Data analysis
Reaction time data and movement time data were used to determine the presence of MNL effects. This was analysed by condition (whether participants completed the normal block or the reversed block first) and by trial type. All participants completed four trial types; normal trials from the consistent block (hereafter referred to as ‘normal’), reversed trials from the consistent block (hereafter referred to as ‘reversed’); and normal and reversed trials from the mixed block (‘mixed normal’ and ‘mixed reversed’). Partial eta squared effect sizes are reported (Cohen 1988) and the Greenhouse-Geisser correction applied where appropriate.
Reaction times
We first explored the effect of Condition (2 between participant levels: Normal First, Reversed First) and trial type (4 within participant levels: consistent normal, consistent reversed, mixed normal and mixed reversed) using a mixed-design ANOVA. A main effect of trial type was found, F(3, 111) = 81.23, p < .001, η
2
p
= .69. Overall, mixed trials showed slower reaction times than consistent trials. There was no main effect of condition, F(1, 37) = .33, p = .571, η
2
p
= .01, but a significant interaction, F(3, 111) = 5.32, p < .05, η
2
p
= .13. These effects can be seen in Fig. 2.
This interaction found in the ‘omnibus’ ANOVA was explored by doing separate analyses for the consistent blocks and the mixed block. First, in the consistent blocks there was no main effect of condition, F(1, 37) = .76, p = .39, η
2
p
= .02, but there was a main effect of trial type, F(1, 37) = 5.63, p = .023, η
2
p
= .13, with normal trials quicker than reversed trials. There was also an interaction between trial type and condition, F(1, 37) = 14.64, p < .001, η
2
p
= .28 where the MNL effect (i.e., normal trials quicker than reversed trials) was only found in the Reversed First condition (see Fig. 2a). This differential presence of a MNL effect depending on condition may reflect a small element of task learning at the start of the experiment. The learning period would be expected to marginally lengthen RTs. Therefore, when ‘normal’ trials were completed first this may have off-set the advantage gained from a MNL.
Second, for the mixed block, again there was no main effect of condition, F(1, 37) = 1.73, p = .196, η
2
p
= .05, but a main effect of trial type, F(1, 37) = 22.80, p < .001, η
2
p
= .38. This time the interaction was not significant, F(1, 37) = .00, p = .950, η
2
p
= .00: normal trials were responded to faster than reversed trials, regardless of the preceding block. Therefore, under high-difficulty conditions in the mixed block, there was a stronger effect of trial type (η
2
p
= .38, compared with η
2
p
= .13 in the consistent blocks), with RTs to normal trials faster than to reversed trials. In addition, the preceding block made no difference to this preference for a culturally orientated MNL.
Movement times
As with the RT data, we first explored the effect of Condition (2 between participant levels: Normal First, Reversed First) and trial type (4 within participant levels: consistent normal, consistent reversed, mixed normal and mixed reversed) using a mixed model ANOVA. A main effect of trial type was found, F(3, 111) = 32.99, p < .001, η
2
p
= .47 (mixed blocks showed slower movement times than consistent blocks). There was no main effect of condition, F(1, 37) = .02, p = .88, η
2
p
= .001, but a significant interaction, F(3, 111) = 12.70, p < .001, η
2
p
= .25 (see Fig. 2b).
This interaction was further explored by running separate analyses for the consistent and mixed blocks. For the consistent blocks, there was no effect of trial type, F(1, 37) = 1.348, p = .253, η
2
p
= .035: there was no difference in MTs for normal vs reversed trials. However, for the mixed block the effect of trial type was significant, F(1, 37) = 23.43, p < .01, η
2
p
= .388: as with the RT data, normal trials showed shorter durations than reversed trials, regardless of the preceding block. None of the interactions were significant (Fs < 1.0)
Distance errors
We next explored the effect of number on the distance error. We removed trials where the participant crossed the line on the wrong side (1.53% of trials). Significantly fewer errors were made in the consistent trials than in the mixed trials, t(38) = −5.01, p < .001, but no other influences on these errors reached significance. The participants were accurate when moving to the middle of the line (‘number 5’), and showed high precision (being within a few millimetres to the left or right of the line centre. The participants were also reasonably accurate when moving to the far extremes (numbers 1 and 9) but showed a bias towards the centre. Conversely, participants showed a bias away from the centre when moving towards numbers 4 and 6. The participants lacked precision (see Fig. 3) when moving towards numbers 3 and 7 but showed no systematic biases (i.e., they were accurate on average when moving to these numbers). These responses make sense as the number line was bounded by the vertical end stop and the centre with these locations providing clear ‘landmarks’. There was increasing uncertainty for numbers away from the centre and this can explain why the data showed a contraction bias (a tendency for the responses to be biased towards the mean of the range—i.e., the numbers 3 and 7). Figure 3 shows the unsigned distance error as a function of target number and illustrates the decreasing precision away from the end and centre of the line. The unsigned distance error was calculated by assigning a positive value to the error whether it was to the left or right of the veridical location.
Average distance errors were collapsed into two groups within trial types; small (numbers 1–4) and large (numbers 6–9). A repeated measures ANOVA with 8 levels revealed a significant effect of number type, F(7, 266) = 23.02, p < .001, η
2
p
= .38. This was due to bigger distance errors being observed for small numbers than large numbers in all trial types (normal, reversed, mixed normal and mixed reversed; all p’s < .001) as can be seen in Table 1.
Table 1 Distance error by trial type and number type in millimetres [95% confidence interval]
One possible reason for the differences in movement time is that the participants showed different spatial accuracy according to the task demand (i.e., there was a speed accuracy trade-off in operation). To check for this possibility, average distance error was explored by trial type (4 within participant levels: normal, reversed, mixed normal and mixed reversed) and condition (2 group levels: Normal First and Reversed First) using a mixed-design ANOVA. No main effects of either trial type, F(3, 111) = 3.04, p > .05, η
2
p
= .08, or condition, F(1, 37) = .32, p = .576, η
2
p
= .01, were observed and there was no interaction, F(3, 111) = 1.83, p = .166, η
2
p
= .05. Thus, the differences in movement time could not be explained by differences in spatial accuracy.
An anonymous reviewer suggested that we explore the extent to which the task affected both the cognitive operations and the movement execution by correlating the reaction time and movement time data across the participants. We found a significant correlation between the average reaction time and movement time within the mixed trials, r(39) = .800, p < .001.