Categories → Causal Inference , Statistics , Study Design
Expected value is a statistical concept that represents the average outcome of a random variable over an extended period or over many occurrences.
It is a measure of what we expect to happen on average, given a particular set of circumstances. In other words, it is the average value of a random variable that is expected to occur over a large number of trials.
In the context of causal inference, the concept of expected value is often used to estimate the causal effect of an intervention or treatment, on an outcome of interest. The expected value of an outcome under a specific treatment or intervention is the average value that we would expect to observe if we were to apply that intervention or treatment repeatedly to a large population.
To estimate the expected value of the outcome under treatment, we need to compare it with the expected value of the outcome under a control or placebo condition. The difference between the two expected values is known as the average treatment effect (ATE).
However, in the real world, it is often not possible to apply the same intervention or treatment repeatedly to a large population - and indeed, this might confound the experiment! Instead, we observe the treatment and control groups once, and we need to estimate the ATE from this observational data.
To do so, we use statistical methods such as regression analysis or propensity score matching to estimate the expected values of the outcome under treatment and control conditions. These methods attempt to adjust for potential confounding variables that may affect the outcome and bias our estimates of the ATE.
In summary, the concept of expected value is essential in causal inference as it helps us estimate the average treatment effect of an intervention or treatment on an outcome of interest. By estimating the expected value of the outcome under treatment and control conditions, we can determine the causal effect of the intervention and make informed decisions about its effectiveness.