\subsubsection{Push Task}
\label{3_push}

\subsubsubsection{Completion Time}
\label{3_push_tct}

On the time to complete a trial, there were two statistically significant effects: %
Hand (\anova{5}{2868}{24.8}, \p[<]{0.001}, see \figref{3-Push-ContactsCount-Hand-Overall-Means}) %
and Target (\anova{7}{2868}{5.9}, \p[<]{0.001}).
%
Skeleton was the fastest, more than None (\qty{+18}{\%}, \p{0.005}), Occlusion (\qty{+26}{\%}, \p[<]{0.001}), Tips (\qty{+22}{\%}, \p[<]{0.001}), and Contour (\qty{+20}{\%}, \p{0.001}).
%
Three groups of targets volumes were identified:
%
(1) sides E, W, and SW targets were the fastest;
%
(2) back and front NE, S, and SE were slower (\p{0.003});
%
and (3) back N and NW targets were the slowest (\p{0.04}).


\subsubsubsection{Contacts}
\label{3_push_contacts_count}

On the number of contacts, there were two statistically significant effects: %
Hand (\anova{5}{2868}{6.7}, \p[<]{0.001}, see \figref{3-Push-ContactsCount-Hand-Overall-Means}) %
and Target (\anova{7}{2868}{27.8}, \p[<]{0.001}).
%
\figref{3-Push-ContactsCount-Hand-Overall-Means} shows the Contacts for each Hand.
%
Less contacts were made with Skeleton than with None (\qty{-23}{\%}, \p[<]{0.001}), Occlusion (\qty{-26}{\%}, \p[<]{0.001}), Tips (\qty{-18}{\%}, \p{0.004}), and Contour (\qty{-15}{\%}, \p{0.02});
%
and less with Mesh than with Occlusion (\qty{-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 (W) and the right (E, SW) were easier to reach than the back ones (N, NW, \p[<]{0.001}).


\subsubsubsection{Time per Contact}
\label{3_push_time_per_contact}

On the mean time spent on each contact, there were two statistically significant effects: %
Hand (\anova{5}{2868}{8.4}, \p[<]{0.001}, see \figref{3-Push-MeanContactTime-Hand-Overall-Means}) %
and Target (\anova{7}{2868}{19.4}, \p[<]{0.001}).
%
It was shorter with None than with Skeleton (\qty{-10}{\%}, \p[<]{0.001}) and Mesh (\qty{-8}{\%}, \p{0.03});
%
and shorter with Occlusion than with Tips (\qty{-10}{\%}, \p{0.002}), Contour (\qty{-10}{\%}, \p{0.001}), Skeleton (\qty{-14}{\%}, \p{0.001}), and Mesh (\qty{-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 (W, SW) and the right (E) sides had higher Timer per Contact than all the other targets (\p{0.005}).
