139 lines
13 KiB
TeX
139 lines
13 KiB
TeX
\section{Results}
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\label{results}
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\subsection{Trial Measures}
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\label{results_trials}
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All measures from trials were analyzed using \LMM or \GLMM with \factor{Visual Rendering}, \factor{Amplitude Difference} and their interaction as within-participant factors, and by-participant random intercepts.
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Depending on the data, different random effect structures were tested.
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Only the best converging models are reported, with the lowest Akaike Information Criterion (AIC) values.
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Post-hoc pairwise comparisons were performed using the Tukey's \HSD test.
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Each estimate is reported with its \percent{95} \CI as follows: \ci{\textrm{lower limit}}{\textrm{upper limit}}.
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\subsubsection{Discrimination Accuracy}
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\label{discrimination_accuracy}
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A \GLMM was adjusted to the \response{Texture Choice} in the \TIFC vibrotactile texture roughness discrimination task, with by-participant random intercepts but no random slopes, and a probit link function (\figref{results/trial_predictions}).
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The \PSEs (\figref{results/trial_pses}) and \JNDs (\figref{results/trial_jnds}) for each visual rendering and their respective differences were estimated from the model, along with their corresponding \percent{95} \CI, using a non-parametric bootstrap procedure (1000 samples).
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The \PSE represents the estimated amplitude difference at which the comparison texture was perceived as rougher than the reference texture \percent{50} of the time, \ie it is the accuracy of participants in discriminating vibrotactile roughness.
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The \level{Real} rendering had the highest \PSE (\percent{7.9} \ci{1.2}{4.1}) and was statistically significantly different from the \level{Mixed} rendering (\percent{1.9} \ci{-2.4}{6.1}) and from the \level{Virtual} rendering (\percent{5.1} \ci{2.4}{7.6}).
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The \JND represents the estimated minimum amplitude difference between the comparison and reference textures that participants could perceive, \ie the sensitivity to vibrotactile roughness differences,
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calculated at the 84th percentile of the predictions of the \GLMM (\ie one standard deviation of the normal distribution) \cite{ernst2002humans}.
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The \level{Real} rendering had the lowest \JND (\percent{26} \ci{23}{29}), the \level{Mixed} rendering had the highest (\percent{33} \ci{30}{37}), and the \level{Virtual} rendering was in between (\percent{30} \ci{28}{32}).
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All pairwise differences were statistically significant.
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\fig[0.7]{results/trial_predictions}{Proportion of trials in which the comparison texture was perceived as rougher than the reference texture, as a function of the amplitude difference between the two textures and the visual rendering.}[
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Curves represent predictions from the \GLMM model (probit link function), and points are estimated marginal means with non-parametric bootstrap \percent{95} \CIs.
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]
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\begin{subfigs}{discrimination_accuracy}{Results of the vibrotactile texture roughness discrimination task. }[][
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\item Estimated \PSE of each visual rendering, defined as the amplitude difference at which both reference and comparison textures are perceived to be equivalent. %, \ie the accuracy in discriminating vibrotactile roughness.
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\item Estimated \JND of each visual rendering. %, defined as the minimum perceptual amplitude difference, \ie the sensitivity to vibrotactile roughness differences.
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]
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\subfig[0.35]{results/trial_pses}
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\subfig[0.35]{results/trial_jnds}
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\end{subfigs}
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\subsubsection{Response Time}
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\label{response_time}
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A \LMM \ANOVA with by-participant random slopes for \factor{Visual Rendering}, and a log transformation (as \response{Response Time} measures were gamma distributed) indicated a statistically significant effect on \response{Response Time} of \factor{Visual Rendering} (\anova{2}{18}{6.2}, \p{0.009}, \figref{results/trial_response_times}).
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Reported response times are \GM.
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Participants took longer on average to respond with the \level{Virtual} rendering (\geomean{1.65}{\s} \ci{1.59}{1.72}) than with the \level{Real} rendering (\geomean{1.38}{\s} \ci{1.32}{1.43}), which is the only statistically significant difference (\ttest{19}{0.3}, \p{0.005}).
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The \level{Mixed} rendering was in between (\geomean{1.56}{\s} \ci{1.49}{1.63}).
