A robust left digit effect arises in number line estimation, whereby the leftmost digits of numerals have an undue influence on placements such that, for example, numbers like 298 are placed far to the left of numbers like 302. Past efforts to motivate more accurate performance using trial-by-trial and summary feedback have not led to a reduction in the left digit effect. In two experiments, we asked whether it is possible to reduce or eliminate the left digit effect in number line estimation through an instructional intervention in which one is explicitly taught about the left digit effect. In Experiment 1 (N = 134), participants completed two blocks (60 trials per block) of a self-paced 0-1,000 number line estimation task and were randomly assigned to either an instruction or a control condition. In Experiment 2 (N = 143), the procedure was enhanced with a learning check, and with additional measures to assess changes in behaviour as a result of instruction. In both experiments, a left digit effect was found in each block of each condition. Although there was evidence that instruction changed behaviour, these changes did not result in any reduction in the left digit effect relative to the control condition. These findings demonstrate that the left digit effect cannot be easily reduced by making people aware of it.

Number line estimation tasks are frequently used to study numerical cognition skills. In a typical version, the bounded number line task, target numerals must be placed on a bounded line labeled only at its endpoints (e.g., with 0 and 100). Placements by adults, while highly accurate, reveal a cyclical pattern of over-and underestimation of target numerals. The pattern suggests use of proportion judgment strategies and is well -captured by cyclical power models. Another systematic number line bias that has recently been observed, but has not yet been considered in modeling efforts, is the left digit effect. Numerals with different leftmost digits (e.g., 39 and 41) are placed farther apart on a line than is warranted. In the current study (N = 60), adult estimates were obtained for all numerals on a 0-100 number line estimation task, and fit of the standard cyclical power model was compared with two modified versions of the model. One modified version included a parameter that underweights the rightward digit's place value (e.g., the ones digit here), and the other used the same parameter to underweight all digits' place values. We found that both modifications provided a considerably better fit for individual and median data than the standard model, and we discuss their relative merits and cognitive interpretations. The data and models suggest how a left digit bias might impact estimates across the number line.

Recent work reveals a left digit effect in number line estimation such that adults' and children's estimates for three-digit numbers with different hundreds-place digits but nearly identical magnitudes are systematically different (e.g., 398 is placed too far to the left of 401 on a 0-1000 line, despite their almost indistinguishable magnitudes; Lai et al., 2018, https://doi.org/10.1111/desc.12657). In two preregistered studies (N = 218), we investigate the scope and malleability of the left digit effect. Experiment 1 used a typical forward-oriented 0-1000 number line estimation task and an atypical reverse-oriented 1000-0 number line estimation task. Experiment 2 used the same forward-oriented typical 0-1000 number line estimation task from Experiment 1, but with trial-by-trial corrective feedback. We observed a large left digit effect, regardless of the orientation of the line in Experiment 1 or the presence of corrective feedback in Experiment 2. Further, analyses using combined data showed that the pattern was present across most stimuli and participants. These findings demonstrate a left digit effect that is robust and widely observed, and that cannot be easily corrected with simple feedback. We discuss the implications of the findings for understanding sources of the effect and efforts to reduce it.

A left digit effect has been broadly observed across judgment and decision-making contexts ranging from product evaluation to medical treatment decisions to number line estimation. For example, $3.00 is judged to be a much greater cost than $2.99, and 801 is estimated strikingly too far to the right of 798 on a number line. Although the consequences of the effects for judgment and decision behavior have been documented, the sources of the effects are not well established. The goal of the current work is to extend investigations of the left digit effect to a new complex judgment activity and to assess whether the magnitude of the effect at the individual level can be predicted from performance on a simpler number skills task on which the left digit effect has also recently been observed. In three experiments (N = 434), adults completed a judgment task in which they rated the strength of hypothetical applicants for college admission and a self-paced number line estimation task. In all experiments, a small or medium left digit effect was found in the college admissions task, and a large effect was found in number line estimation. Individual-level variation was observed, but there was no relationship between the magnitudes of the effects in the two tasks. These findings provide evidence of a left digit effect in a novel multiattribute judgment task but offer no evidence that such performance can be predicted from a simple number skills task such as number line estimation.

