ten paid undergraduate students ( mean age 21    2  years ( sd ) ) participated in the experiment .
three subjects were left - handed according to coren s test coren ( 1993 ) , and all others were right - handed . they were treated in accordance with the local guidelines and signed an informed consent form .
they were naive as to the purpose of the experiments , and none of the subjects reported any known hand deficits .
the stimuli consisted of varying numbers of brass shapes , which were suspended from flexible wires .
the presented shapes were cubes ( edge length 1.5  cm ) , spheres ( radius 0.93  cm ) , and ellipsoids ( radii : 1.22 , 0.81 and 0.81  cm ) . to eliminate weight cues ,
these dimensions were chosen such that the volume , and thus the weight of the shapes , was constant .
1a.fig .  1stimuli and set - up . a shapes that were used in the experiment .
the targets were always spheres , while the distractor was either a cube or an ellipsoid .
the targets were always spheres , while the distractor was either a cube or an ellipsoid .
b picture of a subject grasping the stimuli a custom - built device was used to measure response times .
time measurement was started when the subject touched the stimulus activating the touch - sensitive contact of the device .
the measurement was terminated by a vocal response registered with a headset microphone ( for details about this set - up see plaisier et  al .
before the experiment was started , the subjects were informed of which shapes were the target items and which shapes were distractor items . they were instructed to respond the correct number of target items as fast as possible .
the subjects wore a blindfold and earplugs to avoid any sound cues . prior to a trial
sets of shapes were suspended from flexible wires above the hand , and subjects were instructed to reach upwards to grasp all items simultaneously .
after grasping all items , they were allowed to release items from their hand during the trial .
it was emphasized that they should only release items from their hand if this seemed the most efficient strategy .
subjects were instructed to respond the correct number of target items as fast as possible .
error trials were repeated at the end of a block of trials , and only correct responses were included in the analysis .
the two conditions were performed in separate blocks of trials on separate days in counter - balanced order . in one condition
, a cube was added as distractor item , and in the other condition , an ellipsoid was used as distractor item . in both cases
, spheres were the target items , and the number of spheres had to be judged . in half of the trials ,
a distractor item was present , and the distractor - present and distractor - absent trials were randomly interleaved .
we measured up to 4 items , but did not include this numerosity in the analysis to exclude possible end - effects .
each numerosity was repeated ten times with and without a distractor in the set leading to a total of ( 10    4    2  =) 80 trials per block .
to each block of trials also 15 catch trials were added . in the catch trials ,
the presented set of items could contain up to 4 distractor items with the restriction that the total number of items in the set did not exceed 6 .
this was done to prevent subjects from noticing there was always only one distractor item , but these trials were not included in the analysis .
a similar procedure was used by trick and pylyshyn ( 1993 ) . prior to each block of trials , subjects performed at least 20 training trials , and trials
it was never necessary to exceed 30 training trials . because subjects were instructed to respond as fast as possible , but also correct the error rate should be low in all conditions .
therefore , the error rates are given as an indication that subjects could perform the task correctly . only the response times and item release rates
weighted linear regression was performed on the response times averaged over subjects as well as on the single subjects data .
the quality of fit to the data averaged over subjects will be better , but it is also important to show that the same trend is present for each subject individually .
the last numerosity in the presented range of numerosities normally deviates from linearity and is therefore often excluded from the regression analysis ( e.g trick and pylyshyn 1993 ; watson et  al . 2007 ; trick 2008 ) .
the results from the present study were , however , not significantly different when the largest numerosity was included in the analysis .
furthermore , repeated measures anova was performed on the single - subject regression slopes as well as on the item release rate . to determine the effect on the slope values , we compare the response times slopes to the values of response time slopes found in two previous studies performed without any distractors ( plaisier et  al . 2009a , 2010 ) .
these studies were performed using the same spheres as used in the present study , and the same response time measuring device was used .
sets of up to 7 or 12 items were used , and a regression of a bi - linear function was used to determine the subitizing and counting slope values as well as the transition point between the two regimes .