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\subsubsection{Finger Position and Speed}
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\label{finger_position_speed}
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The frames analyzed were those in which the participants actively touched the comparison textures with a finger speed greater than \SI{1}{\mm\per\second}.
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A \LMM \ANOVA with by-participant random slopes for \factor{Visual Rendering} indicated only one statistically significant effect on the total distance traveled by the finger in a trial of \factor{Visual Rendering} (\anova{2}{18}{3.9}, \p{0.04}, \figref{results/trial_distances}).
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On average, participants explored a larger distance with the \level{Real} rendering (\geomean{20.0}{\cm} \ci{19.4}{20.7}) than with \level{Virtual} rendering (\geomean{16.5}{\cm} \ci{15.8}{17.1}), which is the only statistically significant difference (\ttest{19}{1.2}, \p{0.03}), with the \level{Mixed} rendering (\geomean{17.4}{\cm} \ci{16.8}{18.0}) in between.
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Another \LMM \ANOVA with by-trial and by-participant random intercepts but no random slopes indicated only one statistically significant effect on \response{Finger Speed} of \factor{Visual Rendering} (\anova{2}{2142}{2.0}, \pinf{0.001}, \figref{results/trial_speeds}).
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On average, the textures were explored with the highest speed with the \level{Real} rendering (\geomean{5.12}{\cm\per\second} \ci{5.08}{5.17}), the lowest with the \level{Virtual} rendering (\geomean{4.40}{\cm\per\second} \ci{4.35}{4.45}), and the \level{Mixed} rendering (\geomean{4.67}{\cm\per\second} \ci{4.63}{4.71}) in between.
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All pairwise differences were statistically significant: \level{Real} \vs \level{Virtual} (\ttest{19}{1.17}, \pinf{0.001}), \level{Real} \vs \level{Mixed} (\ttest{19}{1.10}, \pinf{0.001}), and \level{Mixed} \vs \level{Virtual} (\ttest{19}{1.07}, \p{0.02}).
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This means that within the same time window on the same surface, participants explored the comparison texture on average at a greater distance and at a higher speed when in the \RE without visual representation of the hand (\level{Real} condition) than when in \VR (\level{Virtual} condition).
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\begin{subfigs}{results_finger}{Results of the performance metrics for the rendering condition.}[
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Boxplots and geometric means with bootstrap \percent{95} \CI, with Tukey's \HSD pairwise comparisons: * is \pinf{0.05}, ** is \pinf{0.01} and *** is \pinf{0.001}.
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][
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\item Response time at the end of a trial.
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\item Distance travelled by the finger in a trial.
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\item Speed of the finger in a trial.
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]
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\subfig[0.25]{results/trial_response_times}
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\subfig[0.25]{results/trial_distances}
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\subfig[0.25]{results/trial_speeds}
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\end{subfigs}
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\subsection{Questionnaires}
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\label{results_questions}
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%\figref{results/question_heatmaps} shows the median and interquartile range (IQR) ratings to the questions in \tabref{questions} and to the NASA-TLX questionnaire.
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%
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Friedman tests were employed to compare the ratings to the questions (\tabref{questions1} and \tabref{questions2}), with post-hoc Wilcoxon signed-rank tests and Holm-Bonferroni adjustment, except for the questions regarding the virtual hand that were directly compared with Wilcoxon signed-rank tests.
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\figref{results_questions} shows these ratings for questions where statistically significant differences were found (results are shown as mean $\pm$ standard deviation):
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\begin{itemize}
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\item \response{Hand Ownership}: participants slightly feel the virtual hand as their own with the \level{Mixed} rendering (\num{2.3 \pm 1.0}) but quite with the \level{Virtual} rendering (\num{3.5 \pm 0.9}, \pinf{0.001}).
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\item \response{Hand Latency}: the virtual hand was found to have a moderate latency with the \level{Mixed} rendering (\num{2.8 \pm 1.2}) but a low one with the \level{Virtual} rendering (\num{1.9 \pm 0.7}, \pinf{0.001}).
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\item \response{Hand Reference}: participants focused slightly more on their own hand with the \level{Mixed} rendering (\num{3.2 \pm 2.0}) but slightly more on the virtual hand with the \level{Virtual} rendering (\num{5.3 \pm 2.1}, \pinf{0.001}).
