The metaphoric nature of the ordinal position effect

Abstract

Serial orders are thought to be spatially represented in working memory: The beginning items in the memorised sequence are associated with the left side of space and the ending items are associated with the right side of space. However, the origin of this ordinal position effect has remained unclear. It was suggested that the direction of serial order–space interaction is related to the reading/writing experience. An alternative hypothesis is that it originates from the “more is right”/“more is up” spatial metaphors we use in daily life. We can adjudicate between the two viewpoints in Chinese readers; they read left-to-right but also have a culturally ancient top-to-bottom reading/writing direction. Thus, the reading/writing viewpoint predicts no or a top-to-bottom effect in serial order–space interaction; whereas the spatial metaphor theory predicts a clear bottom-to-top effect. We designed four experiments to investigate this issue. First, we found a left-to-right ordinal position effect, replicating results obtained in Western populations. However, the vertical ordinal position effect was in the bottom-to-top direction; moreover, it was modulated by hand position (e.g., left hand bottom or up). We suggest that order–space interactions may originate from different sources and are driven by metaphoric comprehension, which itself may ground cognitive processing.

Keywords

Working memory ordinal position effect SPoARC effect metaphor

Introduction

In everyday life, we must maintain information in working memory (WM) for proper cognitive functioning. This high-level cognitive ability is thought to be grounded in the sensorimotor system (Barsalou, 2008; Dehaene & Cohen, 2007). For instance, recent studies observed an association between serial order in WM and external spatial processing (Abrahamse, van Dijck, & Fias, 2017; Guida, Leroux, Lavielle-Guida, & Noël, 2016; van Dijck & Fias, 2011). Participants responded faster to beginning items in the memorised sequence when they had to press the left hand, whereas the ending items in the memorised sequence were responded to faster when they had to press the right hand (Abrahamse et al., 2017; Abrahamse, van Dijck, Majerus, & Fias, 2014). This phenomenon was termed the ordinal position effect (Ginsburg, van Dijck, Previtali, Fias, & Gevers, 2014), which is also known as the Spatial-Positional Association of Response Codes (SPoARC) effect (Guida & Lavielle-Guida, 2014).

The conditions of this spontaneous serial order coding in spatial format have been explored. Guida et al. (2016) have documented that the ordinal position effect occurred irrespective of whether the remembered verbal items in the sequence were presented in visual or in auditory form. In addition, Ginsburg, Archambeau, van Dijck, Chetail, and Gevers (2017) also noted that the ordinal position effect is domain-general (e.g., it occurs in verbal and visual domains). Furthermore, they found that the ordinal position effect was observed only when the remembered items had a semantic content, and the strength of this effect was significantly related to the semantic content of the to-be-remembered items. Thus, Ginsburg et al. (2017) suggested that semantic activation of the to-be-remembered items is a necessary condition for the spatial coding of serial order.

Some authors have also discussed the origin of the specific left–right direction with which the ordinal position effect in WM has so far typically been observed. Guida and Lavielle-Guida (2014) proposed that the ordinal position effect was culturally determined. Guida et al. (2018) confirmed this experimentally. They tested three groups (left-to-right Western readers, right-to-left Arabic readers, and Arabic-speaking illiterates) and found a left-to-right ordinal position effect for left-to-right Western readers, a right-to-left effect for right-to-left Arabic readers, and no reliable spatial bias for Arabic-speaking illiterates. Guida et al. (2018) postulated that the direction of reading would drive the left-to-right direction of the ordinal position effect.

An alternative theory states that the ordinal position effect is due to a general application of “metaphors we live by” (Lakoff & Johnson, 2003). A careful analysis of everyday speaking and writing led Lakoff and Johnson to conclude that metaphor is pervasive in everyday language, thought, and action (Lakoff & Johnson, 2003, p. 4). They suggested that the human conceptual system is fundamentally metaphorical in nature, which has a basis in our physical and cultural experience. In line with this theory, we suggest that the ordinal position effect might originate from two such spatial metaphors, “more is right” and “more is up.” There are several occasions in daily life that support such metaphors; for the “more is right” metaphor, we can refer to the pervasive writing of “number lines” from left to right in Western cultures (Núñez Rafael, 2011). For the “more is up” metaphor, consider the ubiquitous physical observation that water poured early into a cup will end up at the bottom of that cup, but water poured later ends up at the top. The spatial experience with graphs (x-axis and y-axis) can also support the two spatial metaphors. Correspondingly, we suggest that the early items in the memorised sequence associate with the left side, whereas late items associate with the right side in the horizontal direction (“more is right”). In the vertical direction, the early items associate with the bottom side, whereas late items associate with the top side (“more is up”).

