The influence of representational processes on the numerical distance effect

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)



First Advisor

Richard Anderson

Second Advisor

Dale Klopfer (Committee Member)

Third Advisor

Barbara Moses (Committee Member)

Fourth Advisor

Yiwei Chen (Committee Member)


Research has clearly established that the numerical distance between two Arabic numerals affects reaction times for tasks that involve determining the relative numerical magnitude of those numerals. The present study tested two characteristics of models that explain the effect of numerical distance: whether distance effect-sensitive representational processes occur with the presentation of a single comparate (i.e. a to-be-compared digit) or require two comparates to operate, and whether distance-effect-sensitive representations are static or dynamic. The present research examined the data from three number-comparison experiments that manipulated the asynchronous presentation of the comparates using stimulus onset asynchrony (SOA) and a between-trial repeat of a single comparate. Both manipulations of asynchronous presentation were intended to provide subjects with a head start in encoding the first of a pair of to-be-compared digits without providing a head start for the actual comparison of the digits – thus yielding information about the onset of distance processing in relation to comparate presentation and also to identify whether relevant representations are dynamic or static. Experiments 1 and 2 also included a probe-response task in which subjects selected a numerical probe after being presented with a numerical prime. SOA in the probe-response task was found to moderate the distance effect (thus suggesting that onset of distance effect processing occurred with the first comparate), but SOA did not moderate the distance effect on the number-comparison task (thus suggesting that onset of distance effect processing occurred with the second comparate). This inconsistency, together with evidence from Experiment 3 (below), was interpreted as evidence that each task type used a separate representational pathway.

Experiment 3 did not contain a probe-response task, but instead included an additional number-comparate task condition in which the comparate that the participant selected on the current trial was repeated as one of the comparates presented in the subsequent trial. The distance effect in Experiment 3 was stronger for trials without a repeated comparate than it was for trials with a repeated comparate. This was interpreted as evidence that the comparison process changed the representation of the repeated comparate and that retaining this changed representation reduces the amount of distance effect processing on the subsequent trial. Experiment 3 also yielded evidence that SOA moderated the effect of distance for both comparate-repeat and comparate-non-repeat trials. This moderation was interpreted as evidence that distance effect processing occurs with the onset of the first comparate for whichever representational pathway is given precedence. Thus, it was concluded that the probe-response task was given precedence over the number-comparison task for Experiments 1 and 2 (these experiments contained both task types) but that the number-comparison task had precedence for Experiment 3 (Experiment 3 contained only the number-comparison task). Both the comparate-repeat manipulation results and the SOA manipulation results are consistent with the explanation that dynamic, but not static, representation gives rise to the distance effect. The fact that both the comparate-repeat manipulation and the SOA manipulation moderated the distance effect suggests that the onset of the representational change that gives rise to the distance effect occurs with the presentation of the first comparate, but that substantial processing occurs with the second comparate as well. Overall results from all three experiments suggest that representational change plays a role in creating the distance effect and that this change occurs along task-specific pathways.