4.2 Experiment 1: Peripersonal Space Boundaries Modulated by Objects
4.2.5 Results
Our data consists of reaction times measured from different distances where the tactile stimulus was given for different ball types and launched by either the ball launcher or thrown by the animated avatar. We perform two primary analyses. First, we determine how individual reaction times were influenced by the conditions of the study, and second we determine the peripersonal space boundaries for the (group) conditions of the study.
We first noted that the data contained outliers, such as, for example, trials where a participant forgot to pull the trigger in response to the tactile stimulus. We systematically removed such instances using Tukey’s method of fences. We calculated the upper fence for each reaction time at each distance and condition and removed any reaction time that was greater than the upper fence. The upper fence was the boundary at which a data point would be three standard deviations from the mean. We chose not to calculate the lower fence since this would produce a negative reaction time to compare against, which there were none of. This process removed less than 1% of the data; as noted above, the outliers removed were typically instances where the subject did not respond.
Using IBM SPSS Statistics, we submitted the cleaned data to a repeated measures anaylsis of variance (RM-ANOVA) with factors of distance, social condition (whether the ball was thrown by the animated avatar or launched by the ball launcher) and ball type (spiked or normal). Assumptions were checked and corrected for by SPSS. The RM-ANOVA found main effects of distanceF(4,152) = 521.132,p < 0.001, social condition F(1,38)=18.984,p<0.001, and ball typeF(1,38)=13.170,p <0.01. There were interactions between social condition and ball typeF(1,38) = 8.456,p < 0.01, social condition and distanceF(4,152) = 3.421,p < 0.05, and a three-way interaction between social condition, ball type and distanceF(4,152) = 8.459,p < 0.001.
Bonferroni corrected paired samples t-tests revealed that all reaction times at each distance were significantly different from one anotherp < 0.001, that reaction times were significantly different for social and non-social conditionsp < 0.001(except at 1.6m), and that reaction times were significantly different between ball types p<0.001(except at 1m). Figure 11 offers a visual supplement to these findings.
The exact peripersonal space boundaries are not determined from the raw data depicted in Figure 11.
Rather, to determine the peripersonal space boundaries, we employed the same method of fitting a sigmoid
function to the data and extracting the boundary as used by Serino et al. [2017]. In that work (and others [Canzoneri et al. 2012; Kandula et al. 2017]) the fitting equation is as follows:
y(x)= ymin+ymaxe(x−xc)/b
1+e(x−xc)/b (1)
wherexis theindependentvariable, or the distance of the ball,yis thedependentvariable, or the reaction time;yminandymaxare the upper and lower saturation levels of the sigmoid;xcis the value of the abscissa at the central point of the sigmoid; andbis the slope of the sigmoid at the central point. Bothxcandbvary and are estimated. The parameterxcrepresents the midpoint of the region of greatest increase in reaction time to the visual stimulus, i.e., the boundary of peripersonal space. To determine it, all reaction times for each of the trials for each subject were averaged at each distance for both ball types, giving us a set of(x,y)data points to fit the sigmoid function to. The coefficient of determination (R2) was extracted as a goodness-of-fit measures.
For this experiment, we found the average peripersonal space boundary(xc)over all conditions to be at 1.27 m. The exact boundaries for each condition are as follows: social at 1.27 m, non-social at 1.28 m, normal ball at 1.25 m and spiked ball at 1.29 m. Goodness of fit measures were greater than0.9for all conditions.
To determine if the conditions in this experiment modulated the peripersonal space boundaries found, we first ran Bonferroni corrected paired samples t-tests. These t-tests revealed that the peripersonal space boundaries for the normal and spiked balls were significantly differentt(39) = 0.003,p < 0.01while the social and non-social conditions were not. We next performed a Bayes factors analyses. Bayes factors provide support for the null hypothesis through an odds ratio9. We use the method described by Rouder et al. [2009],
9An online calculator for Bayes factor analyses can be found at http://pcl.missouri.edu/bayesfactor.
which takes into account sample size and adjusts for power. Prior odds were set to 1, which favors neither the null nor the alternative. Comparing social and non-social conditions gives a Jeffrey-Zellner-Siow (JZS) Bayes factor of 8.11 indicating substantial evidence in favor of the null hypothesis. Comparing the spiked and normal ball conditions gives a Bayes factor in favor of the alternative, with a JZS Bayes factor of 10.43. These results strongly indicate that social condition does not modulate the peripersonal space boundaries in this study, but ball type does.
0.200.250.300.350.40
Distance (Meters)
Reaction Time (Seconds)
0.3 0.6 1 1.3 1.6
Reaction Time Per Distance: Social Conditions
Social (Animated Avatar) Non−Social (Ball Launcher)
0.200.250.300.350.40
Distance (Meters)
Reaction Time (Seconds)
0.3 0.6 1 1.3 1.6
Reaction Time Per Distance: Ball Conditions
Normal Ball Spiked Ball
Figure 11: These graphs depict the average reaction time recorded at each perceived distance for both social and non-social (top) and normal and spiked ball (bottom) conditions. We extracted these by collapsing across the appropriate conditions. ©IEEE 2020