The most prominent explanation for the spatial numerical association of response codes (SNARC) effect is the direct mapping account (DMA). The DMA assumes that (a) numbers are represented on a mental number line, (b) this mental number line is mapped to external space, and (c) the better the mapping location corresponds to the response location, the faster the response. The DMA leaves open whether a variation of response locations can (ceteris paribus) influence the location to which numbers are mapped in external space. In order to investigate this question, we varied response key distance during a standard parity judgment and a magnitude judgment task. We found that even drastic manipulations of response key distance did not modulate the SNARC effect. Power and meta-analyses show that this null effect is not due to insufficient statistical power or a poor experimental setup. Thus, our results indicate that, in order for the DMA to explain the SNARC effect, it must assume that the mapping from the mental number line to external space is anchored to response location. For future research, our results suggest that it is not necessary to control the horizontal separation of the response keys in basic SNARC experiments.
BachotJ.GeversW.FiasW.RoeyersH. (2005) Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology Science47: 172–183.
2.
BaroudiJ.OrlikowskiW. (1989) The problem of statistical power in MIS research. MIS Quarterly13: 87–106.
3.
BächtoldD.BaumüllerM.BruggerP. (1998) Stimulus-response compatibility in representational space. Neuropsychologia36: 731–735.
4.
BrainardD. H. (1997) The Psychophysics Toolbox. Spatial Vision10: 433–436.
5.
BullR.BensonP. J. (2006) Digit ratio (2D:4D) and the spatial representation of magnitude. Hormones and Behavior50: 194–199.
6.
BullR.MarscharkM.Blatto-ValleeG. (2005) SNARC hunting: Examining number representation in deaf students. Learning and Individual Differences15: 223–236.
7.
Cardoso-LeiteP.MamassianP.GoreaA. (2009) Comparison of perceptual and motor latencies via anticipatory and reactive response times. Attention, Perception, & Psychophysics71: 82–94.
8.
ChenJ.ProctorR. W. (2014) Conceptual response distance and intervening keys distinguish action goals in the Stroop color-identification task. Psychonomic Bulletin & Review21: 1238–1243.
9.
ChoY. S.ProctorR. W. (2007) When is an odd number not odd? Influence of task rule on the MARC effect for numeric classification. Journal of Experimental Psychology: Learning, Memory, and Cognition33: 832–842.
10.
CohenJ. (1988) Statistical power analysis for the behavioral sciences, (2nd ed.). Hillsdale, NJ: Erlbaum.
11.
CrawfordJ. R.GarthwaiteP. H. (2012) Single-case research in neuropsychology: A comparison of five forms of t-test for comparing a case to controls. Cortex48: 1009–1016.
12.
CrawfordJ. R.HowellD. C. (1998) Comparing an individual’s test score against norms derived from small samples. Clinical Neuropsychologist12: 482–486.
13.
DehaeneS.BossiniS.GirauxP. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General122: 371–396.
14.
DehaeneS.EmmanuelD.MehlerJ. (1990) Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance16: 626–641.
15.
FiasW.BrysbaertM.GeypensF.d’YdewalleG. (1996) The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Mathematical Cognition2: 95–110.
16.
FischerM.MillsR. A.ShakiS. (2010) How to cook a SNARC: Number placement in text rapidly changes spatial–numerical associations. Brain and Cognition72: 333–336.
17.
FischerM.RottmannJ. (2005) Do negative numbers have a place on the mental number line?Psychology Science47: 22–32.
18.
FitousiD.ShakiS.AlgomD. (2009) The role of parity, physical size, and magnitude in numerical cognition: The SNARC effect revisited. Attention, Perception, & Psychophysics71: 143–155.
19.
FranzV. H.LoftusG. R. (2012) Standard errors and confidence intervals in within-subject designs: Generalizing Loftus & Masson (1994) and avoiding biases of alternative accounts. Psychonomic Bulletin & Review19: 395–404.
20.
GeversW.SantensS.DhoogeE.ChenQ.Van den BosscheL.FiasW.VergutsT. (2010) Verbal-spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General139: 180–190.
21.
GeversW.VergutsT.ReynvoetB.CaessensB.FiasW. (2006) Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance32: 32–44.
22.
GöbelS. M.SnowlingM. J. (2010) Number-processing skills in adults with dyslexia. The Quarterly Journal of Experimental Psychology63: 1361–1373.
23.
GreenhouseS. W.GeisserS. (1959) On methods in the analysis of profile data. Psychometrika24: 95–112.
24.
HeisterG.Schroeder-HeisterP.EhrensteinW. H. (1990) Spatial coding and spatio-anatomical mapping: Evidence for a hierarchical model of spatial stimulus–response compatibility. In: W. ProctorR.ReeveT. G. (eds) Stimulus–response compatibility: An integrated perspective, Amsterdam, Netherland: North-Holland, pp. 117–143.
25.
HerreraA.MacizoP.SemenzaC. (2008) The role of working memory in the association between number magnitude and space. Acta Psychologica128: 225–237.
26.
HinesT. M. (1990) An odd effect: Lengthened reaction times for judgments about odd digits. Memory & Cognition18: 40–46.
27.
HubbardE. M.PiazzaM.PinelP.DehaeneS. (2005) Interactions between number and space in parietal cortex. Nature Reviews Neuroscience6: 435–448.