The viewpoints can be disentangled in a Chinese population. Chinese usually read and write left to right, but there is also an existing top to bottom reading/writing culture in which the Chinese characters are written from top to bottom. Although the top-to-bottom reading/writing is used infrequently in everyday life, the traditional reading/writing cultures are still retained (e.g., Chinese calligraphy, Spring Festival couplets). Both viewpoints predict the horizontal ordinal position effect in Chinese. Critically, in the vertical direction, if the ordinal position effect is related to the reading/writing direction, we would observe a vertical effect aligned in the top-to-bottom direction. If it instead originates from the “more is up” metaphor, there should be a vertical effect in the bottom-to-top direction.

The present study thus intended to investigate the origin of the ordinal position effect. We combined a memory task and a classification task (Ginsburg et al., 2017; van Dijck & Fias, 2011). The first step (Experiment 1) is to replicate the horizontal ordinal position effect; we anticipated a left-to-right effect as obtained in Western populations. We then attempt to investigate the ordinal position effect in the vertical direction. Experiments 2 and 3 were first designed to investigate the influence of spatial location (top or bottom) and hand positions on the ordinal position effect, respectively. Experiment 4 further investigated the influence of hand positions with a within-subjects manipulation.

Experiment 1

Participants

Referring to the sample size of previous, high-powered, research (Ginsburg et al., 2017), we recruited 30 right-handed students from South China Normal University (SCNU). All were Mandarin Chinese speakers (26 females, M age 21.37, range = 18-26). They all had normal or corrected-to-normal vision. After the experiment, the participants received modest monetary compensation. The study was approved by the Human Research Ethics Committee for Non-Clinical Faculties, School of Psychology, SCNU. We obtained the informed consent in verbal form from all participants before the experiments.

Material

All experiments used the same stimuli: four fruits (“xī guā”—watermelon, “xīang jīao”—banana, “pú táo”—grape, “jú zǐ”—orange) and four vegetables (“qíe zi”—eggplant, “yáng cōng”—onion, “huáng guā”—cucumber, “wān dòu”—peas) in Chinese characters. These two categories of words were all high frequency and were selected from the SUBTLEX-CH (Cai & Brysbaert, 2010). There were no significant differences between them in word frequencies, t(6) = 0.17, p > .05, or number of strokes, t(6) = –0.45, p > .05.

Procedure

The experiments were performed using E-Prime 2 Professional Software (Psychology Software Tools) in a quiet room. The viewing distance was approximately 50 cm from a 23-inch Liquid Crystal Display (LCD) computer screen with a 1,920 × 1,080 pixel resolution. For each experiment, the participants had to correctly complete 16 blocks. A new sequence was generated for every block. Each block was divided into three subsequent phases: an encoding phase, a classification phase, and a control phase.

During the encoding phase, four words (two fruits and two vegetables) forming a sequence were sequentially presented one at a time on the centre of the screen. They were written in 35-point Courier New font in bold, in white colour on a black background. Participants were first asked to memorise the serial order of words in the order of presentation. When the presented word was successfully encoded, participants pressed the “SPACE” button on the keyboard to go to the next word. The words in the sequence successively proceeded from one to the next, centrally on the screen. To maximise the chance that the four words were correctly maintained in the order of presentation, following the final word, there was a 2,500 ms blank screen interval for rehearsal.

After rehearsal, the classification phase started. Participants were asked to horizontally place their left index finger on the “D” key (left side of space) and the right index finger on the “L” key (right side of space). Half of the participants were instructed to press the left key for “fruits” and the right key for “vegetables,” whereas the other half received the opposite mapping. In this phase, all words (four memorised words and four other non-memorised words) from the classification set were randomly presented twice. There was a restriction that two consecutive trials did not contain the same word. Participants were instructed to classify the presented word as fruit or vegetable, and only respond to the memorised words from the encoding phase (go/no-go paradigm). Each trial started with a fixation cross in the centre of the screen. After 500 ms, a word appeared centrally. If this word belonged to the memorised sequence, participants had to quickly and accurately judge it as fruit or vegetable. The word appeared until the participant made a motor response or the response deadline (1,500 ms) was reached, followed by an inter-trial interval with a blank screen for 1,000 ms. Then the next trial was initiated. The speed and accuracy of motor responses were collected via button presses on the keyboard.

