## 2 Materials and Methods
### Analysis
#### 2.5.1 Main Analyses  
First, we checked whether participants' responses were consistent between the two genders. For this purpose, we formed four \(2\times 2\) contingency tables (one per Q1 through Q4) where the entries of each table corresponded to the gender and the counts of participants' preference between (sham) human- or robot-controlled trial in each of Q1 through Q4. We then applied \(\chi^{2}\) tests on these tables to examine whether participants' gender had a significant effect on their responses. Next, we determined whether any of the experiment's design factors had a significant effect on participants' responses to Q1 through Q5. These factors were the order of the two trials (i.e., whether the (sham) human- or robot-controlled trial was carried out first), supposed gender of the operator in (sham) human-controlled trial, and the interaction between these two factors. We then adapted a general linear model (GLM) [37] approach. The inputs to GLM were the two experiment's factors and their interaction (i.e., an N \(\times\) 3 matrix where N = 30 denotes the number of participants). The output from GLM was the participants' responses to Q1 through Q5. This resulted in five separate tests, one per questionnaire's item. For each of these models, we used their corresponding coefficients (i.e., models' weights) and applied ANOVA on them to determine whether any of the two experiment's design factors and/or their interaction had a significant effect on participants' responses. We then examined participants' overall preference between (sham) human- and robot-controlled trials. To this end, we counted the total number of times that each participant responded by selecting \"when it was controlled by the robot\" versus \"when it was controlled by the human\" to Q1 through Q4 (i.e., collectively). We then performed a bootstrap (10,000 simulation runs) test (i.e., random sampling with replacement) on the difference between these counts (i.e., count((sham) human-controlled)-count(robot-controlled)) at 99.0% confidence interval (CI) (i.e., \(p<0.01\) significance level). We then considered the following null hypothesis. **Hypothesis 1 (H1). **: _The difference between the number of times that participants preferred (sham) human-controlled versus robot-controlled was non-significant._  
We tested Hypothesis 1 against the following alternative hypothesis. **Hypothesis 2 (H2). **: _Participants preferred (sham) human-controlled trial significantly differently from robot-controlled trial._  
The choice of 99.0% CI resulted in \(p<0.01\) significant level. In this respect, a 99.0% CI that did not contain zero would confirm a significant difference between these preferences at \(p<0.01\). Furthermore, the average value associated with this CI (i.e., mean[count((sham) human-controlled)-count(robot-controlled)]) would indicate which trial the participants' preferences were significantly inclined to. Precisely, the average value \(>0.0\) would indicate a significant inclination of participants' preferences toward (sham) human-controlled (i.e., with respect to the order of subtraction count((sham) human-controlled)-count(robot-controlled)). On the other hand, it would identify the opposite (i.e., robot-controlled preferences) if this average value \(<0.0\). We also applied this bootstrap (10,000 simulation runs) test of significant difference at 99.0% CI (i.e., \(p<0.01\)) on participants' responses to Q5. For this test, we considered the following null hypothesis. **Hypothesis 3 (H3). **: _Participants perceived (sham) human- and robot-controlled trials were the same._  
We tested Hypothesis 3 against the following alternative hypothesis. **Hypothesis 4 (H4). **: _Participants perceived the two trials were significantly different._  
This test allowed us to verify whether participants realized the two trials were based on the same robot-arm motion controller or they mentally construed them differently.