# Analysis of Surface EMG Parameters in the Overhead Deep Squat Performance
## 2 Materials and Methods
### Statistical Analysis of sEMG Parameters  
Statistical analysis was performed to establish whether there are relationships between the degree of correctness of exercise performance (in this case, deep squat) and parameters %MVC, \(MF\), \(MDF\), and \(kurt\) calculated based on sEMG of the individual muscles: deltoid muscle, latissimus dorsi muscle, gluteus muscle, rectus femoris, vastus medialis, and biceps femoris. Statistical analysis was performed by TIBCO Software Inc. (2017), Statistica (data analysis software system), version 13.  
The nonparametric Kruskal-Wallis ANOVA and multiple comparison post hoc Dunn's tests with Bonferroni correction were applied for groups 1-3 for the muscles of the lower part of the body, and the Mann-Whitney U test for muscles of the upper part of the body. For all statistical analyses, the significance \(\alpha\)-level was set to 0.05. For a more complete interpretation of the obtained results, the effect size was also calculated for the Kruskal-Wallis, post hoc Dunn's tests, and Mann-Whitney U test. Such an approach allows assessment of the practical meaning of the obtained results, especially their statistical significance. Two indexes were used to calculate the size effect, \(\eta^{2}\) for Kruskal-Wallis and \(r\) for the post hoc Dunn's and Mann-Whitney U tests. The parameters \(\eta^{2}\) and \(r\) measuring the effects size are expressed by the following formulas [37], respectively:  
\begin{table}
\begin{tabular}{l l l} \hline
**Muscle 1** & **Muscle 2** & **Functional Relationship** \\ \hline Rectus femoris (RF) & Biceps femoris (BF) & Agonist–antagonist \\  & & (Knee extension vs. flexion) \\ Vastus medialis (VM) & Biceps femoris (BF) & Synergistic–antagonist \\  & & (Anterior vs. posterior thigh) \\ Deltoid (D) & Latissimus dorsi (L) & Shoulder stabilizers \\  & & (elevation vs. extension/adduction) \\ \hline \end{tabular}
\end{table}
Table 2: Selected muscle pairs for \(CAI\) computation based on functional biomechanics of the deep squat.  
\[\eta^{2}=\frac{H-k+1}{N-k}, \tag{11}\]  
where \(H\) is the value of Kruskal-Wallis test statistic, \(k\) is the number of groups, and \(N\) is the sample size,  
\[r=\frac{|Z|}{\sqrt{N}}, \tag{12}\]  
where \(Z\) is the value of the Dunn Z test statistic, and \(N\) is the sample size (i.e., the sum of samples of each group).  
In the case of the Kruskal-Wallis test, parameter \(\eta^{2}\in(0,0.01)\) is defined as a very small effect size, \(\eta^{2}\in(0.01,0.05)\) is a small effect size, \(\eta^{2}\in(0.06,0.13)\) is a moderate effect size, and \(\eta^{2}>0.14\) is a large effect size [38]. The \(r\) parameter measures the effect size based on the \(Z\) statistic of the [PERSON]'s test. In this case, if \(r\in(0.1,0.29)\) (small effect size), this means that differences between groups exist, but they are relatively weak and hard to notice in the data, so they could be less practically significant. In the case \(r\in(0.3,0.49)\) (moderate effect size), the differences between groups are noticeable, and the differences that are statistically significant could also be practically significant even though they are not too big. If the \(r>0.5\), the effect size is large, and it indicates strong differences between groups. In this case, the differences are clear and could be easily noticed in the analyzed data; such results have potentially high practical significance [38].