ten paid undergraduate students ( mean age 21    2  years ( sd ) ) participated in the experiment .
three subjects were left - handed according to coren s test coren ( 1993 ) , and all others were right - handed . they were treated in accordance with the local guidelines and signed an informed consent form .
they were naive as to the purpose of the experiments , and none of the subjects reported any known hand deficits .
the stimuli consisted of varying numbers of brass shapes , which were suspended from flexible wires .
the presented shapes were cubes ( edge length 1.5  cm ) , spheres ( radius 0.93  cm ) , and ellipsoids ( radii : 1.22 , 0.81 and 0.81  cm ) . to eliminate weight cues ,
these dimensions were chosen such that the volume , and thus the weight of the shapes , was constant .
the targets were always spheres , while the distractor was either a cube or an ellipsoid .
the targets were always spheres , while the distractor was either a cube or an ellipsoid .
b picture of a subject grasping the stimuli a custom - built device was used to measure response times .
time measurement was started when the subject touched the stimulus activating the touch - sensitive contact of the device .
the measurement was terminated by a vocal response registered with a headset microphone ( for details about this set - up see plaisier et  al .
before the experiment was started , the subjects were informed of which shapes were the target items and which shapes were distractor items .
they were instructed to respond the correct number of target items as fast as possible .
the subjects wore a blindfold and earplugs to avoid any sound cues . prior to a trial
sets of shapes were suspended from flexible wires above the hand , and subjects were instructed to reach upwards to grasp all items simultaneously .
after grasping all items , they were allowed to release items from their hand during the trial .
it was emphasized that they should only release items from their hand if this seemed the most efficient strategy .
subjects were instructed to respond the correct number of target items as fast as possible .
error trials were repeated at the end of a block of trials , and only correct responses were included in the analysis .
the two conditions were performed in separate blocks of trials on separate days in counter - balanced order . in one condition
, a cube was added as distractor item , and in the other condition , an ellipsoid was used as distractor item . in both cases , spheres were the target items , and the number of spheres had to be judged . in half of the trials ,
a distractor item was present , and the distractor - present and distractor - absent trials were randomly interleaved .
we measured up to 4 items , but did not include this numerosity in the analysis to exclude possible end - effects .
each numerosity was repeated ten times with and without a distractor in the set leading to a total of ( 10    4    2  =) 80 trials per block .
to each block of trials also 15 catch trials were added . in the catch trials ,
the presented set of items could contain up to 4 distractor items with the restriction that the total number of items in the set did not exceed 6 .
this was done to prevent subjects from noticing there was always only one distractor item , but these trials were not included in the analysis .
a similar procedure was used by trick and pylyshyn ( 1993 ) . prior to each block of trials , subjects performed at least 20 training trials , and trials
because subjects were instructed to respond as fast as possible , but also correct the error rate should be low in all conditions .
therefore , the error rates are given as an indication that subjects could perform the task correctly .
weighted linear regression was performed on the response times averaged over subjects as well as on the single subjects data .
the quality of fit to the data averaged over subjects will be better , but it is also important to show that the same trend is present for each subject individually .
the last numerosity in the presented range of numerosities normally deviates from linearity and is therefore often excluded from the regression analysis ( e.g trick and pylyshyn 1993 ; watson et  al . 2007 ; trick 2008 ) .
the results from the present study were , however , not significantly different when the largest numerosity was included in the analysis .
furthermore , repeated measures anova was performed on the single - subject regression slopes as well as on the item release rate . to determine the effect on the slope values , we compare the response times slopes to the values of response time slopes found in two previous studies performed without any distractors ( plaisier et  al . 2009a , 2010 ) .
these studies were performed using the same spheres as used in the present study , and the same response time measuring device was used .
sets of up to 7 or 12 items were used , and a regression of a bi - linear function was used to determine the subitizing and counting slope values as well as the transition point between the two regimes .
the error rates were overall low . for the distractor - absent trials , error rates were 0.5% in the cube condition and 0.75% in the ellipsoid condition . in the distractor - present trials , the error rates were 3 and 4.25% , respectively .
response times averaged over subjects as a function of the number of items with a cube as distractor are shown in fig . 