The last phase (control phase) was designed to make sure that participants had maintained the memorised sequence in the correct order. Three pairs of words were randomly selected from the memorised sequence and presented successively on the screen. For each pair, the two words were always neighbouring items in the memorised sequence. Participants were required to indicate if the first word was presented before or after the second word in the sequence. If the first word was presented before the second word, they had to press the “O” button; if it was not, they had to press the “N” button. There was no time limit for responding. As long as there was an error, the block was presented again after this control phase. We only included the blocks with a 100% correct control phase in the data analysis.

Data analysis

For each participant, the go trials with incorrect responses and RTs more than 2 SDs from the individual mean were removed from further analysis. The mean reaction times (RTs) of the remaining trials were calculated for each experimental condition. Following Ginsburg et al. (2017), we first applied a repeated-measures analysis of variance (ANOVA) with the variables ordinal position in WM (4: 1-4) and response side (2: left vs. right). A significant interaction between ordinal position and response side indicates an ordinal position effect. We also applied a different method to test the ordinal position effect, namely, the linear regression approach (Fias, Brysbaert, Geypens, & d’Ydewalle, 1996). For each position in WM (from 1 to 4), we computed the difference in RT (dRT: right minus left spatial location). The dRTs were entered in a regression analysis for each participant separately, with position as predictor. A negative regression slope indicates that the early items in the memorised sequence are responded to faster with the left, and the late items are responded to faster with the right, which suggests that there is a left-to-right ordinal position effect in the horizontal direction. Then, we performed an independent-samples t test to evaluate whether the regression weights of the group deviated significantly from zero. Finally, we performed a Bayesian one-sample t test on the regression slopes (Eidswick, 2012; Wagenmakers, Wetzels, Borsboom, & van der Maas, 2011).

Results and discussion

One student with more than 2 SDs above the mean errors was excluded. Trials with incorrect responses (error rate for all trials was 5.8%; 1.2% for no-go trials and 10.5% for go trials) and RTs more than 2 SDs from the individual mean (4.5%) were removed from the analysis. Participants accomplished an average 17.14 blocks (SD = 1.77) before they correctly performed 16 blocks. The average RT of the classification phase was 838.03 ms (SD = 210.19 ms). There was no speed-accuracy trade-off for the go trials (r = –.29, p > .05). The distribution of RTs was acceptably normal (skewness = 0.05).

The RTs were entered in a 4 (WM position: 1/2/3/4) × 2 (response side: left/right) repeated-measures ANOVA. There was a main effect of WM position, F(3, 84) = 7.655, p < .001, $η_{p}^{2}$ = .22. The RTs of each position were 822, 852, 861, and 863 ms, which increased gradually. A polynomial contrast confirmed this linear trend, F(1, 28) = 14.41, p = .001, $η_{p}^{2}$ = .34. The interaction between WM position and response side was significant, F(3, 84) = 13.81, p < .001, $η_{p}^{2}$ = .33; the left-side responses were faster for the beginning items than the ending items, and the right-side responses were faster for the ending items than the beginning items. The linear regression also yielded a significant result, slope = –40.58 (SD = 36.53); t(28) = –5.98, p < .001 (Figure 1a). A Bayes factor (BF₁₀) of 9,707.42 strongly supports the presence of the ordinal position effect.

Figure 1.

The ordinal position effect of experiments. The difference in RT (dRT) as a function of position in the working memory (WM) sequence. (a) Experiment 1. The dRTs were obtained by subtracting the average left-hand RTs from the average right-hand RTs. (b) Experiment 2. (c) Experiment 3. (d) Experiment 4. The dRTs in Experiments 2, 3, and 4 were obtained by subtracting the bottom-side RTs from the top-side RTs.

The results of Experiment 1 confirmed the presence of a horizontal ordinal position effect in Chinese participants, as found in previous studies with Western participants (Ginsburg et al., 2017; Guida et al., 2018).

Experiment 2

Given the replication of the horizontal ordinal position effect in Experiment 1 in a Chinese population, we now turn to our main focus and investigate the ordinal position effect in the vertical direction.

