# Concurrent Validity of the Inertial Measurement Unit _Vmaxpro_ in Vertical Jump Estimation
## 4 Discussion  
This study aimed to analyze the concurrent validity of the IMU Vmaxpro when compared to a criterion instrument based on a motion capture system for the estimation of VJH in the CMJ in high-level female volleyball athletes. The main results show a positive linear dependence between both instruments, with correlations that can be interpreted as very high (\(r_{s}\) = 0.847), similar to those obtained in other studies. In this research, the accelerometer was placed between L4 and L5, in the same position as the reflective marker used by the MoCAP system to detect position, in order to be as close as possible to the hypothetical center of mass. Comparing our results with studies that used an equivalent arrangement on the body (IMU on the hip), [PERSON] and [PERSON] [11] obtained similar results for the correlation between IMU and MoCAP with very high Pearson correlation coefficients (\(r\) = 0.89). These values are slightly lower than those obtained by [PERSON] et al. [10], which found almost perfect correlations (\(r\) > 0.90). On the other hand, placing the accelerometer on the torso does not show very different correlations when compared to our study, with values of \(r\) ranging from 0.72 to 0.95 [18; 19; 46]. In the same way, very high correlations are obtained when comparing IMUs against FP. In general, the results obtained are closer to perfect correlation (\(r\) = 1) than those obtained against MoCAP, with values ranging from \(r\) = 0.70 to \(r\) = 0.95 [38; 46; 47; 48]. Therefore, the correlation values are in line with other studies and can be considered acceptable in terms of validation. However, [PERSON]'s correlations or their nonparametric equivalent (Spearman), although often used in validation studies, are not the most appropriate tool to assess the dependence between two devices since they do not provide information about the nature of the correlation and do not distinguish between data pairings. In contrast, [PERSON]'s CCC does make this distinction, and for the relationship between _Vmaxpro_ and MoCAP, values of \(\rho_{\text{C}}\) = 0.22 are obtained, indicating a low correlation. The precision value is \(\rho\) = 0.861 (very high), while the accuracy value is \(C_{b}\) = 0.2611 (low). Consequently, the factor inherent to precision is the most important factor in the low final value observed for CCC, indicating that the pairs are far from the perfect \(x\) = \(y\) line, which raises suspicions of systematic error even though the precision seems high. The Passing-Bablok regression plot (Figure 3) can help to better interpret this correlation. The intercept has a value of 8.463 cm, thus indicating that the systematic error is high, which confirms what was observed for CCC. However, the slope does not differ much from the value of 1 (1.067), indicating that the correlation is high, as discussed in the previous paragraph (\(r_{s}\) = 0.847). Furthermore, the results of the regression analysis led to an equation H\({}_{\text{MoCAP}}\) = 8.463 + 1.067 H\({}_{Vmaxpro}\), which allows for predicting the mean height values of MoCAP (considered as a gold standard) from the mean height values of _Vmaxpro_. Therefore, the observed high systematic error can be corrected, allowing for valid data by simply applying the fitting equation [2]. On the other hand, the random error can be quantified by the values of the standard error of the estimated (SEE), which, in this study, shows a value of 1.67 cm. The random error is quantified as moderate (standardized SEE of 0.36) [49], in agreement with the study by [PERSON] et al. [47] who compared the results of the _Vert_ accelerometer when estimating the VJH in CMJ jumps with arm mobilization (Abalakov) and found standardized SEE values of 0.32 (moderate). On the other hand, if the IMU is placed on the forefoot, larger random errors are observed (2.70 cm) than those observed in our study [50]. Similarly, [PERSON] et al. [51] found values with larger errors placing the IMU in the forefoot (SEE = 4.5 cm).