\subsection{Push Task}
\label{push}

\subsubsection{Completion Time}
\label{push_tct}

On the time to complete a trial, there were two statistically significant effects: %
\factor{Hand} (\anova{5}{2868}{24.8}, \pinf{0.001}, see \figref{results/Push-ContactsCount-Hand-Overall-Means}) %
and \factor{Target} (\anova{7}{2868}{5.9}, \pinf{0.001}).
\level{Skeleton} was the fastest, more than \level{None} (\percent{+18}, \p{0.005}), \level{Occlusion} (\percent{+26}, \pinf{0.001}), \level{Tips} (\percent{+22}, \pinf{0.001}), and \level{Contour} (\percent{+20}, \p{0.001}).

Three groups of targets volumes were identified:
(1) sides \level{R}, \level{L}, and \level{LF} targets were the fastest;
(2) back and front \level{RB}, \level{F}, and \level{RF} were slower (\p{0.003});
and (3) back \level{B} and \level{LB} targets were the slowest (\p{0.04}).

\subsubsection{Contacts}
\label{push_contacts_count}

On the number of contacts, there were two statistically significant effects: %
\factor{Hand} (\anova{5}{2868}{6.7}, \pinf{0.001}, see \figref{results/Push-ContactsCount-Hand-Overall-Means}) %
and \factor{Target} (\anova{7}{2868}{27.8}, \pinf{0.001}).

Less contacts were made with \level{Skeleton} than with \level{None} (\percent{-23}, \pinf{0.001}), \level{Occlusion} (\percent{-26}, \pinf{0.001}), \level{Tips} (\percent{-18}, \p{0.004}), and \level{Contour} (\percent{-15}, \p{0.02});
and less with \level{Mesh} than with \level{Occlusion} (\percent{-14}, \p{0.04}).
This indicates how effective a visual hand rendering is: a lower result indicates a smoother ability to push and rotate properly the cube into the target, as one would probably do with a real cube.

Targets on the left (\level{L}, \level{LF}) and the right (\level{R}) were easier to reach than the back ones (\level{B}, \level{LB}, \pinf{0.001}).

\subsubsection{Time per Contact}
\label{push_time_per_contact}

On the mean time spent on each contact, there were two statistically significant effects: %
\factor{Hand} (\anova{5}{2868}{8.4}, \pinf{0.001}, see \figref{results/Push-MeanContactTime-Hand-Overall-Means}) %
and \factor{Target} (\anova{7}{2868}{19.4}, \pinf{0.001}).

It was shorter with \level{None} than with \level{Skeleton} (\percent{-10}, \pinf{0.001}) and \level{Mesh} (\percent{-8}, \p{0.03});
and shorter with \level{Occlusion} than with \level{Tips} (\percent{-10}, \p{0.002}), \level{Contour} (\percent{-10}, \p{0.001}), \level{Skeleton} (\percent{-14}, \p{0.001}), and \level{Mesh} (\percent{-12}, \p{0.03}).
This result suggests that users pushed the virtual cube with more confidence with a visible visual hand rendering.
On the contrary, the lack of visual hand constrained the participants to give more attention to the cube's reactions.

Targets on the left (\level{L}, \level{LF}) and the right (\level{R}) sides had higher \response{Timer per Contact} than all the other targets (\p{0.005}).

\begin{subfigs}{push_results}{Results of the push task performance metrics for each visual hand rendering.}[
    Geometric means with bootstrap \percent{95} \CI
    and Tukey's \HSD pairwise comparisons: *** is \pinf{0.001}, ** is \pinf{0.01}, and * is \pinf{0.05}.
  ][
  \item Time to complete a trial.
  \item Number of contacts with the cube.
  \item Time spent on each contact.
  ]
  \subfig[0.32]{results/Push-CompletionTime-Hand-Overall-Means}
  \subfig[0.32]{results/Push-ContactsCount-Hand-Overall-Means}
  \subfig[0.32]{results/Push-MeanContactTime-Hand-Overall-Means}
\end{subfigs}
