On the choice of adequate randomization ranges for limiting the use of unwanted cues in same-different, dual-pair, and oddity tasks

Abstract

A major concern when designing a psychophysical experiment is that participants may use a stimulus feature (cue) other than that intended by the experimenter. One way to avoid this problem is to apply random variations to the corresponding feature across stimulus presentations to make the unwanted cue unreliable. An important question facing experimenters who use this randomization (roving) technique is how large the randomization range should be to ensure that the participants cannot achieve a certain proportion correct by using the unwanted cue, while at the same time avoiding unnecessary interference of the randomization with task performance. Previous researchers have provided formulas for the selection of adequate randomization ranges in yes-no and multiple-alternative forced choice tasks. In this article, we provide figures and tables that can be used to select randomization ranges that are better suited to experiments involving a same-different, dual-pair, or oddity task.

Figure 1

Pc_unwanted as a function of Δ/R for the same-different, 4IAX, 4IAX AB-versus-BA, yes-no, and 2I-2AFC paradigms. Each line type corresponds to a single paradigm, as indicated in the inset legend. Pc_unwanted refers to the maximal proportion of correct responses that can be achieved based on an unwanted cue, the use of which is limited by the application of a random rove drawn for a uniform (or “rectangular”) distribution with a range (or “width”) of R. Δ denotes the “size” of the unwanted cue, as defined in the text.

Figure 2

Pc_unwanted as a function of Δ/R for the three- and four-interval oddity, 3AFC, and 4AFC paradigms. Each line type corresponds to a single paradigm, as indicated in the inset legend. Pc_unwanted refers to the maximal proportion of correct responses that can be achieved based on an unwanted cue, the use of which is limited by the application of a random rove drawn for a uniform (or “rectangular”) distribution with a range (or “width”) of R. Δ denotes the “size” of the unwanted cue, as defined in the text.

Figure 3

Pc_unwanted produced by a continuous roving distribution (solid dark line) and a discrete distribution with eight bins (circles) as a function of Δ/R for various psychophysical paradigms (represented by different panels). The lower bound of the 95% confidence interval around Pc_unwanted values obtained using a continuous roving distribution is shown as a dotted line. The 95% confidence interval was determined based on the assumption of binomial variability, with the parameter N (number of trials) of the binomial distribution set to 100.