Method

In total, 32 new right-handed students from SCNU (23 females, M age = 20.28, range = 18-23) participated in Experiment 2. The material and procedure were the same as in Experiment 1. The only changes were in the classification phase; we rotated the keyboard 90° counterclockwise (Shaki & Fischer, 2012), and all participants were asked to vertically align the left index finger on the “D” key (bottom side of space) and right index finger on the “L” key (top side of space). Half of the participants were instructed to press the bottom key for “fruits” and the top key for “vegetables,” and vice versa for the other half.

Similar to Experiment 1, we first applied a repeated-measures ANOVA with the variables ordinal position in WM (4: 1-4) and response side (2: bottom vs. top), and then applied the linear regression approach (Fias et al., 1996) to detect the ordinal position effect. We computed the dRT of each position in WM (dRT: top minus bottom spatial location). The dRTs were then entered in a regression analysis for each participant separately, with position as predictor. A negative regression slope indicates that the early items in the memorised sequence are responded to faster with the bottom side, and the late items are responded to faster with the top side. Such finding would suggest a bottom-to-top ordinal position effect in the vertical direction.

Results and discussion

Three students with more than 2 SDs above the mean errors were excluded. Trials with incorrect responses (error rate for all trials was 7.5%; 1.5% for no-go trials and 13.5% for go trials) and RTs more than 2 SDs from the individual mean (5.0%) were removed from the analysis. Participants accomplished an average 17.45 blocks (SD = 1.86) before they correctly performed 16 blocks. The average RT of the classification phase was 856.93 ms (SD = 217.28 ms). There was no speed-accuracy trade-off for the go trials (r = .16, p > .05). The distribution of RTs was acceptably normal (skewness = 0.35).

The 4 (WM position: 1/2/3/4) × 2 (response side: bottom/top) repeated-measures ANOVA indicated that there was a main effect of WM position, F(3, 84) = 5.74, p = .001, $η_{p}^{2}$ = .17. The RTs of each position were 844, 871, 866, and 881 ms, which increased gradually. A polynomial contrast confirmed this increasing trend, F(1, 28) = 14.54, p = .001, $η_{p}^{2}$ = .34. Most importantly, the interaction between WM position and response side was significant, F(3, 84) = 10.10, p < .001, $η_{p}^{2}$ = .27; the bottom-side responses were faster for the beginning items than the ending items, and the top-side responses were faster for the ending items than the beginning items. The linear regression approach indicated a significant effect, slope = –34.30 (SD = 38.72); t(24) = –4.771, p < .001 (Figure 1b). A BF₁₀ of 472.71 strongly supports the presence of the vertical ordinal position effect.

Experiment 2 clearly showed a vertical ordinal position effect in Chinese participants. In line with the metaphor theory, the effect aligned in the bottom-to-top direction. During the classification phase of Experiment 2, participants vertically aligned their left hand on the bottom side and their right hand on the top side throughout the entire experiment. In principle, two factors could be responsible for this ordinal position effect. One is the “more is up” metaphor. Alternatively, however, the fact that the right hand was located on the top side might have driven the effect. From this perspective, the effect would still be due to a left-to-right factor. To differentiate between these possibilities, we conducted Experiment 3, where we investigated the vertical ordinal position effect again but reversed the hand-key mapping of Experiment 2.

Experiment 3

In Experiment 3, the left hand was placed on the top side and the right hand on the bottom side. If the vertical ordinal position effect is related to the response hands (and thus to a left-to-right alignment), the bottom-to-top effect observed in Experiment 2 would be reversed. Instead, if the ordinal position effect is due to the spatial “more is up” metaphor, it would be unchanged. Finally, if the effect is reduced relative to Experiment 2, there is evidence that both factors play a role.

Method

In total, 33 new right-handed students from SCNU (23 females, M age = 20.70, range = 18-26) participated in Experiment 3. The material and procedure were identical to Experiment 2, except for the hand-key mapping in the classification phase. All participants placed their left index finger on the “L” key (top side of space) and right index finger on the “D” key (bottom side of space) to respond. Half of the participants were instructed to press the top key for “fruits” and the bottom key for “vegetables,” and vice versa for the other half.

Results and discussion

One student with more than 2 SDs above the mean errors was excluded. Trials with incorrect responses (error rate for all trials was 8.3%; 1.3% for no-go trials and 15.2% for go trials) and RTs more than 2 SDs from the individual mean (4.6%) were removed from the analysis. Participants accomplished an average 17.63 blocks (SD = 1.56). The average RT of the classification phase was 882.24 ms (SD = 221.46 ms). There was no speed-accuracy trade-off for the go trials (r = –.21, p > .05). The RT distribution was acceptably normal (skewness = 0.24).

