A/B testing in marketing analytics is a method used to compare a new variation (treatment) against an existing variation (control) to determine if the new variation performs better in terms of a specific Key Performance Indicator (KPI). Variations can include changes to website button shapes, adding features, or testing new creatives, among other things. The goal is to measure the effect of the treatment compared to the control.

To conduct a randomized experiment for A/B testing, you need to randomly assign the new variation (treatment) to a group of subjects, while another group continues with the existing variation (control). This randomization ensures that the two groups are comparable on average, and any observed effect can be attributed to the treatment itself. The direct comparison between the treatment and control groups allows for a causal inference of the treatment's effectiveness.

Observational data is data that is collected without manipulating the environment or conditions, simply observing and recording what naturally occurs. An example is analytics data from website visitors. It differs from experimental data, which is gathered through controlled experiments where variables are manipulated to observe the effects. Observational data is often used when randomized experiments are not feasible, but it comes with the risk of confounding factors that can lead to incorrect causal inferences.

Causal effects cannot be claimed from observational data without randomization because the groups being compared may have inherent differences that affect the outcome. Without randomization, there's no way to ensure that the only difference between the groups is the variable being tested. This lack of control can lead to confounding effects, where other factors influence the results, making it impossible to determine if the observed effect is truly caused by the variable of interest.

Propensity model matching is a technique in causal inference used to control for confounding effects when comparing groups in observational studies. It involves finding and matching subjects from treatment and control groups who are similar across various metrics, except for the treatment itself. By creating comparable groups, this method aims to mimic a randomized experiment, allowing for a more accurate estimation of the true causal effect of the treatment. Variations of this technique include weighting and stratifying, but all share the same goal of equalizing groups across confounders to enable direct comparison.