Estimating linear effects in ANOVA designs: The easy way

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

doi:10.3758/s13428-011-0172-y

Cited by 51 publications

(59 citation statements)

References 21 publications

(31 reference statements)

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“…The slope of the linear relationship captures the essence of the mapping in the expected latency differences between the two responses within the range of a given magnitude. The advantage of such linear trend analysis is that it quantifies the effect size of both the slope and the proportion of variability accounted for (Pinhas et al 2012).…”

Section: Discussionmentioning

confidence: 99%

“…The weights of the linear trend were determined by the range of target numbers which equidistantly shifted so that the sum of weights is zero. For the equally spaced number magnitude levels, weights were −4.5, −3.5, −2.5, −1.5, −.5, .5, 1.5, 2.5, 3.5, 4.5 for the target number from 0 to 9, respectively (Pinhas et al 2012). In this study, if there is an association between distance and number, a negative or positive linear relationship between dRT and number magnitude should be observed.…”

Section: Discussionmentioning

confidence: 99%

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Beyond the SNARC effect: distance–number mapping occurs in the peripersonal space

2015

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Estimating distance of objects relative to one's body is important for interaction with the environment. Given that distance is an interval of magnitude describing space, distance and the commonly used estimations of magnitude, i.e., numbers, may share a common representation system (the ATOM theory, Walsh in Trends Cogn Sci 7(11):483-488, 2003). The current study systematically examined the association between distance and number representations on both the sagittal and transverse axes on the transverse plane in the peripersonal space. Participants in Experiment 1 judged the parity of digits by pressing one of two buttons (both were in front of participants): One was near the body and the other away from it. We found that near responses were faster when paired with smaller numbers and far responses with larger numbers. When one button was set in front and the other in back in Experiment 2, no mapping was found. In Experiment 3, when both buttons were on the right side aligned with the transverse axis, small-near and large-far mapping were found. However, no such effect was found on the left side. These results suggest that numbers are mapped onto the whole transverse plane of the peripersonal space, not only a left-right oriented number line.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Beyond the SNARC effect: distance–number mapping occurs in the peripersonal space

2015

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“…To have normally distributed scores, Pearson's r values were Fisher ztransformed. These SNARC effect sizes were taken as a measure of the strength of SNAs in terms of the fit of dRTs to the regression lines (Pinhas, Tzelgov, & Ganor-Stern, 2012;Tzelgov, Zohar-Shai, & Nuerk, 2013).…”

Section: Parity Judgment and Magnitude Classification Tasksmentioning

confidence: 99%

How and why do number-space associations co-vary in implicit and explicit magnitude processing tasks?

2017

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Evidence for number-space associations in implicit and explicit magnitude processing tasks comes from the parity and magnitude SNARC effect respectively. Different spatial accounts were suggested to underlie these spatial-numerical associations (SNAs) with some inconsistencies in the literature. To determine whether the parity and magnitude SNAs arise from a single predominant account or taskdependent coding mechanisms, we adopted an individual differences approach to study their correlation and the extent of their association with arithmetic performance, spatial visualization ability and visualization profile. Additionally, we performed moderation analyses to determine whether the relation between these SNAs depended on individual differences in those cognitive factors. The parity and magnitude SNAs did not correlate and were differentially predicted by arithmetic performance and visualization profile respectively. These variables, however, also moderated the relation between the SNAs. While positive correlations were observed in object-visualizers with lower arithmetic performances, correlations were negative in spatial-visualizers with higher arithmetic performances. This suggests the predominance of a single account for both implicit and explicit SNAs in the two types of visualizers. However, the spatial nature of the account differs between object-and spatial-visualizers. No relation occurred in mixed-visualizers, indicating the activation of taskdependent coding mechanisms. Individual differences in arithmetic performance and visualization profile thus determined whether SNAs in implicit and explicit tasks co-varied and supposedly relied on similar or unrelated spatial coding mechanisms. This explains some inconsistencies in the literature regarding SNAs and highlights the usefulness of moderation analyses for understanding how the relation between different numerical concepts varies between individuals.

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“…The classical method to estimate the SNARC effect was proposed by Fias et al (1996) and generalized lately (Pinhas et al, 2012; Tzelgov et al, 2013). The SNARC can be described as the relation between number magnitude and reaction time differences – dRTs estimated separately for each individual.…”

Section: Introductionmentioning

confidence: 99%

“…The regression slope is interpreted then as a measure of the SNARC effect in a given subject. To test whether the SNARC effect is significant in the sample under investigation, individual standardized or non-standardized slopes are compared to 0 by means of a one-sample t -test (see generalization of this approach to more complex experimental designs by Pinhas et al, 2012 and Tzelgov et al, 2013). …”

Section: Introductionmentioning

confidence: 99%

Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

Cipora

Wood

2017

Front. Psychol.

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The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not difficult to detect a SNARC effect within a group, but it has been quite unusual to find group differences. Is the SNARC effect as it is usually estimated using regression slopes largely insensitive to group differences, and are there design parameters necessary to increase sensitivity in group comparison analyses? Using numerical simulations, we provide evidence that both sample size and the number of stimulus repetitions, as well as intra-individual variability, contribute in a substantial way to the probability of detecting an existing SNARC effect. Our results show that the adequate choice of either sample size or number of repetitions per experimental cell does not fully compensate for a poor choice of the other parameter. Moreover, repeated failures to find significant group differences in the SNARC effect can be explained by insufficient power. Fortunately, increasing the number of repetitions to about 20 and testing at least 20 participants provides in most cases sufficient sensitivity to reliably detect the SNARC effect as well as group differences. Power plots are provided, which may help to improve both the economy and sensitivity of experimental design in future SNARC experiments, or, more generally when regression slopes are estimated intra-individually.

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Estimating linear effects in ANOVA designs: The easy way

Cited by 51 publications

References 21 publications

Beyond the SNARC effect: distance–number mapping occurs in the peripersonal space

Beyond the SNARC effect: distance–number mapping occurs in the peripersonal space

How and why do number-space associations co-vary in implicit and explicit magnitude processing tasks?

Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

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