2a , and response times with an ellipsoid as distractor are shown in fig . 
the response times for the distractor - absent trials are shown in black and those for the distractor - present trials are shown in gray .
this yielded in the condition with a cube as distractor , a distractor - absent slope of 0.2 s / item and a distractor - present slope of 0.6 s / item .
for the condition with the ellipsoid as distractor , the distractor - absent slope was found to be 1.1 s / items , and the distractor - present slope was 1.6  s / item.fig . 
2response times averaged over subjects for the distractor - present and distractor - absent trials .
a condition with a cube as distractor and b condition with an ellipsoid as distractor .
the solid lines indicate linear regression to the response times , and the error bars indicate the between subjects standard deviation response times averaged over subjects for the distractor - present and distractor - absent trials . a condition with a cube as distractor and b condition with an ellipsoid as distractor .
the solid lines indicate linear regression to the response times , and the error bars indicate the between subjects standard deviation linear regression was also performed on the single - subject data .
the values from the single - subject slopes averaged again over subjects and the standard deviation between subjects are reported here .
this yielded in the cube condition a distractor - absent slope of 0.2    0.1 s / item ( r  =  0.8    0.1 ) and a distractor - present slope of 0.6    0.2 s / item ( r  =  0.9    0.1 ) .
for the ellipsoid condition , this yielded a distractor - absent slope of 1.1    0.3 s / item ( r  =  0.99    0.02 ) and a distractor - present slope of 1.6    0.6 s / item ( r  =  0.98    0.02 ) .
a 2    2 ( distractor shape    distractor presence ) repeated measures anova was performed on the single - subject slopes .
there was an effect of distractor shape ( f(1 ,  9 )  =  47 ,  p  <  0.001 ) and of distractor presence ( f(1 ,  9 )  =  22 ,  p  =  0.001 ) .
the percentage of trials in which items were released from the hand is shown in fig . 
a 2    2 ( distractor shape    distractor presence ) repeated measures anova was performed on the item release rates .
this showed an effect of distractor shape ( f(1 ,  9 )  =  34 ,  p  <  0.001 ) as well as distractor presence ( f(1 ,  9 )  =  107 ,  p  <  0.001 ) and an interaction effect ( f(1 ,  9 )  =  7 ,  p  =  0.025).fig . 
3item release rate collapsed over all numerosities and averaged over subjects for distractor - present and distractor - absent trials in both conditions .
the error bars indicate the between - subjects standard deviation item release rate collapsed over all numerosities and averaged over subjects for distractor - present and distractor - absent trials in both conditions .
our results show that subitizing slopes increased when a distractor was added , regardless of the saliency of the distractor .
when the distractor was a cube , the numerosity judgment slope increased from 0.2 to 0.6 s / item .
when the distractor was an ellipsoid , slopes increased from 1.1 to 1.6 s / item . in two previous studies into haptic numerosity judgment , we measured the subitizing and counting slopes when the items were spheres ( plaisier et  al . 2009a , 2010 ) .
slope values were found to be 0.17 and 0.2 s / items in the subitizing regime and 0.8 s / item and 1.2 s / item in the counting regime .
the slopes found in the present study for the ellipsoid condition have a value comparable to counting slopes .
the slope values for the cube condition were , however , clearly below counting slope values .
the distractor - absent slope was in this case in the same range as subitizing slopes that were found previously .
this shows that adding a distractor increases numerosity judgement slopes , but subitizing was still possible in the cube condition .
the distractor - absent slope in the cube condition was comparable to previously found subitizing slope values , but the distractor - absent slope in the ellipsoid condition was clearly in the range of generally found counting slopes .
the stimulus was , however , the same in both cases . since a cube among spheres is highly salient subjects knew in the cube condition immediately after grasping , the set whether there were distractors present .
when cubes were detected , they should be ignored while judging the numerosity , and this resulted in an increase in the slope .
an ellipsoid among spheres , on the other hand , is not salient , and serial search is needed to find it .
