𝗖𝗮𝘂𝘀𝗮𝗹 𝗔𝗜 𝗘𝘅𝗽𝗹𝗮𝗶𝗻𝗲𝗱: 𝗗𝗮𝘆 𝟳 - 𝗠𝗲𝗮𝘀𝘂𝗿𝗶𝗻𝗴 𝗖𝗮𝘂𝘀𝗮𝗹 𝗜𝗺𝗽𝗮𝗰𝘁 We’ve laid the basics of causality: correlation vs. causation, the do-operator, confounders, interventions, counterfactuals, and DAGs/SCMs. Now, let’s get practical with tools to measure causal impact: 𝗔𝗧𝗘, 𝗖𝗔𝗧𝗘, 𝗔𝗧𝗧, and 𝗦𝗦𝗕. These metrics turn "why" into "how much". 𝗗𝗲𝗳𝗶𝗻𝗶𝘁𝗶𝗼𝗻𝘀 • 𝗔𝗧𝗘 (Average Treatment Effect): The average impact of a treatment (e.g., a discount) across everyone. Think: "How much does a 10% discount boost sales overall?" 𝗔𝗧𝗘 = 𝗘[Y|𝗱𝗼(X=1)] - 𝗘[Y|𝗱𝗼(X=0)] • 𝗖𝗔𝗧𝗘 (Conditional Average Treatment Effect): ATE, but for specific groups (e.g., high-income customers). It’s personalised: "How does the discount affect this segment?" 𝗖𝗔𝗧𝗘 = 𝗘[Y|𝗱𝗼(X=1), Z=z] - 𝗘[Y|𝗱𝗼(X=0), Z=z] • 𝗔𝗧𝗧 (Average Treatment Effect on the Treated): The effect only for those who got the treatment. "For customers who took the discount, how much did it drive sales?" 𝗔𝗧𝗧 = 𝗘[Y|𝗱𝗼(X=1), X=1] - 𝗘[Y|𝗱𝗼(X=0), X=1] • 𝗦𝗦𝗕 (Simple Selection Bias): The naive difference in outcomes (e.g., sales with vs. without discount) without causal adjustment. 𝗦𝗦𝗕 = 𝗘[Y|X=1] - 𝗘[Y|X=0] 𝗛𝗼𝘄 𝗧𝗵𝗲𝘆’𝗿𝗲 𝗥𝗲𝗹𝗮𝘁𝗲𝗱 ATE is the big-picture benchmark, averaging across all (treated or not). CATE zooms into subgroups, slicing ATE by conditions (e.g. age, location). ATT narrows to the treated, answering "Did it work for them?". SSB is the trap, the correlation disguised as causation. Studies designed to establish causality propose methods to nullify the SSB, for instance via Randomised Controlled Trials (RCTs), or simulated interventions with causal diagrams. 𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗘𝘅𝗮𝗺𝗽𝗹𝗲 Summer data: 50 attacks with high ice cream sales (X=1), 5 with low (X=0). There is an observed correlation. We find SSB = 50 − 5 = 45. SSB purposely captures Z’s effect, not X’s. A DAG models this: no X→Y, just Z→X (more ice cream sales) and Z→Y (more shark attacks), since seasonality Z confounds. After highlighting the confounder Z, we can adjust by setting Z=1 and Z=0 to look at the CATE and deducing the presence of a causal link. Noticing this confounder can also make us want to look at the ATE between ice cream sales and shark attacks, and find a value close to 0. 𝗪𝗵𝘆 𝗜𝘁’𝘀 𝗣𝗼𝘄𝗲𝗿𝗳𝘂𝗹 • Precision: ATE/CATE/ATT quantify true effects, not just association • Action: Guides decisions, either broad campaigns (ATE) or targeted tweaks (CATE) • Reality Check: SSB exposes why naive stats fail 𝗧𝗮𝗸𝗲𝗮𝘄𝗮𝘆: 𝗔𝗧𝗘, 𝗖𝗔𝗧𝗘, 𝗔𝗧𝗧, 𝗮𝗻𝗱 𝗦𝗦𝗕 𝗮𝗿𝗲 𝗖𝗮𝘂𝘀𝗮𝗹 𝗔𝗜’𝘀 𝗺𝗲𝗮𝘀𝘂𝗿𝗶𝗻𝗴 𝘁𝗼𝗼𝗹𝘀, 𝘁𝘂𝗿𝗻𝗶𝗻𝗴 𝗰𝗮𝘂𝘀𝗮𝗹 𝗶𝗻𝘀𝗶𝗴𝗵𝘁𝘀 𝗶𝗻𝘁𝗼 𝗮𝗰𝘁𝗶𝗼𝗻𝗮𝗯𝗹𝗲 𝗻𝘂𝗺𝗯𝗲𝗿𝘀. #CausalAI #DataScience #Causality #ArtificialIntelligence #AIExplained #ATE #CATE #ATT #SSB
