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Reaction beats intention A. E. Welchman et al. 3
reliably (s , 1.2 ms) with negligible lag. The centre-to-
centre spacing of the buttons was 35 cm (experiment 1) or
15 cm (experiments 2, 3). Participants sat at either end of
a 140 cm long table. Only for experiment 3, a 20-inch
LCD located 120 cm from the participant was used for the
visual display of symbolic button presses. In particular, a
row of three squares on a black background was presented
(one for each button, spatially arranged to correspond to a
real opponent). The colour of these squares changed from
red to white to depict the periods during which the opponent
was pressing the button. The behaviour of the opponent was
thus marked in an abstract manner that reflected only the
state of the buttons (i.e. there was no movement and no
schematic illustration of the opponent).
(c) Procedure
Participants initially took part in a training session to familiar-
ize themselves with the task. They were instructed to start a
trial by resting their right-hand on the central button (the
‘home key’), then move to hit the button on their right, then
on their left, and then return to the central button and keep
it depressed (figure 1a). Participants were informed that a
variable delay was imposed on each trial (no details given),
so they had to wait for some time before starting their move-
ment. The random start delay was drawn from a normal
distribution (m ¼ 2500 ms; s ¼ 500 ms). Moving too early
caused a warning tone, indicating an early movement error.
If participants missed a button, or hit buttons out of sequence,
a different tone sounded. On the basis of either error type, the
trial was aborted and then repeated.
In competitive situations, participants sat facing another
human player, or a display depicting their opponent’s
button presses. Testing sessions lasted approximately 1 h,
yielding around 170 data points per condition per participant
for experiment 1, 100 for experiment 2 and 120 for exper-
iment 3. The relative number of initiated and reactive
movements within this total varied between participants
(i.e. as a dynamic competition, this depended on the behav-
iour of individuals). In most situations, participants
completed a side-to-side movement. However, experiment 2
also considered front-back movements. Here, the board on
which the buttons were mounted was rotated by 908 and
re-attached to the table, aligned to the participant’s midline.
(d) Data analysis
Response times and movement execution times were calcu-
lated using signals from the capacitive buttons. The
‘reaction time’ was defined as the time difference between
the first participant’s centre button switching to an off
(low) state, and their opponent’s centre button switching to
an off state (figure 1b). The ‘execution time’ for the first
movement phase was defined as the time between the
centre button being in a low (off) state and the right
button being in a high (on) state. Subsequent movement
phases were similarly calculated, with the total execution
time defined as the time between the centre button being
low (movement start) and high (movement end). Our use
of capacitive buttons meant that downward force was not
required—rather light touch was sufficient to keep buttons
in a high (on) state, thus movement onset was defined as
the moment at which the hand moved away from the buttons.
Data analysis considered the distribution of movement
execution times produced when participants moved before
(initiated movements) or after (reactive movements) their
opponents (figure 1c). Following Luce (1986), we quantified
these distributions using the harmonic mean to provide a
robust statistic suitable for non-Gaussian data (in fact,
using the arithmetic mean or the median made little differ-
ence). As participants could independently elect to initiate
a given trial at very similar times, some ‘reactive’ movements
might have in fact been ‘initiated’. We therefore discarded
trials on which a participant’s reaction time was below
100 ms (6.8% trials), reasoning that anything faster would
be unlikely to result from a reaction (note that this 100 ms
exclusion criteria corresponds to the time difference between
the buttons being lifted, rather than any aspect of the
opponent’s behaviour that might signal their intention to
move). (We ensured that this 100 ms exclusion criterion
did not bias our findings by analysing our data without con-
straining the reaction time, and the results were unchanged.)
We used further criteria to deal with outliers in the movement
times (Ratcliff 1993). One possibility was that a ‘reactor’
would miss their opponent’s movement, responding with a
considerable delay and thus in a non-competitive manner.
To avoid this possibility, data were excluded if the reaction
time exceeded 500 ms (3.5% of trials). Finally, on some
trials a participant would complete the sequence by correct-
ing for a missed button, producing a long, uncompetitive
execution time. Therefore, trials on which the execution
time exceeded 1000 ms (experiment 1) or 800 ms (experi-
ments 2, 3) were excluded (0.5% of trials). (Note that the
larger movement amplitude required in experiment 1 pro-
duced longer execution times.) While error rates were
generally low, some participants produced an unacceptably
large number of errors, making their data unreliable. We
excluded one subject from experiment 2, and four subjects
from experiment 3 because of a high proportion of slow reac-
tion and slow execution errors (defined as more than 25%
errors in two or more conditions).
3. RESULTS
(a) Experiment 1
To investigate whether there was an advantage for reactive
movements, we considered within-subject differences in
movement execution times for trials on which partici-
pants initiated the movement sequence compared with
trials on which they reacted following the movement of
their opponent (figure 1c). We found that execution
times were quicker by an average of 21 ms when partici-
pants reacted to their opponent’s movement (figure 2a;
t9 ¼ 4.406, p ¼ 0.002), an improvement of around 9 per
cent. This ‘reactive advantage’ was most pronounced for
the first movement of the three-button press sequence
(figure 2b,c), quickening responses by around 14 per
cent of the mean movement execution time. Moreover,
the advantage was maximal when participants moved
approximately 200 ms after the opponent (electronic sup-
plementary material). However, as the reactive advantage
in movement execution (mean ¼ 21 ms) was less than the
participant’s reaction time to the movement of their
opponent (mean ¼ 207 ms), reactors rarely beat initiators
(e.g. compare the difference between the red boxplots for
a participant with the extent of their reaction time (blue
boxplots) from figure 1c).
The proportion of failures to hit one of the buttons in
the sequence increased for reactive movements,
suggesting that increased speed is associated with reduced
Proc. R. Soc. B