On the interchangeability of presentation order for cause and effect: Experimental tests of cue and outcome-density effects

Studies of cue-outcome contingency learning demonstrate outcome-density effects: participants typically overestimate contingencies when the outcome event is relatively frequent. Equivalent cue-density effects occur, although these have been examined less often. Few studies have simultaneously examined both event density effects or have manipulated the presentation order of the events, limiting knowledge of whether these phenomena share underlying principles. We report three well-powered experiments to address those gaps. Participants judged the effectiveness of a medical treatment after viewing a series of pairings for two events, a cause (treatment given vs. not) and an effect (patient recovered vs. not). Experiment 1 manipulated both event densities independently. We then manipulated the presentation order for the cause and the effect, alongside a manipulation of effect density (Experiment 2a) or cause density (Experiment 2b). Experiment 1 found a large main effect of event density (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>η</mml:mi><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math> = .55), which was qualified by a significant interaction between event type and density level (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>η</mml:mi><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math> = .10) whereby effect density had greater impact than cause density. Experiments 2a and 2b found effects for effect density (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>η</mml:mi><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math> = .60) and cause density (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>η</mml:mi><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math>= .31). The effects of cause-effect presentation order were always small and non-significant. We conclude that effect-density manipulations had substantial impact on contingency judgements, and cause-density manipulations less so. Moreover, it matters little which event (cause or effect) is seen first. These findings have implications for contingency, associative, probabilistic, and causal models of contingency judgement; primarily, that people may be more sensitive to the causal status of events than to their temporal order of presentation.