\subsection{Discrimination of Vibration Techniques}
\label{technique_results}

Seven participants were able to correctly discriminate between the two vibration techniques, which they described as the contact vibration (being the \level{Impact} technique) and the continuous vibration (being the \level{Distance} technique) respectively.
Seven participants said they only felt differences of intensity with a weak one (being the \level{Impact} technique) and a strong one (being the \level{Distance} technique).
Six participants did not notice the difference between the two vibration techniques.
There was no evidence that the ability to discriminate the vibration techniques was correlated with the participants' haptic or \AR/\VR expertise (\pearson{0.4}), nor that it had a statistically significant effect on the performance in the tasks.
As the tasks had to be completed as quickly as possible, we hypothesize that little attention was devoted to the different vibration techniques.
Indeed, some participants explained that the contact cues were sufficient to indicate whether the cube was being properly pushed or grasped.
Although the \level{Distance} technique provided additional feedback on the interpenetration of the finger with the cube, it was not strictly necessary to manipulate the cube quickly.

\subsection{Questionnaire}
\label{questions}

\figref{results_questions} shows the questionnaire results for each vibrotactile positioning.
The results of each question were analyzed using non-parametric \ANOVA on an \ART model.
Statistically significant effects were further analyzed with post-hoc pairwise comparisons with Holm-Bonferroni adjustment.
Wilcoxon signed-rank tests were used for main effects and \ART contrasts procedure for interaction effects.
Only significant results are reported.

\paragraph{Vibrotactile Rendering Rating}
\label{vibration_ratings}

There was a main effect of \factor{Positioning} (\anova{4}{171}{27.0}, \pinf{0.001}, see \figref{results/Question-Vibration Rating-Positioning-Overall}).
Participants preferred \level{Fingertips} more than \level{Wrist} (\p{0.01}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Proximal} more than \level{Wrist} (\p{0.007}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
And \level{Wrist} more than \level{Opposite} (\p{0.01}) and \level{Nowhere} (\pinf{0.001}).

\paragraph{Positioning \x Hand Rating}
\label{positioning_hand}

There were two main effects of \factor{Positioning} (\anova{4}{171}{20.6}, \pinf{0.001}) and of \factor{Hand} (\anova{1}{171}{12.2}, \pinf{0.001}).
Participants preferred \level{Fingertips} more than \level{Wrist} (\p{0.03}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Proximal} more than \level{Wrist} (\p{0.003}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Wrist} more than \level{Opposite} (\p{0.03}) and \level{Nowhere} (\pinf{0.001});
And \level{Skeleton} more than \level{No Hand} (\pinf{0.001}).

\paragraph{Workload}
\label{workload}

There was a main effect of \factor{Positioning} (\anova{4}{171}{3.9}, \p{0.004}, see \figref{results/Question-Workload-Positioning-Overall}).
Participants found \level{Opposite} more fatiguing than \level{Fingertips} (\p{0.01}), \level{Proximal} (\p{0.003}), and \level{Wrist} (\p{0.02}).

\paragraph{Usefulness}
\label{usefulness}

There was a main effect of \factor{Positioning} (\anova{4}{171}{38.0}, \p{0.041}, see \figref{results/Question-Usefulness-Positioning-Overall}).
Participants found \level{Fingertips} the most useful, more than \level{Proximal} (\p{0.02}), \level{Wrist} (\pinf{0.001}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Proximal} more than \level{Wrist} (\p{0.008}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Wrist} more than \level{Opposite} (\p{0.008}) and \level{Nowhere} (\pinf{0.001});
And \level{Opposite} more than \level{Nowhere} (\p{0.004}).

\paragraph{Realism}
\label{realism}

There was a main effect of \factor{Positioning} (\anova{4}{171}{28.8}, \pinf{0.001}, see \figref{results/Question-Realism-Positioning-Overall}).
Participants found \level{Fingertips} the most realistic, more than \level{Proximal} (\p{0.05}), \level{Wrist} (\p{0.004}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Proximal} more than \level{Wrist} (\p{0.03}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
\level{Wrist} more than \level{Opposite} (\p{0.03}) and \level{Nowhere} (\pinf{0.001});
And \level{Opposite} more than \level{Nowhere} (\p{0.03}).

\begin{subfigs}{results_questions}{Boxplots of the questionnaire results for each vibrotactile positioning.}[
    Pairwise Wilcoxon signed-rank tests with Holm-Bonferroni adjustment: *** is \pinf{0.001}, ** is \pinf{0.01}, and * is \pinf{0.05}.
    Higher is better for \textbf{(a)} vibrotactile rendering rating, \textbf{(c)} usefulness and \textbf{(c)} fatigue.
    Lower is better for \textbf{(d)} workload.
  ]
  \subfig[0.24]{results/Question-Vibration Rating-Positioning-Overall}
  \subfig[0.24]{results/Question-Workload-Positioning-Overall}
  \subfig[0.24]{results/Question-Usefulness-Positioning-Overall}
  \subfig[0.24]{results/Question-Realism-Positioning-Overall}
\end{subfigs}
