# Can IMU Provide an Accurate Vertical Jump Height Estimate?
## 3 Results  
Table 1 shows the results of the descriptive statistical analysis for the CMJ and SQJ height calculated using the FT method is for both IMU and FP. Regarding the CMJ variables, i.e., CMJ_FP and CMJ_IMU, the mean jump height (Mean \(\pm\) SD) of 30.29 \(\pm\) 3.41 and 30.11 \(\pm\) 3.25 cm, was calculated from the FP and IMU data, respectively. The results of JH from FP data were in the range of 24.83 to 38.32 cm, with the coefficient of variation (cV) of 11.26%, while the range of JH results from IMU data was 24.60-39.14 cm, with the cV of 10.78%. In both cases, the results of the Shapiro-Wilk test were non-significant (W = 957, \(p\) = 0.339 for CMJ_FP; W = 0.953, \(p\) = 0.276 for CMJ_IMU), indicating a normal distribution of the results. In relation to the SQJ_FP and SQJ_IMU, the mean JH of 27.36 \(\pm\) 2.67 and 27.54 \(\pm\) 3.43 cm were determined, respectively. The calculated JH results are in the range of 22.15-32.65 and 19.13-33.16 cm for the respective variables. In both cases, the results were normally distributed (W = 0.983, \(p\) = 0.925 for SQJ_FP; W = 0.972, \(p\) = 0.684 for SQJ_IMU). Table 2 summarizes the results of the validity analysis of the VJ height measurement using an individual IMU placed on the metatarsal part of the foot versus an FP as a criterion device. Regarding the CMJ, the difference in the JH results calculated from FP and IMU data was not statistically significant (t = 0.897, \(p\) = 0.379). The Cohen's d of 0.176 indicates a negligible difference in the results between the two devices, which is further supported by the McV value of 1.896. The Bland-Altman analysis yielded a bias of \(-\)0.18 cm and 95% LOA of \(-\)2.26 to 1.9 cm. The determined ICC value was 0.975. In relation to the SQJ, the difference of the JH results calculated from FP and IMU data was not statistically significant (t = \(-\)0.564, \(p\) = 0.578), with a negligible effect size of 0.111. The determined MC value was low (3.556) while the ICC value was 0.921. The Bland-Altman analysis yielded a bias of 0.18 cm and 95% LOA of \(-\)3.14 to 3.5 cm. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline \multirow{2}{*}{**N**} & \multirow{2}{*}{**Min**} & \multirow{2}{*}{**Max**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**SEM**} & \multirow{2}{*}{**SD**} & \multirow{2}{*}{**CV [\%]**} & \multirow{2}{*}{**W**} & \multirow{2}{*}{**\(p\)**} \\  & & **[cm]** & & & & & & & & \\ \hline CMJ\_FP & 26 & 24.83 & 38.32 & 30.29 & 0.67 & 3.41 & 11.26 & 0.957 & 0.339 \\ \hline CMJ\_IMU & 26 & 24.60 & 39.14 & 30.11 & 0.64 & 3.25 & 10.78 & 0.953 & 0.276 \\ \hline SQJ\_FP & 26 & 22.15 & 32.65 & 27.36 & 0.52 & 2.67 & 9.76 & 0.983 & 0.925 \\ \hline SQJ\_IMU & 26 & 19.13 & 33.16 & 27.54 & 0.67 & 3.43 & 12.45 & 0.972 & 0.684 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics and normality of the distribution of counter-movement (CMJ) and squat jump (SQJ) height, as estimated based on the flight-time (FT) determined from a force plate (FP) and an inertial measurement unit (IMU). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Concurrent Validity IMU vs. FP** \\ \hline \multirow{2}{*}{FP (95\% CI) [cm]} & \multirow{2}{*}{30.29 \(\pm\) 3.41 (28.98; 31.6)} & \multirow{2}{*}{27.36 \(\pm\) 2.67 (26.33; 28.39)} \\  & IMU (95\% CI) [cm] & 30.11 \(\pm\) 3.25 (28.86; 31.36)} & \multirow{2}{*}{27.54 \(\pm\) 3.43 (26.22; 28.86)} \\  & \(t\)-test (t, \(p\), d) & (0.897, 0.379, 0.176)} & (\(-\)0.564, 0.578, 0.111) \\ \hline ICC (95\% CI) & 0.975 (0.944; 0.989) & 0.921 (0.825; 0.965) \\ \hline McV [\%] & 1.896 & 3.556 \\ \hline Bias (95\% CI) [cm] & \(-\)0.18 (\(-\)0.6; 0.24) & 0.18 (\(-\)0.49; 0.85) \\ \hline Lower LOA (95\% CI) [cm] & \(-\)2.26 (\(-\)2.99; \(-\)1.54) & \(-\)3.14 (\(-\)4.3; \(-\)1.97) \\ \hline Upper LOA (95\% CI) [cm] & 1.9 (1.17; 2.63) & 3.5 (2.34; 4.66) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Concurrent validity of an inertial measurement unit (IMU) vs. a force plate (FP) for vertical jump height estimation.