Abstract: Introduction
There are three main theoretical criteria of assessing interactive influences of two causes on effects: the cross-product ratio, the interaction contrast of Cheng and Novick’s (1990, 1992) probabilistic contrast model, and Novick and Cheng’s (2004) causal power theory. As to how human assess interactive influences of two causes on effects, there is no definite convincing conclusion in a few relevant studies on the issue. Two experiments were conducted to examine how college students would qualitatively and quantitatively estimate interactive influences of two generative causes on effects, and which of the three criteria their estimates would conform to.
Method
Participants were first-grade college students without having learned statistics. Stimulus materials as problems of assessing interactive influences of two generative causes (Medicines A & B) on effects (headaches) were similar to Figure 10 in Novick and Cheng’s (2004), but with different parameter sets. Both experiments used within-subject design, and each experiment included three different conditions with different parameter sets. Each condition was a problem of assessing interactive influences of two generative causes on effects. In each condition, 80 patients were randomly assigned to one of four groups: one that received no medicines (the control group), one that received one of the medicines, one that received a different medicine, and the last one that received both medicines together. Parameter sets of the two experiments were shown in Table 1. Columns 3-6 in the table were event frequencies.
Experiment 1 with 45 participants examined their qualitative estimates of directions (mutual enhancement, no interaction or mutual inhibition) of interactive influences of two generative causes on effects in three different conditions. In each condition, participants were required to estimate which kind of the above three directions the interactive influence of two generative causes on effects is. Experiment 2 with another 46 participants examined their quantitative estimates of interactive influences of two generative causes on effects in three different conditions. In each condition, participants were required to estimate, in the group that received both medicines together, the sum of corresponding simple influences of two generative causes on effects, and the magnitude of the mutual enhancement (namely interactive influence) of two generative causes on effects.
The logic of the designs of the two experiments was to make the corresponding predictions for interactive influences of two generative causes on effects by the three criterions different from each other, so as to examine which of the three criterions participants’ estimates would conform to.
Table 1
Parameter sets and results of ExperimentsⅠ&Ⅱ
Condition A & B absent A only present B only present A & B present Cross-product ratio Interaction contrast Interactive causal power Results
ExperimentⅠ 一 0/20 4/20 6/20 14/20 ∝ 0.2 0.46 41answers of mutual enhancement
二 0/20 8/20 10/20 18/20 ∝ 0 0.67 34 answers of no interaction
三 0/20 10/20 8/20 14/20 ∝ -0.2 0 36 answers of mutual inhibition
ExperimentⅡ 一 0/20 5/20 5/20 15/20 ∝ 0.25 0.55 32.91±12.68
二 0/20 8/20 10/20 18/20 ∝ 0 0.67 8.26±14.92
三 0/20 5/20 0/20 10/20 ∝ 0.25 0.33 31.80±12.21

Results
The results of the two experiments are shown as the last column in Table 1. The results from Experiment 1 showed that most participants’ qualitative estimates of directions of interactive influences conformed to the directions of interaction contrasts rather than the directions of causal powers. The results from Experiment 2 showed that participants’ mean estimates of mutual enhancement of two generative causes on effects increased with interaction contrasts regardless of causal powers, and conformed to the varying directions of interaction contrasts

Key words: causes, effects, interaction, interaction contrasts, causal powers