# Concurrent Validity of the Inertial Measurement Unit _Vmaxpro_ in Vertical Jump Estimation
## 3 Results  
### Validation of _Vmaxpro_  
No statistically significant differences were found between sessions two and three in either instrument (\(p\) = 0.684 for _Vmaxpro_ and \(p\) = 0.549 for MoCAP). Therefore, both sessions can be considered equivalent in terms of the total number of recorded jumps.  
Table 2 shows the values of [PERSON]'s correlation coefficient, [PERSON]'s concordance correlation coefficient, and [PERSON]'s test results for paired samples between the _Vmaxpro_ and the MoCAP criterion instrument, showing a strong correlation value for [PERSON]'s correlation and CCC values, indicating weak concordance correlation. There are also statistically significant differences between the paired data for the heights of the two instruments (\(p\) < 0.001), with a mean difference between the two of 10.58 cm and an ES of large (\(g\) = 2.4) [45].  
The Passing and [PERSON] regression analysis (Figure 2) shows a fit equation expressed as \(\text{H}_{\text{MoCAP}}\) = 8.463 + 1.067 \(\text{H}_{Vmaxpro}\) (cm). This equation describes the association between the two devices, showing the existence of a linear relationship between MoCAP and _Vmaxpro_ that is very good since the slope is almost no different from unity. Therefore, both instruments behave similarly when they measure the same sample; in other words, the precision of _Vmaxpro_ is similar to that of the reference system. However, the intercept is very large, which shows a systematic error, indicating that _Vmaxpro_ underestimates VJH when compared to MoCAP. [PERSON]'s correlation coefficient was calculated \(r_{s}\) = 0.847 (\(p\) < 0.001), implying a very strong correlation. Likewise, a SEE of 1.67 cm was obtained, indicating that the regression model can fit the data. Furthermore, the analysis of the residual plot reveals no appreciable trends and shows no significant difference with the linearity condition in the Cusum test (\(p\) = 0.17) [39].  
The Bland-Altman plots (Figure 3) show systematic error values of 10.6 cm (95% CI 10.29-10.86 cm), meaning that the _Vmaxpro_ IMU provides estimations 10.6 cm less than the MoCAP reference system. Furthermore, the LoAs are 15.2 cm (95% CI 14.73-15.71 cm) for the upper limit and 5.96 cm (95% CI 5.47-6.45 cm) for the lower limit with 97.3% of the points falling within the LoA, so the agreement between devices is high given that the dispersion of differences is low. The fit line, _Difference_ = 8.849 + 0.0518-_Mean_, refers to the existence of proportional bias in which a steep slope indicates the absence of heteroscedasticity of the error. In this case, a slightly increasing slope (0.0518) is found, but  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\text{H}_{Vmaxpro}\) (cm) & \(\text{H}_{\text{MoCAP}}\) (cm) & **Diff. (cm)** & **ES (g)** & \(\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text  
according to the bivariate Pearson product-moment correlation of \(r^{2}=0.009\), the _Vmaxpro_ does not add proportional error to the measure (\(r^{2}=<\)0.2). The maximum allowable differences were determined as \(\pm\)19.1 cm with both LoAs falling within this range, i.e., all the data included in the LoA are within the predefined limit of clinical agreement.  
Figure 3: The solid black line indicates the mean of the differences (systematic error); dotted lines indicate the upper and lower LoA; dashed line represents the line of perfect agreement (null difference). The dotted and dashed line represents the regression line of the differences; shaded areas = area of the LoAs; CI of 95% indicated between parentheses.  
Figure 2: Correlation analysis between MoCAP system and _Vmaxpro_ IMU through Passing and Bablok regression (**a**): the continuous line represents the regression line; the shaded area represents the confidence intervals for 95% of the regression line; the grey line is the \(x=y\) line; \(r_{s}\) represents [PERSON]’s correlation coefficient; SEE standard error of the estimate. (**b**) Residuals plot: No trend is shown, so linearity is assumed.