The statistical analyses were identical to the previous experiments. A significant main effect of WM position was found, F(3, 93) = 8.73, p < .001, $η_{p}^{2}$ = .22. The RTs of each position were 858, 889, 897, and 913 ms, which increased gradually. A polynomial contrast confirmed this linear trend, F(1, 31) = 21.51, p < .001, $η_{p}^{2}$ = .41. However, the interaction between WM position and response side was not significant, F(3, 93) = 1.16, p = .33, $η_{p}^{2}$ = .04. We then used the linear regression approach to further investigate this interaction. Although the slope was negative, there was no significant effect, slope = –2.48 (SD = 48.40); t(31) = –0.29, p = .77 (Figure 1c). A BF₁₀ of 0.20 also does not support the presence of the vertical ordinal position effect.

Finally, we conducted a mixed-design ANOVA with experiments (2: Experiment 2 vs. Experiment 3), WM position (4: 1/2/3/4), and response side (2: bottom/top) to indicate whether there was an interaction between Experiments 2 and 3. The main effect of WM position was still significant, F(3, 177) = 13.87, p < .001, $η_{p}^{2}$ = .19. The interaction between WM position and respond side was also significant, F(3, 177) = 4.85, p = .003, $η_{p}^{2}$ = .08, indicating that the bottom-side responses were faster for the beginning items, whereas the top-side responses were faster for the ending items. More importantly, there was a significant three-way interaction between experiments, WM position, and response side, F(3, 177) = 5.23, p < .01, $η_{p}^{2}$ = .08, suggesting that ordinal position effect is influenced by the hand-key mappings. Finally, we conducted Experiment 4, counterbalancing the hand-key mappings within participants, to replicate the ordinal position effect in the vertical direction and to investigate whether the influence of hand-key mappings on the ordinal position effect can also be found when manipulated on a subject-specific basis.

Experiment 4

Method

In total, 33 new right-handed students from SCNU (19 females, M age = 21.36, range = 18-25) participated in this experiment. The material and procedure were identical to Experiment 2, except for the manipulation of the hand-key mapping in the classification phase. All participants performed two hand-key mappings; 18 participants started with placing their left index finger on the bottom-side (D) key and right index finger on the top-side (L) key (Group A), and the other participants started with the opposite hand-key mapping (Group B). Half of the participants were instructed to press the top key for “fruits” and the bottom key for “vegetables,” and vice versa for the other half.

Results and discussion

Two students from group A with more than 2 SDs above the mean errors were excluded. Trials with incorrect responses (error rate for all trials was 9.2%; 7.5% for no-go trials and 10.9% for go trials) and RTs more than 2 SDs from the individual mean (4.7%) were removed from the analysis. Participants accomplished an average 17.58 blocks (SD = 1.46). The average RT of the classification phase was 859.58 ms (SD = 201.92 ms). There was no speed-accuracy trade-off for the go trials (r = –.30, p > .05). The distribution of RTs was acceptably normal (skewness = 0.03).

The RTs were entered in a 2 (mapping: Mapping 1/Mapping 2) × 4 (WM position: 1/2/3/4) × 2 (response side: bottom/top) repeated-measures ANOVA. The main effect of WM position was significant, F(3, 87) = 4.02, p = .01, $η_{p}^{2}$ = .12. The RTs of each position were 848, 872, 877, and 889 ms, which increased gradually. A polynomial contrast confirmed this linear trend, F(1, 29) = 8.39, p < .01, $η_{p}^{2}$ = .22. The interaction between WM position and response side was not significant, F(3, 87) = 1.62, p = .19, $η_{p}^{2}$ = .05. We then used the linear regression approach to further investigate this interaction. This more sensitive method indicated that there was a significant effect, slope = –16.96 (SD = 41.49); t(31) = –2.28, p < .05 (Figure 1d). A BF₁₀ of 1.78 was observed providing an anecdotal evidence for the presence of the vertical ordinal position effect in bottom-to-top direction.

