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Confidence interval

As explained in Causal Inference for Data Science

A confidence interval is an interval estimate that expresses uncertainty about an unknown population parameter under a specified confidence procedure.

A confidence interval estimates the range of results that could arise if the same data-generating process were sampled repeatedly. It helps express how much a causal estimate, such as the average treatment effect (ATE), may vary because of sampling variability. section 8.2

Why an interval matters

Suppose one dataset produces a positive ATE, but a new sample produces a negative ATE. The conflicting estimates may reflect sampling variability rather than a changed causal process. A confidence interval summarizes the range of results that repeated samples might produce. section 8.2

Two broad routes can produce confidence intervals:

  • Use resampling methods that rely on simulations and computational power. section 8.2
  • Use an analytical formula derived for the specific problem when such a formula is available. section 8.2
  • Apply implemented procedures through the DoubleML library in R or Python when working with advanced causal estimates. section 8.0
Figure 8.7 If we repeat the process of obtaining and analyzing data, we get different results. We need confidence intervals to assess how much these different results may change.
figure

Shows why repeated samples produce different estimates and why an interval is useful for assessing that variation. section 8.2

How Causal Inference for Data Science covers it

How deep it goes
Defines repeated-sampling intuition and two estimation routes, while stopping short of detailed introductory-statistics theory.
Examples
Uses positive and negative ATEs from different samples and a repeated-sampling figure to illustrate estimate variation.
What it assumes
Assumes familiarity with causal estimates and ATEs, while introducing sampling variability and two interval-estimation approaches.
What you can do after
Apply confidence intervals through resampling, analytical formulas, or the DoubleML library in R or Python.
How it connects
Connects confidence intervals with causal inference, average treatment effects, sampling variability, resampling, analytical formulas, and DoubleML.
Cover of Causal Inference for Data Science
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