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those magnitudes are unimportant. However, recent evidence shows that numbers with similar magnitudes but different leftmost digits are estimated very differently. For example, 798 is placed systematically much too far to the left of 801 in a 0-1000 NLE task by children aged 7-11 and adults. Here we ask whether this left digit effect generalizes to two-digit numerals in a 0-100 NLE task and whether it emerges in younger children. Children aged 5-8 (Study 1, N = 73), adults (Study 2, N = 44), and children aged 9-11 (Study 3, N = 27) completed a standard 0-100 NLE task on a touchscreen tablet. We observed left digit effects for two-digit numerals in children aged 8-11 and adults, with large effect sizes, demonstrating that these effects generalize to smaller numerical ranges. Left digit effects were not apparent in 5- to 7-year-olds, suggesting that these effects do not emerge at younger ages for smaller, more familiar numerical ranges. We discuss developmental emergence of left digit effects in number line estimation and implications within and beyond the field of cognitive development.

Minimal group paradigms investigate social preferences arising from mere group membership. We asked whether demand characteristics contribute to children's apparent minimal group bias in a preregistered experiment (N = 160). In a group condition, we attempted to replicate findings of bias following assignment to minimal groups. A second closely matched no-group condition retained potential demand characteristics while removing group assignment. Parallel bias in the no-group condition would suggest that demand characteristics contribute to findings of apparent ingroup bias. Three main findings emerged. First, in the group condition, ingroup preference emerged in one of three bias measures only. Second, this preference emerged even though participants evaluated ingroup/outgroup photos varying in race/ethnicity between trials. Third, the measure that yielded ingroup preferences in the group condition produced no parallel bias in the no group condition, consistent with the view that mere membership in a group, not experimental demand, leads to minimal ingroup preferences. (c) 2020 Elsevier Inc. All rights reserved.

Introduction Recent work reveals a new source of error in number line estimation (NLE), theleft digit effect(Lai, Zax, et al., 2018), whereby numerals with different leftmost digits but similar magnitudes (e.g., 399, 401) are placed farther apart on a number line (e.g., 0 to 1,000) than is warranted. The goals of the present study were to: (1) replicate the left digit effect, and (2) assess whether it is related to mathematical achievement. Method Participants were all individuals (adult college students) who completed the NLE task in the laboratory between 2014 and 2019 for whom SAT scores were available (n = 227). Results We replicated the left digit effect but found its size was not correlated with SAT math score, although it was negatively correlated with SAT verbal score for one NLE task version. Conclusions These findings provide further evidence that individual digits strongly influence estimation performance and suggest that this effect may have different cognitive contributors, and predict different complex skills, than overall NLE accuracy.

When allocating resources, people often diversify across categories even when those categories are arbitrary, such that allocations differ when identical sets of options are partitioned differently (partition dependence). The first goal of the present work (Experiment 1) was to replicate an experiment by Fox and colleagues in which graduate students exhibited partition dependence when asked how university financial aid should be allocated across arbitrarily partitioned income brackets. Our sample consisted of community members at a liberal arts college where financial aid practices have been recent topics of debate. Because stronger intrinsic preferences can reduce partition dependence, these participants might display little partition dependence with financial aid allocations. Alternatively, a demonstration of strong partition dependence in this population would emphasize the robustness of the effect. The second goal was to extend a high transparency modification to the present task context (Experiment 2) in which participants were shown both possible income partitions and randomly assigned themselves to one, to determine whether partition dependence in this paradigm would be reduced by revealing the study design (and the arbitrariness of income categories). Participants demonstrated clear partition dependence in both experiments. Results demonstrate the robustness of partition dependence in this context.

Partition dependence, the tendency to distribute choices differently based on the way options are grouped, has important implications for decision making. This phenomenon, observed in adults across a variety of contexts such as allocating resources or making selections from a menu of items, can bias decision makers toward some choices and away from others. Only one study to date (Reichelson, Zax, Patalano, & Barth, Quarterly Journal of Experimental Psychology, 72, 1029-1036, 2019) has investigated the developmental trajectory of this phenomenon. In the current study we investigate children's and adults' susceptibility to partitioning effects in a child-friendly resource allocation task. In Experiment 1 (N = 80), adults distributed 12 food tokens to animals at the zoo. Based on previous findings that older children show weaker partition dependence in this task, we predicted that adults might exhibit reduced partition dependent behavior: they showed none. In Experiment 2 (N = 272), we used a less transparent task with only five food tokens, predicting that both adults and children (ages 3-10 years) would show partition dependence. Children, but not adults, made partition dependent resource allocations, with younger children exhibiting greater effects than older children. These experiments provide further evidence that children's decisions, like adults' (in other tasks), are influenced by the arbitrary partitioning of the available options. This work supports previous findings that younger children may be more susceptible to these effects, and maps developmental change in partition dependent behavior from early childhood to adulthood on this child-friendly partition dependence task.