How deeply does Causal Inference for Data Science cover mean difference?

Defines the statistic, relates it to intervention means and the ATE, and demonstrates bias, but defers a full adjustment treatment.

Mean difference

As explained in Causal Inference for Data Science

A difference in means is a sample statistic obtained by subtracting the mean outcome for one group from the mean outcome for another group.

A mean difference subtracts the average outcome for one group from the average outcome for another: mean(O | T = 1) − mean(O | T = 0). It describes how outcomes differ between treated and untreated groups, but the difference is causal only when group assignment supports that interpretation. section 2.5 section 2.5.1

Randomized treatment

In an RCT or A/B test, random assignment removes confounding from treatment assignment. The observed mean difference therefore estimates the causal effect directly, without applying the adjustment formula. section 2.5.1

For a causal calculation, compare the two intervention quantities: E[O | do(T = 1)] and E[O | do(T = 0)]. Their difference is the average treatment effect (ATE). The observed mean difference, E[O | T = 1] − E[O | T = 0], estimates it reliably only under suitable assumptions or after adjustment. section 2.5

Why naive differences can mislead

A synthetic dataset with an unobserved confounder produces a naive mean difference of 1.0004 even though the treatment effect is −2. An instrumental-variable estimate of −1.8898 is much closer to the target. section 9.3

Table 2.6 Exercise results

True ATE
E[ O\| T = 1] – E[ O\| T = 0]
adjustment(1) – adjustment(0)
Estimation of ATE

Use the exercise table to compare the true ATE, observed mean difference, adjusted estimates, and final ATE estimation. section 2.5

How Causal Inference for Data Science covers it

Cover of Causal Inference for Data Science

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Related concepts

regression discontinuity designuses · Regression discontinuity design is a causal inference method that estimates treatment effects by comparing observations near a cutoff where treatment assignment changes.
average treatment effect estimationmeasures · Average treatment effect estimation quantifies the population-average difference in outcomes that would result from two alternative treatments or interventions.
experimentationused by · Experimentation is the deliberate testing of an idea, intervention, or alternative by observing outcomes to gather evidence or compare effects.
treatment effectmeasures · A treatment effect is the difference in an outcome attributable to receiving an intervention or exposure rather than a comparison condition.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.