# Concurrent Validity of the Inertial Measurement Unit _Vmaxpro_ in Vertical Jump Estimation
## 2 Materials and Methods
### Statistical Analysis  
Descriptive data are shown as mean and standard deviation. The normality of the data was verified using the Kolmogorov-Smirnov test, resulting in a non-normal sample for MoCAP (\(p=0.011\)). To assess the degree of agreement and the presence of systematic error between the two instruments, [PERSON]'s concordance coefficient (CCC) was calculated. This statistic is expressed as \(\rho_{c}=\rho\times C_{b}\), providing information on how close the pairing data in both devices are (\(\rho\), precision) for VJ and how close to ideality this line is (\(C_{b}\), accuracy), where ideal fit is represented by a straight-line \(x=y\)[34]. The results obtained are classified as \(<\)0.9 (poor), 0.90-0.95 (moderate), 0.95-0.99 (substantial), and \(\geq\)0.99 (near perfect) [35]. In addition, a correlational analysis was performed by determining [PERSON]'s bivariate correlation coefficient (\(r_{s}\)) since the size and non-normal nature of the sample [36] discourage the use of [PERSON]'s coefficient. For interpretation, the following criteria were used: \(\leq\)0.1 (trivial), 0.1-0.3 (low), 0.3-0.5 (moderate), 0.5-0.7 (high), 0.7-0.9 (very high), and \(\geq\)0.9 (almost perfect) [37; 38]. The Passing and Bablok regression [39] for nonparametric samples was used for the regression analysis to determine the existence of a linear relationship between the paired data from both instruments. The relationship between two variables can be described using the equation \(y=ax+b\), which allows for the prediction of the values of the dependent variable \(y\) based on the values of the independent variable \(x\). The parameter \(a\) represents the slope, which ideally should be 1, and provides information on the proportional differences between the two methods. On the other hand, \(b\) is the cut-off point with the \(x\)-axis (intercept) which, in its ideal value, would be 0 and represents the systematic differences between the two devices in a quantitative approach. The standard error of the estimated (SEE) was also calculated; the lower the SEE values, the closer the points are to the regression line and therefore the lower the error in the estimation. To check the applicability of Passing and Bablok regression, the Cusum test resulting in a \(p\)-value less than 0.05 indicates no linear relationship between the Mocap and _Vmaxpro_. To analyze the existence of systematic error, significant differences in the values of the _Vmaxpro_ and the criterion instrument were calculated using a Wilcoxon test for paired samples, and the effect size (ES) was determined as bias corrected Hedges ES [40]. The differences expressed as \(g\) were interpreted according to [PERSON] et al. [40] as trivial (\(<\)0.2), small (0.2-0.6), moderate (0.6-1.2), and large (\(>\)1.2). In the same way, the existence of significant differences between sessions 1 and 2 was studied using the Wilcoxon test (intradevice and between sessions), interpreting that the nonexistence of these differences (\(p>0.05\)) indicates that both sessions are equivalent, and therefore, the data can be used in a summative way in the determination of the validity of the _Vmaxpro_. Figure 1: Experimental design: CMJ = countermovement jumping; ADM, the amplitude of movement exercises; MoCAP = 3D motion capture system; Vmaxpro = inertial measurement unit. The level of agreement between the VJH data of the two matched devices was assessed using Bland-Altman plots, which allows for the determination of the systematic error and its limits of agreement for 95% (LoA = 1.96 SD). The maximum allowable differences between devices were calculated from the coefficients of variation (CV) of each method according to the expression \((\text{CV}^{2}\text{\text{\text{\text{V}}}maxpro}+\text{CV}^{2}\text{\text{\text{ MoCAP}}})^{1/2}\)[41]. If the 95% confidence limits of the upper LoA are below the maximum allowable difference and the lower LoA is above the maximum allowable difference, the methods do not disagree [42].