The three-way interaction between response mapping, WM position, and response side was also not significant, F(3, 87) = 0.66, p = .58, $η_{p}^{2}$ = .02. We then applied the linear regression approach to each response mapping separately to further study the interaction. The regression slopes for two mappings were both negative but not significant—Mapping 1: slope = –16.41 (SD = 71.58), t(30) = –1.28, p = .21; Mapping 2: slope = –8.86 (SD = 49.55), t(30) = –1.00, p = .33. The results of paired-sample t test indicated that the difference between the regression slopes of two mappings was not significant, t(30) = –0.48, p = .64. These results suggest that there is no significant influence of response mapping on the vertical ordinal position effect. However, a more statistically powerful comparison across experiments does suggest that hand-key mapping may have some effect: The size of the ordinal position effect of Experiment 4 (slope = –16.96) was in between that of Experiment 2 (slope = –34.30) and Experiment 3 (slope = –2.48).

Given that the only difference among the three experiments is the manipulation of the hand-key mappings, we next conducted a one-way ANOVA on the regression slopes of all experiments that used the vertical direction (3: Experiments 2, 3, and 4) to directly compare the effects and reveal the impact of hand locations. Levene’s test results supported the homogeneity of variances for the experiment groups (p = .82). The ANOVA results indicated that there existed significant differences among the regression slopes, F(2, 89) = 4.13, p < .05, suggesting that the hand-key mappings affected the ordinal position effect in the vertical direction. A further multiple comparisons analysis (Least Significance Difference [LSD] method) indicated that only the ordinal position effect of Experiment 2 was significantly different from that of Experiment 3 (p < .01). Thus, we suggest that both hands (by definition left-to-right oriented) and vertical direction may play a role in the vertical ordinal position effect.

General discussion

The purpose of this study was to investigate the origin of the ordinal position effect. We designed four experiments to explore this issue in Chinese readers. In Experiment 1, we replicated the horizontal ordinal position effect, which aligned in the left-to-right direction. The subsequent experiments were conducted to investigate the core issue. In Experiment 2, we found the vertical ordinal position effect in the bottom-to-top orientation, which suggested that early items in the memorised sequence were associated with the bottom side, whereas late items were associated with the top side. In this experiment, the left hand was placed on the bottom side and the right hand on the top side. Although this design reduced the interference from the counterbalancing of hand-key mapping (Shaki & Fischer, 2012), the procedure confounded spatial location (top or bottom) with the response hands. We therefore designed Experiment 3, in which the left hand was placed on the top side and the right hand on the bottom side. Although there still was a negative regression slope, we did not find a significant effect. We then counterbalanced the hand-key mappings within participants to explore the vertical ordinal position effect again in Experiment 4. We observed a weak but significant effect in bottom-to-top orientation; Its effect size was in between Experiments 2 and 3. The results of a one-way ANOVA, comparing the effect size of Experiments 2 to 4 in vertical direction, suggest that both hand positions and the vertical direction play a role in the vertical ordinal position effect.

The left-to-right ordinal position effect was previously explained by the reading/writing culture (Guida et al., 2018), which suggests that the direction of serial order–space interaction relates to the reading/writing direction. In line with this view, the mental whiteboard hypothesis (Abrahamse et al., 2017; Abrahamse et al., 2014) suggests that storage and retrieval processes of serial order in WM are based on the spatial attention system (Abrahamse et al., 2014). The brain might generate an internal spatial template to “write down” items and capture item sequences in WM like writing the serial items on a sheet of paper (Abrahamse et al., 2017). Abrahamse et al. (2017) and Abrahamse et al. (2014) have considered the reading/writing experience as one potential shaper of the filling direction on the internal spatial template. In the horizontal direction, the reading/writing direction may influence the spatial-positional associations. However, in the vertical direction, we did not observe the top-to-bottom ordinal position effect in Chinese readers, who still retain the top-to-bottom reading/writing culture. We therefore suggest that the ordinal position effect cannot be exclusively based on the reading/writing direction. We propose the more general metaphor theory to account for these results. In the horizontal direction, a “more is right” spatial metaphor may drive the ordinal position effect; because the concept “more” is associated with “right” (Lakoff & Johnson, 2003), a left-to-right spatial-positional association follows as a result. For the vertical dimension, we propose that the effect may originate at least partially from the “more is up” metaphor; the concept “more” is oriented “up” (Lakoff & Johnson, 2003), which leads the bottom-to-top spatial-positional associations.

