The measurement of approximate number system acuity across the lifespan is compromised by congruency effects

Abstract

Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults' ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.

The interplay between non-symbolic number and its continuous visual properties revisited: Effects of mixing trials of different types

“…This hypothesis is supported by the stability of the reversed diameter effect: It is present not only across different trial presentation modes (blocked vs. mixed) but also across different dot generation protocols. In fact, the effect has been replicated by studies using the Panamath method for generating dot comparison stimuli (Clayton et al, 2015; Norris et al, 2019). This is an important finding as some concerns have been raised about the replicability of findings in dot comparison tasks across different dot generation protocols (Inglis & Gilmore, 2014; Smets et al, 2015).…”

NASCO: A new method and program to generate dot arrays for non-symbolic number comparison tasks

“…We specify "on average" as Panamath differs from the original Dehaene's script in a way that dot sizes are heterogeneous within an array: Panamath indeed allows a random variation of each individual Item Size of maximum 20% of the mean size. Critically, since Panamath follows Dehaene et al's (2005) method, it has the same limitations (see Clayton et al, 2018;Dakin et al, 2011;Norris & Castronovo, 2016;Norris et al, 2018). In other words, Panamath does not control for the array extent and the density within the image (i.e, CH and MO).…”

“…The numerosity (i.e., the information about the number of elements) is indeed intrinsically intertwined with non-numerical magnitudes, such as the luminance or the extent of the array (see for instance, Gebuis & Reynvoet, 2012). Previous studies showed that numerical judgments are substantially impacted by the total surface occupied by all items (Guillaume, Nys, Mussolin, & Content, 2013), by the individual size of the elements (Henik, Gliksman, Kallai, & Leibovich, 2017), by the item density (Dakin, Tibber, Greenwood, Kingdom, & Morgan, 2011), and by the size of the convex hull (CH) (i.e., the smallest convex polygon encompassing all elements; Norris, Clayton, Gilmore, Inglis, & Castronovo, 2018).…”

Preschoolers' Associations Between Space and Numbers Can Be Biased by Surface Area

“…Since previous studies examining children's spatial-numerical associations by means of dot comparison tasks kept surface area constant across trials, these findings indicate that preschoolers can display SNARC-effects during conditions in which fewer dots take up the same surface area as the set containing more dots (see e.g., Ebersbach et al, 2014;Patro et al, 2016;Patro & Haman, 2012). However, our finding likely implies that other competing parameters such as density of the stimuli or convex hull (i.e., the smallest possible perimeter that can be drawn around an array; c.f., Norris, Clayton, Gilmore, Inglis, & Castronovo, 2019) could similarly affect SNARC-effects when dot comparison tasks are used. Since (in-)congruency of nonnumerical and number information yields particularly strong effects in children as opposed to adults (Szűcs et al, 2013, also see White et al, 2012), nonsymbolic number comparison tasks may overestimate associations between horizontal space and number in young children.…”