this is also indicated by the larger item release rate in the ellipsoid condition than in the cube condition .
releasing items from the hand is normally an indication of serial processing ( plaisier et  al .
therefore , subjects visited each item subsequently regardless of whether a distractor was present in the ellipsoid condition .
still , in this case , the slope was larger when a distractor was present .
so , although items were processed in a serial fashion , the presence of a distractor increased the response time per item . note that this difference in slope can not be caused by the fact that in distractor - present trials , the total number of items was larger than in the distractor - absent case .
this causes a larger offset of the response times , but does not affect the slopes .
also in vision , it was found that the slope for small sets of items increased when a distractor was added , even if this was a highly salient distractor ( trick and pylyshyn 1993 ) .
similar to our results , also the slope for distractor - absent trials differed depending on the type of distractor used .
when a non - salient distractor was used , subitizing was possible for the distractor - absent trials , but the slope was larger than when a salient distractor was used .
the effects reported here for haptic subitizing in the presence of a distractor are therefore comparable to those found in vision .
the effect of adding a single distractor to the set was in the haptic case , however , more pronounced than in the visual case .
our results suggest a modality - independent process underlying subitizing . trick and pylyshyn ( 1993 ) concluded from the fact that subitizing was only possible when the targets  pop - out from among the distractors that there is a pre - attentive stage of item individuation in subitizing .
they proposed that there are fingers of instantiation ( finst s ) that can be used to point to individual items in the visual field ( see pylyshyn 2001 for a review ) .
fingers do not need to be attributed to item properties , such as color , shape or even position . although this visual theory might be extended to include the haptic modality , an alternative explanation which is
it has been shown that humans can hold a limit number of chunks of information in their working memory .
such a capacity limit would result in the same upper limit for subitizing in vision and touch which generally seems to be true ( see cowan 2001 for an overview ) .
peterson and simon ( 2000 ) computationally showed that when varying numbers of dots are placed on a two - dimensional grid , there are many more recurrent patterns for small numerosities ( < 4 ) than for larger numerosities .
they then showed that their neural network displayed subitizing - like behavior after a learning period .
such a pattern recognition explanation is , however , less likely in the haptic case as the objects were not fixed in space .
therefore , a capacity limit in short term memory would be the best candidate for a modality transcending explanation for the occurrence of subitizing . nor in the present study , nor in the study by ( trick and pylyshyn 1993 ) was the subitizing slope unaffected by adding distractors .
it is clearly not caused by impairment of the subitizing process as the subitizing slopes were at their normal values in distractor - absent trials when pop - out targets were used .
if first the targets were pre - attentively selected and then put into memory chunks , we would not expect the subitizing slope to be affected at all for pop - out targets .
therefore , it seems that either distractors can not be completely ignored during subitizing or the total set size is determined first and the distractors are subtracted afterwards to arrive at the number of targets .
either way , salient distractors impair subitizing in both vision and haptics although they do not prevent subitizing like non - salient distractors do .
  
 subitizing refers to fast and error - free numerosity judgment for small ( < 4 ) sets of items . for larger sets , the slower process of  
 counting is used . 
 counting has a serial character , whereas subitizing is believed to have a parallel character . 
 while subitizing was initially found in vision , it has been shown to exist in touch as well . in vision , it has been demonstrated that adding distractor items to a set of target items influences numerosity judgment of the target items . 
 subitizing was in this case only possible if the distractor item is highly salient among the targets . in the present study , we investigated the effect of adding a distractor item on haptic judgement of a set of target items . 
 to this end , we asked subjects to judge the number of spheres grasped in their hand . 
 either a cube or an ellipsoid could be added to the set . 
 a cube among spheres has been shown to be highly salient , while an ellipsoid among spheres is not . 
 our results show that adding a distractor item led to an increase in the response time slopes regardless of the distractor shape . 
 subitizing was , however , only possible in the case of a salient distractor . 
 this is in agreement with results from vision . 
Methods
Participants
Stimuli and apparatus
Procedure
Analysis
Results
Discussion