Randomization provides the "reasoned basis for inference" in an experiment. Yet some approaches to analyzing experiments ignore the special structure of randomization. Simple, familiar approaches like regression models sometimes give wrong answers when applied to experiments. Approaches exploiting randomization deliver more reliable inferences than methods neglecting it. Randomization inference should be the first method we reach for when analyzing experiments.
Adjusting for observed factors does not elevate an observational study to the reliability of an experiment. P-values are not appropriate measures of the strength of evidence in an observational study. Instead, sensitivity analysis allows us to identify the magnitude of hidden biases that would be necessary to invalidate study conclusions. This leads to a strength-of-evidence metric appropriate for an observational study.
Observational studies involve more uncertainty than randomized experiments. Sensitivity analysis offers an approach to quantifying this uncertainty.