## 3 Statistical Data Processing  
It is feasible to collect data on the impacts of mobile devices on the psychological and physical health of the users to measure the impacts of active usage of smart technology. Correlation analysis was used to establish the relationships and the degree of dependence between individual variables. The most commonly used correlation coefficient is the Pearson coefficient \((r)\) for linear correlation, which is calculated by the formula [16]:  
\[r=\frac{P}{S_{X}S_{Y}} \tag{1}\]  
where \(P\)--moment of the products; \(S_{X}\)--standard deviation of the variable \(X\); and \(S_{Y}\)--standard deviation of the variable \(Y\). The moment of the products \((P)\) is calculated as:  
\[P=\frac{\sum XY}{n-1}-\frac{\sum X\sum Y}{n(n-1)} \tag{2}\]  
where \(\sum X\)--sum of \(X\) values; \(\sum Y\)--sum of \(Y\) values; \(\sum XY\)--sum of products of \(X\) and \(Y\); and \(n\)--sample size.  
Another statistical criterion that is successfully used to determine changes in the responses and/or conditions of subjects as a result of an experimental intervention is Student's \(t\)-test for related samples, which involves research design \"before-and-after\". It has the ability to work with small volumes of data, and there is measurement \"before the intervention\", measurement \"after the intervention\", and the recording of statistically significant differences in the values of the tested variables. The empirical value of the t-test is calculated by the formula [16]:  
\[t_{E}=\frac{|\bar{d}|}{\sqrt{\frac{\sum d^{2}-nd^{2}}{n^{2}-n}}} \tag{3}\]  
where \(d=X_{2}-X_{1}\) is the difference between two measured values of each object, \(n\) is the number of observed objects, and \(df\) are the degrees of freedom \(df=n-1\).  
Among the most powerful statistical techniques for studying causal relationships is ANOVA (Analysis of Variance). One-way ANOVA provides analysis of the variation of a quantitatively dependent variable--for example, the degree of internet addiction caused by an independent qualitative or quantitative variable--for example, the age group. According to the null hypothesis, ANOVA is used to test the assumption of whether several means are equal, allowing determination of not only the differences between them but also which exact mean values differ from the others.  
Table 1 shows the formulas for calculating the one-way ANOVA. The notations are as follows: \(SSb\)--sum of between-group squares; \(SSw\)--sum of within-group squares; \(SST\)--total sum of squares; \(K\)--degrees of freedom; \(nj\)--size (number of measurements) for each of the \(k\) samples (groups); \(\bar{x_{j}}\)--sample mean for the \(j\)-th group; \(\bar{x}\)--total mean; \(\bar{x_{ij}}\)--mean of the \(i\)-th individual from the \(j\)-th group; and \(n\)--total sample size. From the presented Table 1, it is clear that the \(F\)-ratio is obtained by dividing the between-group mean square \(MS_{b}\) by the within-group mean square \(MS_{w}\):  
\[F=\frac{MS_{b}}{MS_{w}} \tag{4}\]  
Therefore, the logic of ANOVA is based on the decomposition of the total variance of the variable into two key components: the between-group variance (deviations of the group means from the total arithmetic mean) and within-group variance (individual deviations of the values from the mean within a category (group)).  
The [PERSON]'s \(F\)-test is checked according to the significance level \(\alpha\) (usually equal to or less than 0.05) and the degrees of freedom \(K\), as follows: for the between-group variance \(K_{1}=k-1\), where \(k\) is the number of groups compared (degrees of freedom of the numerator); and for the within-group variance \(K_{2}=n-k\), where \(n\) is the sample size (degrees of freedom of the denominator).