\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.
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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).
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Six participants did not notice the difference between the two vibration techniques.
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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.
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As the tasks had to be completed as quickly as possible, we hypothesize that little attention was devoted to the different vibration techniques.
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Indeed, some participants explained that the contact cues were sufficient to indicate whether the cube was being properly pushed or grasped.
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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}

\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-Usefulness-Positioning-Overall}
  \subfig[0.24]{results/Question-Realism-Positioning-Overall}
  \subfig[0.24]{results/Question-Workload-Positioning-Overall}
\end{subfigs}

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

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

There was a main effect of Positioning (\anova{4}{171}{27.0}, \pinf{0.001}).
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Participants preferred \level{Fingertips} more than \level{Wrist} (\p{0.01}), \level{Opposite} (\pinf{0.001}), and No Vibration (\pinf{0.001});
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\level{Proximal} more than \level{Wrist} (\p{0.007}), \level{Opposite} (\pinf{0.001}), and No Vibration (\pinf{0.001});
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And \level{Wrist} more than \level{Opposite} (\p{0.01}) and No Vibration (\pinf{0.001}).

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

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

\subsubsection{Workload}
\label{workload}

There was a main effect of Positioning (\anova{4}{171}{3.9}, \p{0.004}).
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Participants found \level{Opposite} more fatiguing than \level{Fingertips} (\p{0.01}), \level{Proximal} (\p{0.003}), and \level{Wrist} (\p{0.02}).

\subsubsection{Usefulness}
\label{usefulness}

There was a main effect of Positioning (\anova{4}{171}{38.0}, \p{0.041}).
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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});
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\level{Proximal} more than \level{Wrist} (\p{0.008}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
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\level{Wrist} more than \level{Opposite} (\p{0.008}) and \level{Nowhere} (\pinf{0.001});
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And \level{Opposite} more than \level{Nowhere} (\p{0.004}).

\subsubsection{Realism}
\label{realism}

There was a main effect of Positioning (\anova{4}{171}{28.8}, \pinf{0.001}).
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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});
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\level{Proximal} more than \level{Wrist} (\p{0.03}), \level{Opposite} (\pinf{0.001}), and \level{Nowhere} (\pinf{0.001});
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\level{Wrist} more than \level{Opposite} (\p{0.03}) and \level{Nowhere} (\pinf{0.001});
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And \level{Opposite} more than \level{Nowhere} (\p{0.03}).
