Embodied markedness of parity? Examining handedness effects on parity judgments

Abstract

Parity is important semantic information encoded by numbers. Interestingly, there are hand-based effects in parity judgment tasks: right-hand responses are faster for even and left-hand responses for odd numbers. As this effect was initially explained by the markedness of the words even vs. odd and right vs. left, it was denoted as the linguistic markedness of response codes (MARC) effect. In the present study, we investigated whether the MARC effect differs for right and left handers. We conducted a parity judgment task, in which right- and left-handed participants had to decide whether a presented single or two-digit number was odd or even by pressing a corresponding response key. We found that handedness modulated the MARC effect for unit digits. While we replicated a regular MARC effect for right handers, there was no evidence for a MARC effect for left handers. However, closer inspection revealed that the MARC effect in left handers depended on the degree of left-handedness with a reversed MARC effect for most left-handed participants. Furthermore, although parity of tens digits interfered with the processing of unit digits, the MARC effect for tens digits was not modulated by handedness. Our findings are discussed in the light of three different accounts for the MARC effect: the linguistic markedness account, the polarity correspondence principle, and the body-specificity hypothesis.

Appendices

Appendix A: Regression analysis and MANOVA

In addition to the analyses reported in the main article, we analyzed RT via regression analyses and MANOVAs. The first step in the separate analysis of levels (item level and participant level) was regressing SNARC and MARC effects. This was done separately for single- and two-digit numbers in line with our hypothesis. We estimated SNARC and MARC effects for each participant by conducting linear regression analyses separately for each participant.

For single-digit numbers, Nuerk et al., (2004) showed that zero differs from other even digits regarding its parity status. Therefore, we excluded all items containing zero from further analyses. The linear regression analysis for single-digit numbers included the following predictor variables: unit magnitude, unit parity, and hand as well as the interactions unit magnitude × hand (i.e., the SNARC effect) and unit parity × hand (i.e., the MARC effect). Prior to data analyses, the predictor variables hand, unit parity, and handedness were effect coded, and the predictor unit magnitude was centered. For the analysis of two-digit numbers, we considered the following predictor variables in our analyses: unit magnitude, tens magnitude, unit parity, tens parity, and hand as well as the two-way interactions unit magnitude × hand, tens magnitude × hand, unit parity × hand, and tens parity × hand.

Statistical analyses were run using R (R Development Core Team, 2014). Contrast effects were calculated using the ghlt function from the R package multcomp (Hothorn et al., 2008).

Influences of gender and handedness

Through the regression analyses we obtained six dependent variables of interest: SNARC and MARC effects for single-digit numbers and SNARC and MARC effects for unit and tens digits of two-digit numbers. In Table 5, we depicted the effect estimates. Only SNARC effect estimates for single-digit numbers and unit digits of two-digit numbers were significantly different from zero in the whole sample. Moreover, we found a significant parity congruity effect with faster responses when the parity of unit and tens digits was congruent [M = 22.72 ms, t(28) = 7.13, p < 0.001, 95 % CI [16.19, 29.24]]. Next, we examined the influence of handedness and gender on SNARC and MARC effect estimates. We additionally included gender as a control variable in our analyses to ensure that the influence of handedness on the SNARC and MARC effects might not be masked by an interaction with gender.

Table 5 SNARC and MARC effect estimates for single-digit numbers and units and tens digits of two-digit numbers for the whole sample

To control for dependencies among SNARC and MARC effects, we first conducted two multivariate analyses of variance (MANOVA) with factors handedness (right vs. left) and gender (male vs. female) as independent variables for the three SNARC and the three MARC effect estimates separately. MANOVAs were run using the R package car (Fox & Weisberg, 2011), using Type III error estimation implying subjects as a random factor, which is also the default in SPSS.

The MANOVA for SNARC effects revealed a significant main effect of gender [Pillai- trace = 0.42, F(3,23) = 5.64, p = .005, η ² = 0.42], but no significant main effect of handedness [Pillai-trace = 0.07, F(3,23) = 0.59, p = .630, η ² = 0.09] and no significant interaction [Pillai-trace = 0.09, F(3,23) = 0.78, p = .515, η ² = 0.06]. Contrarily, the MANOVA for MARC effects showed a significant main effect of handedness [Pillai- trace = 0.31, F(3,23) = 3.38, p = .035, η ² = 0.31], but no significant main effect of gender [Pillai-trace = 0.17, F(3,23) = 1.57, p = .223, η ² = 0.17] and no significant interaction [Pillai- trace = 0.10, F(3,23) = 0.90, p = .457, η ² = 0.10].