In addition, the spatial metaphor hypothesis can explain why the vertical effect was influenced by the spatial hand locations. When the left hand was assigned to the bottom side and the right hand to the top side (Experiment 2), there were no conflicts between the early-left and early-bottom associations, or between late-right and late-top associations. However, when the hand-key mapping was reversed, the left hand was assigned to the top side and the right hand to the bottom side. We suggest that the left-early associations worked against the top-late associations, and right-late associations against the bottom-early associations. This might contribute to the lack of vertical ordinal position effect in Experiment 3 and the weak effect in Experiment 4. According to this rationale, some authors might argue that the ordinal position effect in Experiment 1, where there is only one force at work (early-left associations), should be weaker than that in Experiment 2, where the two forces (early-left and early-bottom associations) are together and push in the same direction. Although our results showed that the size of the ordinal position effect in Experiment 1 (slope = –40.58) was slightly larger than that of Experiment 2 (slope = –34.30), the t test suggested that there was no significant difference between them, t(956) = –0.64, p > .05.

However, in Experiment 4, we did not observe a significant influence of hand-key mappings on the vertical ordinal position effect. This may simply be due to a lower power relative to the analysis comparing Experiments 2 and 3. Alternatively, this discrepancy may have resulted from the use of a within-subjects design; perhaps implementing both mappings (left hand up and left hand down) influences the way the task is performed. This explanation, of course, remains speculative at this time.

Although we discussed them separately, this spatial metaphor (Lakoff & Johnson, 2003) is also compatible with the mental whiteboard hypothesis (Abrahamse et al., 2017; Abrahamse et al., 2014); spatial metaphors may drive the directionality of use of the mental whiteboard. However, it remains to be shown how the metaphor theory can explain the “reversed” right/left directionality of the ordinal position effect observed by Guida et al. (2018). We suggest that because of the strong influence of the reading/writing direction, right-to-left readers develop a more dominant “left is more” metaphor. Although this is of course post hoc and remains to be empirically investigated, it allows for a potential reconciliation of the two viewpoints; here, reading/writing direction is just one potential generator of metaphors that guide our actions in horizontal dimension.

In general, our data suggest a diversity of potential factors underlying the ordinal position effect. One other potentially relevant factor is individual differences in how subjects address the task. Individual differences in task processing are often considered a nuisance that muddy the underlying spatial associations. However, if metaphors generate these associations, and if people use different metaphors, consideration of individual differences may well be crucial for understanding (spatial) associations in such tasks.

Metaphoric comprehension has been proposed to describe another spatial-association phenomenon (Winter & Teenie, 2013), the SNARC (Spatial-Numerical Associations of Response Code) effect (Dehaene, Bossini, & Giraux, 1993). This reflects the tendency that small numbers are responded to faster with the left side, whereas large numbers are responded to faster with the right side (Göbel, Shaki, & Fischer, 2011; Hartmann, Grabherr, & Mast, 2012; Zebian, 2005). For the horizontal SNARC effect, Winter and Teenie (2013) proposed that the “more is right” metaphor may explain how numbers are represented in the horizontal direction. In addition to the horizontal spatial-numerical associations, several studies have investigated it in the vertical direction (Gevers, Lammertyn, Notebaert, Verguts, & Fias, 2006; Hartmann, Gashaj, Stahnke, & Mast, 2014; Hung, Hung, Tzeng, & Wu, 2008; Ito & Hatta, 2004; Schwarz & Keus, 2004; Shaki & Fischer, 2012). Most studies of the vertical SNARC effect have indicated that small numbers are associated with the bottom side of space, and large numbers with the top (Hartmann et al., 2012; Ito & Hatta, 2004; Schwarz & Keus, 2004; Sell & Kaschak, 2012; Winter & Teenie, 2013). Some researchers put forward the “more is up” spatial metaphor (Gevers et al., 2006; Hartmann et al., 2012; Sell & Kaschak, 2012; Shaki & Fischer, 2012; Winter & Teenie, 2013). Like for the spatial ordinal position effect, we suggest that all these spatial associations may be special cases of metaphoric comprehension, and that more generally, space, order, and number interactions derive from metaphoric, culturally determined comprehension (Lakoff & Johnson, 2003; Verguts & Chen, 2017).

Footnotes

Acknowledgements

We are extremely grateful to Xiangyan Zeng for his technical help in completing the experimental procedure.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

This work was supported by grants from the National Natural Science Foundation of China (Grants 31671135 and 31300834 to Q.C.) and the Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2016) to Q.C.

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