causation, and the difficulties in establishing causal claims.
Correlation is Not Causation
Data analysis often falters by misinterpreting coincidences as causes. A lurking variable, also known as a **confounder**, frequently drives the observed relationship.
Here's a rewritten version of similar length: Ice cream sales and crime rates often rise together. Does one cause the other? Find out what's really happening below.
Certainly not. Warmer temperatures (the confounder) drive both higher ice cream purchases and more outdoor activity, which then boosts crime rates.
The Fundamental Problem of Causal Inference
The central issue: we can't see how a person changes with and without something simultaneously. The other outcome, the **unseen reality**, is obscured. Hover to see this path.
Path 1: Receives Treatment
Outcome A
Path 2: No Treatment
Outcome B
II. Causal Frameworks
Causality's study demands formal language; Structural Causal Models (SCMs) leverage graphs. Crafting a Directed Acyclic Graph (DAG) helps illuminate their function.
Interactive DAG Builder
To add variables, click the canvas; they become nodes. Drag between nodes to build causal paths (edges). The tool then analyzes these paths, identifying key ones and suggesting control variables for estimating the causal effect of 'T' (Treatment) on 'Y' (Outcome), if estimation is feasible.
Instructions
- **Add Node:** Click empty space
- **Add Edge:** Drag from node to node
- **Name Node:** Double-click a node
- **Reset:** Use button below
Analysis Results
Add nodes named 'T' and 'Y' to begin.
III. Experimental Methods
RCTs, considered the gold standard, use randomization to form comparable groups. This exploration investigates how these trials isolate cause-and-effect relationships.
Randomization Simulator
Here's a rewritten version of similar length: You have 20 individuals and an initial characteristic (like age). Randomize them into Treatment and Control using the 'Randomize' button. Observe group balance on this characteristic. Though individual randomizations can vary, the process balances the groups overall.
Treatment Group (0)
Avg. Age: N/A
Control Group (0)
Avg. Age: N/A
Standardized Difference: N/A
(A value < 0.1 is considered well-balanced)
IV. Quasi-Experimental Methods
In situations lacking RCTs, we employ quasi-experimental approaches, analyzing observed data. These methods hinge on innovative designs and core assumptions to approximate experimental rigor.
Regression Discontinuity (RDD) Simulator
RD design applies when a cutoff score determines treatment. We presume those near the cutoff are alike; a jump in outcome indicates the treatment's impact. Bandwidth adjustment reveals how effect estimates vary with data selection around the threshold.
Estimated Treatment Effect
0
Difference-in-Differences (DiD) Simulator
DiD analyzes outcome changes over time, contrasting treated and untreated groups. Its core relies on the **Parallel Trends Assumption**: groups would evolve similarly absent treatment. Flip the assumption to explore its effect.
DiD Estimated Effect
0