Question

can statistical analysis show causation? why or why not?

what evidence can statistical analysis provide?

Answer 1

The results of statistical analyses are parts of principled arguments about causality.

    If correlation (in the broad sense) remains after taking into account (controlling, rendering unlikely) plausible rival hypotheses, it does imply (support, suggest, indicate, make plausible) causation.

    In experimental studies, active manipulation of independent variables, and random assignment to conditions, go a long way toward minimizing the plausability of rival hypotheses. If there is a correlation between treatment and score on a dependent variable (i.e,. if there is a difference among treatment groups) after rejecting consistency with merely random process, a causal relation hypothesis is supported.

Causality is the area of statistics that is commonly misunderstood and misused by people in the mistaken belief that because the data shows a correlation that there is necessarily an underlying causal relationship. The use of a controlled study is the most effective way of establishing causality between variables.