Next, we examined main effects of gender in the univariate analyses for the SNARC effect. We found a significant effect of gender for the SNARC effect for unit digits of two-digit numbers [F(1,25) = 15.40, p < 0.001, η ² = 0.38]. However, the main effect of gender was not significant for the single-digit SNARC effect [F(1,25) = 2.50, p = .127, η ² = 0.09] and the SNARC effect of tens digits [F(1,25) = 2.99, p = .192, η ² = 0.11]. P values were corrected for multiple comparisons using the method suggested by Holm, (1979). Slopes for male participants were steeper than for female participants for the SNARC effect for unit digits (see Table 6).

Table 6 Gender effect (SNARC) and handedness effect (MARC) of men and women and right and left handers, respectively

In the univariate analyses for the MARC effect and the main effect of handedness, we observed marginally significant effects of handedness for the single-digit MARC effect [F(1,25) = 4.89, p = .086, η ² = 0.16], the MARC effect for unit digits of two-digit numbers [F(1,25) = 5.05, p = .086, η ² = 0.17], and the MARC effect for tens digits of two-digit numbers [F(1,25) = 3.37, p = .086, η ² = 0.12]. Again, p values were corrected for multiple comparisons using the method suggested by Holm, (1979). There was a regular single-digit MARC effect and a two-digit MARC effect for unit digits for right handers, whereas these two MARC effects were reversed for left handers (see Table 6).

Degree of handedness

In the main text we also analyzed the interaction between handedness as a categorical and a continuous predictor. The corresponding analysis is a multivariate multiple regression analysis with the dependent variables single-digit MARC effect and MARC effect for unit digits of two-digit numbers and the predictor variables handedness (right vs. left handers), degree of handedness (HQ value) and their interaction.

The multivariate multiple regression revealed a marginally significant main effect of handedness [Pillai-trace = 0.19, F(2,24) = 2.87, p = .076, η ² = 0.31]. However, the main effect of degree of handedness was not significant [Pillai-trace = 0.02, F(2,24) = 0.24, p = .788, η ² = 0.02]. More importantly, we found a significant interaction between handedness and degree of handedness [Pillai-trace = 0.23, F(2,24) = 3.62, p = .042, η ² = 0.23]. Thus, we observed that slopes for degree of handedness differed between right and left handers.

Univariate regression analyses conducted separately for the single-digit MARC effect and the MARC effect for unit digits of two-digit numbers revealed that the interaction was significant for the single-digit MARC effect [slope estimate = −3.34 ms, SE = 1.21 ms, t(25) = −2.74, p = .022] and marginally significant for the MARC effect for unit digits of two-digit numbers [slope estimate = −2.01 ms, SE = 1.00 ms, t(25) = −2.02, p = .054]. Again, p values were corrected for multiple comparisons using the method suggested by Holm, (1979). The interaction for the single-digit MARC indicated that the MARC effect increased with a decreasing degree of handedness for left handers [slope estimate = 3.47 ms, SE = 1.46 ms, t(25) = 2.38, p = .025]. However, for right handers we did not find a significant influence of the degree of handedness on the MARC effect [slope estimate = −3.21 ms, SE = 1.95 ms, t(25) = −1.65, p = .112]. We found a similar pattern for the MARC effect for unit digits of two-digit numbers. Again, the MARC effect increased with decreasing degree of handedness for left handers [slope estimate = 2.55 ms, SE = 1.19 ms, t(25) = 2.13, p = .043], but the slope for right handers was negative but not significantly different from zero [slope estimate = −1.47 ms, SE = 1.60 ms, t(25) = −0.92, p = .365].

Appendix B: replication of Tan and Dixon, (2011)

We also investigated, whether we could replicate the findings of Tan and Dixon, (2011). Therefore, we coded trials as either same response trials, when two consecutive trials were answered by the same hand or as different response trials, when two consecutive trials were answered with different hands. Differing from the study by Tan and Dixon, (2011), there were no same stimulus subsequent trials.

Single-digit numbers

Tan and Dixon, (2011) found that neither the SNARC effect nor the MARC effect differed between same and different response trials. To replicate these findings, we compared models with and without the three-way interaction of unit magnitude × hand (i.e., the SNARC effect) × repetition condition (same vs. different response) and the interaction unit parity × hand (i.e., the MARC effect) × repetition condition (same vs. different response). As the random effect structure would have been too large to be estimated with our sample size, we included only the relevant random effects, when testing for modulation of the SNARC and/or the MARC effect by the repetition condition (cf. main article and Barr et al., 2013). Fixed effects included in the reference model were the three-way interactions unit magnitude × hand × repetition condition and unit parity × hand × repetition condition, and the respective lower level interactions and main effects.

