The choice of stimulus values to test in any experiment is a critical component of good experimental design. This study examines the consequences of random and systematic sampling of data values for the identification of functional relationships in experimental settings. Using Monte Carlo simulation, uniform random sampling was compared with systematic sampling of two, three, four, or N equally spaced values along a single stimulus dimension. Selection of the correct generating function (a logistic or a linear model) was improved with each increase in the number of levels sampled, with N equally spaced values and random stimulus sampling performing similarly. These improvements came at a small cost in the precision of the parameter estimates for the generating function.

A video game was adapted to investigate the effect of the number of alternatives on causal judgment in a complex environment involving targets with delayed outcomes. Participants were presented with groups of potential targets. Each target (the candidate cause) fired at random relative to the others, with one target in each group causing a delayed explosion (the effect). The participants were tasked with discriminating which of the potential targets was producing the effect. Experiment 1 revealed a main effect of delay on discriminability but no effect of the number of alternatives. However, latencies did increase as the number of alternatives increased, suggesting that discriminability was maintained by compensating with longer observation times. But, a similar increase in latency for longer delays did not offset the detrimental impact of an increase in cause—effect delay. Experiment 2 replicated the outcome under conditions in which participants were always required to observe for 16 s before making a decision; under the most difficult conditions, however, the limited viewing time started to reveal an effect of the number of alternatives on the participants’ ability to discriminate a true cause from foils. Evidence suggests that participants’ decisions were determined primarily by differences in the number of cause-effect contiguities experienced for the true cause versus the foils.

A first-person shooter video game was adapted for the study of causal decision making within dynamic environments. Participants chose which of three potential targets in each of 21 groups was producing distal explosions. The source of the explosion effect varied in the delay between the firing of its weapon and its effect (0.0, 0.5, 1.0, and 2.0 s), the probability that the weapon caused the effect (50%, 75%, and 100%), and the occurrence of auditory events that filled the delay. In Experiment 1, participants' choice accuracy was highest with short delays but was not affected by probability; participants often compensated for lower probability by increasing their latencies, and thus the number of outcomes sampled. In Experiment 2, a broad range of delays (0-2 s) and probabilities (20%-100%) were randomly sampled for each cause; the results largely replicated those of the prior experiment. The experiments demonstrate people's ability to successfully modulate their environmental sampling in the face of uncertainty due to lower cause-effect probabilities, but not in the presence of longer cause-effect delays.

Continuous causation, in which incremental changes in one variable cause incremental changes in another, has received little attention in the causal judgment literature. A video game was adapted for the study of continuous causality in order to examine the novel cues to causality that are present in these paradigms. The spatial proximity of an object to an "enemy detector" produced auditory responses as a function of the object's proximity. Participants' behavior was a function of the range of the effect's auditory sensitivity and the moment-to-moment likelihood of detection. This new paradigm provides a rich platform for examining the cues to causation encountered in the learning of continuous causal relations.

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