28.
HubbardE. M.RanziniM.PiazzaM.DehaeneS. (2009) What information is critical to elicit interference in number-form synaesthesia?Cortex45: 1200–1216.
29.
HungY.HungD. L.TzengO. J.-L.WuD. H. (2008) Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition106: 1441–1450.
30.
IshiharaM.Jacquin-CourtoisS.FloryV.SalemmeR.ImanakaK.RossettiY. (2006) Interaction between space and number representations during motor preparation in manual aiming. Neuropsychologia44: 1009–1016.
31.
ItoY.HattaT. (2004) Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect. Memory & Cognition32: 662–673.
32.
JonasM.ElokaO.StephanJ.FranzV. H. (2014) Need for space: The key distance effect depends on spatial stimulus configurations. PLoS ONE9, e91432: 1–12.
33.
KeusI. M.JenksK. M.SchwarzW. (2005) Psychophysiological evidence that the SNARC effect has its functional locus in a response selection stage. Cognitive Brain Research24: 48–56.
34.
KeusI. M.SchwarzW. (2005) Searching for the functional locus of the SNARC effect: Evidence for a response-related origin. Memory & Cognition33: 681–695.
35.
LakensD.SchneiderI. K.JostmannN. B.SchubertT. W. (2011) Telling things apart: The distance between response keys influences categorization times. Psychological Science22: 887–890.
MillerJ. (1985) A hand advantage in preparation of simple keypress responses—Reply to Reeve and Proctor (1984). Journal of Experimental Psychology: Human Perception and Performance11: 221–233.
38.
MoyerR. S.LandauerT. K. (1967) Time required for judgements of numerical inequality. Nature215: 1519–1520.
39.
MüllerD.SchwarzW. (2007) Is there an internal association of numbers to hands? The task set influences the nature of the SNARC effect. Memory and Cognition35: 1151–1161.
40.
NettN.FringsC. (2013) Things can be cold apart: No influence of response categories and labels on the distance effect in Stroop tasks. Experimental Psychology61: 142–148.
41.
NuerkH.-C.IversenW.WillmesK. (2004) Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect. The Quarterly Journal of Experimental Psychology Section A57: 835–863.
42.
NuerkH.-C.WoodG.WillmesK. (2005) The universal SNARC effect. The association between number and magnitude and space is amodal. Experimental Psychology52: 187–194.
43.
PelliD. G. (1997) The VideoToolbox software for visual psychophysics: Transforming numbers into movies. Spatial Vision10: 437–442.
44.
PriftisK.ZorziM.MeneghelloF.MarenziR.UmiltaC. (2006) Explicit versus implicit processing of representational space in neglect: Dissociations in accessing the mental number line. Journal of Cognitive Neuroscience18: 680–688.
45.
ProctorR. W.ChenJ. (2012) Dissociating influences of key and hand separation on the stroop color-identification effect. Acta Psychologica141: 39–47.
46.
ProctorR. W.ChoY. S. (2006) Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin132: 416–442.
47.
R Development Core Team. (2008). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org.
48.
RielloM.RusconiE. (2011) Unimanual SNARC effect: Hand matters. Frontiers in Psychology2: 372.
49.
SantensS.GeversW. (2008) The SNARC effect does not imply a mental number line. Cognition108: 263–270.
50.
SchwarzW.KeusI. M. (2004) Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses. Perception & Psychophysics66: 651–664.
51.
SchwarzW.MüllerD. (2006) Spatial associations in number-related tasks. A comparison of manual and pedal responses. Experimental Psychology53: 4–15.
52.
ShakiS.FischerM. H.PetrusicW. M. (2009) Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review16: 328–331.
53.
ShimizuH. (2002) Measuring keyboard response delays by comparing keyboard and joystick inputs. Behavior Research Methods, Instruments, & Computers34: 250–256.
54.
SokalR. R.RohlfJ. F. (1995) Biometry, San Francisco, CA: W.H. Freeman.
55.
StinsJ. F.MichaelsC. F. (2000) Stimulus-response compatibility for absolute and relative spatial correspondence in reaching and in button pressing. Quarterly Journal of Experimental Psychology A53: 569–589.
56.
ThomaschkeR.KieselA.HoffmannJ. (2011) Response specific temporal expectancy: Evidence from a variable foreperiod paradigm. Attention, Perception, & Psychophysics73: 2309–2322.
57.
TzelgovJ.Zohar-ShaiB.NuerkH.-C. (2013) On defining quantifying and measuring the SNARC effect. Frontiers in Psychology4: 302.
58.
Van DijckJ.-P.FiasW. (2011) A working memory account for spatial-numerical associations. Cognition119: 114–119.
59.
Van DijckJ.-P.GeversW.FiasW. (2009) Numbers are associated with different types of spatial information depending on the task. Cognition113: 248–253.
60.
VierckE.KieselA. (2010) Congruency effects between number magnitude and response force. Journal of Experimental Psychology: Learning, Memory, and Cognition36: 204–209.
61.
WoodG.NuerkH.-C.WillmesK. (2006) Crossed hands and the SNARC effect: A failure to replicate Dehaene, Bossini and Giraux (1993). Cortex42: 1069–1079.
62.
WoodG.WillmesK.NuerkH.-C.FischerM. H. (2008) On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly50: 489–525.