First, we compared models with and without the three-way interaction between unit magnitude, hand, and repetition condition. Hence, we included the three-way interaction between unit magnitude, hand, and repetition condition as well as all lower level interactions and main effects as random effects. Second, we compared models with and without the three-way interaction between unit parity, hand, and repetition condition. Similarly, random effects were the three-way interaction between unit parity, hand, and repetition condition as well as all lower level interactions and main effects. Both likelihood ratio tests were not significant replicating the finding of Tan and Dixon, (2011) that neither the SNARC nor the MARC effect differed between same or different response trials.

Tan and Dixon, (2011) reported that including the interaction between unit parity and repetition condition increased the model fit to the data. To test for the presence of such an interaction, we used a model including the following fixed effects as a reference model: unit magnitude, unit parity, hand, response condition, and the two-way interactions unit magnitude × hand, unit parity × hand and unit parity × response condition. Moreover, we used the maximum random effects structure. We compared the reference model with the model excluding the interaction between unit parity and response condition. In contrast to Tan and Dixon, (2011), we did not find clear evidence but a tendency for the presence of the interaction, because the likelihood ratio test just failed to become significant [χ ²(1) = 3.68, p = .055]. Therefore, we omitted the interaction between unit parity and response condition. Finally, we compared models with and without response condition. The likelihood ratio test was significant, indicating that removing the response condition would reduce the model fit to the data [χ ²(1) = 17.81, p < 0.001]. Participants responded to same response trials about 26.30 ms (SE = 5.02 ms) faster than to different response trials.

Taken together, we were able to replicate most findings of Tan and Dixon, (2011). We found that neither the SNARC nor the MARC effect dependent on the repetition condition. Moreover, we found faster responses for same response trials than different response trials.

Two-digit numbers

For two-digit numbers, Tan and Dixon, (2011) found no evidence for an interaction between the SNARC effect and response condition, and for an interaction for the parity congruity effect and response condition, but evidence for an interaction between unit parity and response condition. We applied the same procedure as in the main article to analyze interactions of response condition with other predictors. We used the difference between different response trials and same response trials as dependent variable. Moreover, we removed the intercept as a fixed as well as a random effect in the subsequent analyses. Thereby, the number of fixed effects was reduced to unit magnitude, unit parity, tens parity, hand and the two-way interactions between unit magnitude and hand (i.e., the SNARC effect) and between unit parity and tens parity. Because we analyzed the difference between response conditions, all of these predictors indicated interactions with response condition (cf. main article).

The model including the maximum random effects structure did not converge. Hence, we included unit magnitude, hand and the interaction between unit magnitude and hand as random effects when comparing models with and without the interaction between unit magnitude and hand. For the comparison of models with and without the interaction between unit parity and tens parity we included unit parity, tens parity and the interaction between unit parity and tens parity as random effects.

Replicating the findings of Tan and Dixon, (2011), neither of the likelihood ratio tests was significant [interaction unit magnitude × hand: χ ²(1) < 0.01, p = .999; interaction unit parity × tens parity: χ ²(1) = 0.25, p = .616]. Thus, we did not find evidence for an interaction between the SNARC effect and response condition or for an interaction between the parity congruity effect and response condition.

To test for the interaction between unit parity and response condition, we used the reduced model including unit magnitude, unit parity, tens parity and hand as fixed effects as a reference model. Then, we compared models with and without unit parity as a predictor. The likelihood ratio test was significant, indicating that the response condition effect differed between even and odd numbers [χ ²(1) = 29.28, p < 0.001]. For even numbers, responses were faster, when two consecutive numbers were answered with the same hand, but for odd numbers, responses were faster, when the hands differed (estimate = 17.33 ms, SE = 2.47). We also compared models including and excluding the other predictors (i.e., unit magnitude, tens parity and hand). The likelihood ratio test revealed that all of them could be omitted without reducing the model fit to the data substantially [χ ²(3) = 0.06, p = .996].

To sum up, we replicated all findings of Tan and Dixon, (2011) regarding interactions with response condition. We found no evidence for an interaction between the SNARC effect and response condition or for an interaction between the parity congruity effect and response condition. However, there was evidence for an interaction between unit parity and response condition.