A third variable can rescue a comparison or wreck it, depending on whether it is a common cause or a common effect. This is the one move behind Lesson 6 (the violent-movies collider) and Lesson 19 (Simpson's paradox on a tree). Get the rule here, then both of those land as the same trick. ← all activities
Drag arrow strengths. Build a confounder (Z → X and Z → Y) and watch X–Y correlate even with no arrow between them — then condition on Z and watch it vanish. Then build a collider (X → C and Y → C), see X and Y uncorrelated — then condition on C and watch a correlation appear from nothing.