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While an [[experiment]] ensures, in [[Law of large numbers|expectation]], that potential outcomes (and all covariates) are equivalently distributed in the treatment and control groups, this is not the case in an [[observational study]]. In an observational study, units are not assigned to treatment and control randomly, so their assignment to treatment may depend on unobserved or unobservable factors. Observed factors can be statistically controlled (e.g., through [[regression analysis|regression]] or [[Matching (statistics)|matching]]), but any estimate of the ATE could be [[confounding|confounded]] by unobservable factors that influenced which units received the treatment versus the control.

While an [[experiment]] ensures, in [[Law of large numbers|expectation]], that potential outcomes (and all covariates) are equivalently distributed in the treatment and control groups, this is not the case in an [[observational study]]. In an observational study, units are not assigned to treatment and control randomly, so their assignment to treatment may depend on unobserved or unobservable factors. Observed factors can be statistically controlled (e.g., through [[regression analysis|regression]] or [[Matching (statistics)|matching]]), but any estimate of the ATE could be [[confounding|confounded]] by unobservable factors that influenced which units received the treatment versus the control.

虽然实验确保了潜在的结果(以及所有的协变量)在处理组和对照组中是等价分布的，但是在观察性研究中，情况并非如此。在观察性研究中，处理组单位并不是随机分配和控制的，因此处理单位的分配可能取决于未观测或不可观测的因素。观察到的因素可以在统计学上加以控制(例如，通过回归或匹配) ，但是任何关于平均处理效应的估计都可能被不可观察的因素混淆，这些因素影响了哪些单位接受了处理，哪些单位没有接受处理。

虽然实验确保了潜在结果以及所有协变量在处理组和对照组中的等价分布，但是在观察性研究中，情况并非如此。在观察性研究中，处理组单位并不是随机分配和受人为控制，因此处理单位的分配可能取决于未观测到或不可观测的因素。观察到的因素可以在统计学上加以控制(例如，通过回归或匹配) ，但是任何关于平均处理效应的估计都可能与不可观察因素混淆，这些因素影响了哪些单位接受了处理，哪些单位没有接受处理。

== Formal definition ==

== Formal definition ==