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\item \response{Hand Distraction}: the virtual hand was slightly distracting with the \level{Mixed} rendering (\num{2.1 \pm 1.1}) but not at all with the \level{Virtual} rendering (\num{1.2 \pm 0.4}, \p{0.004}).
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\end{itemize}
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\begin{subfigs}{results_questions}{Boxplots of the questionnaire results for the virtual hand renderings.}[
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Pairwise Wilcoxon signed-rank tests with Holm-Bonferroni adjustment: * is \pinf{0.05}, ** is \pinf{0.01} and *** is \pinf{0.001}.
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][
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\item Hand ownership.
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\item Hand latency.
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\item Hand reference.
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\item Hand distraction.
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]
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\subfig[0.18]{results/questions_hand_ownership}
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\subfig[0.18]{results/questions_hand_latency}
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\subfig[0.18]{results/questions_hand_reference}
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\subfig[0.18]{results/questions_hand_distraction}
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\end{subfigs}
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Overall, participants' sense of control over the virtual hand was very high (\response{Hand Agency}, \num{4.4 \pm 0.6}), felt the virtual hand was quite similar to their own hand (\response{Hand Similarity}, \num{3.5 \pm 0.9}), and that the \VE was very realistic (\response{Virtual Realism}, \num{4.2 \pm 0.7}) and very similar to the real one (\response{Virtual Similarity}, \num{4.5 \pm 0.7}).
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The overall workload (mean NASA-TLX score) was low (\num{21 \pm 14}), with no statistically significant differences found between the visual renderings for any of the subscales or the overall score.
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The textures were also overall found to be very much caused by the finger movements (\response{Texture Agency}, \num{4.5 \pm 1.0}) with a very low perceived latency (\response{Texture Latency}, \num{1.6 \pm 0.8}), and to be quite realistic (\response{Texture Realism}, \num{3.6 \pm 0.9}) and quite plausible (\response{Texture Plausibility}, \num{3.6 \pm 1.0}).
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The vibrations were felt a slightly weak overall (\response{Vibration Strength}, \num{4.2 \pm 1.1}), and the vibrotactile device was perceived as neither distracting (\response{Device Distraction}, \num{1.2 \pm 0.4}) nor uncomfortable (\response{Device Discomfort}, \num{1.3 \pm 0.6}).
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Participants were mixed between feeling the vibrations on the surface or on the top of their finger (\response{Vibration Location}, \num{3.9 \pm 1.7}); the distribution of scores was split between the two poles of the scale with \level{Real} and \level{Mixed} renderings (\percent{42.5} more on surface or on finger top, \percent{15} neutral), but there was a trend towards the top of the finger in VR renderings (\percent{65} \vs \percent{25} more on surface and \percent{10} neutral), but this difference was not statistically significant neither.
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\begin{tab}{questions2}
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{NASA-TLX questions asked to participants after each \factor{Visual Rendering} block of trials.}
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[
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Questions were bipolar 100-points scales (0~=~Very Low and 100~=~Very High, except for Performance where 0~=~Perfect and 100~=~Failure), with increments of 5.
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%Participants were shown only the labels for all questions.
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]
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\begin{tabularx}{\linewidth}{l X}
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\toprule
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\textbf{Code} & \textbf{Question} \\
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\midrule
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Mental Demand & How mentally demanding was the task? \\
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Temporal Demand & How hurried or rushed was the pace of the task? \\
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Physical Demand & How physically demanding was the task? \\
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Performance & How successful were you in accomplishing what you were asked to do? \\
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Effort & How hard did you have to work to accomplish your level of performance? \\
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Frustration & How insecure, discouraged, irritated, stressed, and annoyed were you? \\
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\bottomrule
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\end{tabularx}
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\end{tab}
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%\figwide{results/question_heatmaps}{%
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%
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% Heatmaps of the questionnaire responses, with the median rating and the interquartile range in brackets on each cell.
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%
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% (Left) point Likert scale questions (1=Not at all, 2=Slightly, 3=Moderately, 4=Very, 5=Extremely).
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%
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% (Middle) point Likert scale questions (1=Extremely A, 2=Moderately A, 3=Slightly A, 4=Neither A nor B, 5=Slightly B, 6=Moderately B, 7=Extremely B) with A and B being the two poles of the scale.
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%
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% (Right) Load Index (NASA-TLX) questionnaire (lower values are better).
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%}
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