# Test-Retest Repeatability of Human Gestures in Manipulation Tasks
## 2 Materials and Methods
### Data Analysis  
Data analysis was conducted with custom Matlab(r) (MathWorks, Natick, MA, USA) routines. Raw data of linear accelerations were processed to obtain the accelerations' magnitude after removing the gravitational acceleration. Single gestures were extracted from the entire acquisition by means of windows with a length of three seconds, which was imposed by the regular pace of the green LEDs at 20 bpm. In addition, gestures were distinguished between abrupt and normal movements based on the occurrence of the visual and acoustic alarms. Subsequently, values of acceleration root mean square (RMS) were estimated for each signal considering all the windows within the same movement type. Accordingly, the analysis differentiated movements into three groups: normal movements, abrupt movements caused by a visual alarm and abrupt movements generated by the acoustic buzzer. Since the application of the Shapiro-Wilk test (2-tails, significance level: \(\alpha=0.05\)) demonstrated a non-normal distribution of data, a non-parametric statistical analysis was performed on acceleration RMS values with the following tests:  
* Mann-Whitney U test (2-tails, significance level: \(\alpha=0.05\)) to verify the eventual presence of differences between males and females;
* Mann-Whitney U test (2-tails, significance level: \(\alpha=0.05\)) to verify the eventual presence of differences among the three test modalities (_rFR_, _IFR_, _ILA_);
* Wilcoxon test (2-tails, significance level: \(\alpha=0.05\)) to investigate the eventual presence of statistical differences among normal movements; visual, abrupt movements; and acoustic, abrupt movements, for each modality.  
As suggested in the literature [20], the test-retest modality can be applied to study the repeatability of the proposed task over time. Test-retest repeatability was evaluated using SPSS(r) V22.0 (IBM, Armonk, NY, USA) statistical package. Accordingly, in this analysis, the acceleration of RMS values of test and retest were used for the estimation of repeatability. A common measure of repeatability is represented by the intraclass correlation coefficient (ICC), which is calculated as the ratio between the true variance and the total variance of the variable of interest [21]. This dimensionless index assumes values inside the range [\(-\)1, 1], highlighting a higher repeatability the closer it reaches 1. In general, two slightly different models of ICC are adopted as measures of relative repeatability of a single measurement [22]. The ICC (3,1) does not consider the effect of any systematic bias as part of the measurement error. On the contrary, the ICC (1,1) assumes all within-subject variability to be a part of the measurement error. These two models produce the same result if no systematic error is present [19]. Another common measure of repeatability is represented by the coefficient of variation (CV), which is the percentage ratio between the standard deviation and the mean of a value distribution [23]. The repeatability improves the lower the CV.  
In this work, the test-retest repeatability was evaluated in four conditions:  
* Considering all participants (all);
* Excluding the outliers, automatically identified as participants with acceleration RMS values exceeding 1.5 times the interquartile range above the 75 th quartile or below the 25 th quartile (no_o);
* Considering only the participants who performed the retest after less than 45 days from the test (u_45);
* Considering only the participants who performed the retest after at least 45 days from the test (o_45).  
Hence, for each of these four conditions, the test-retest repeatability was assessed through ICC (1,1), ICC (3,1) and CV estimated for each group of movements (normal; abrupt, visual alarm; abrupt, acoustic alarm) and for each modality (_rFR_, _IFR_, _ILA_).