# Eye Movement Parameters in Children with Reading Difficulties
## 2 Method
### Saccadic Eye Movement Evaluation
The saccadic eye movement amplitude was calculated based on raw data analysis. The amplitude of saccadic eye movements was determined in Microsoft Excel using the following equation (Equation (1)):  
\[Amplitude=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}, \tag{1}\]  
where \(x_{1}\) and \(x_{2}\) are the horizontal gaze coordinates before and after the saccade, respectively (px), and \(y_{1}\) and \(y_{2}\) are the vertical gaze coordinates before and after the saccade, respectively (px). In order to estimate saccadic eye movement accuracy, only the first saccade towards the saccadic target was taken into account. saccadic eye movement accuracy was calculated in Microsoft Excel using the following equation (Equation (2)):  
\[Accuracy=1-\frac{S_{e}}{T_{e}}, \tag{2}\]  
where \(S_{e}\) represents the landing error (cm) and \(T_{e}\) represents the distance between the gaze position after the saccade and the center of the saccadic target (cm). Landing error \(S_{e}\) represents the vector size between the coordinates of the gaze direction after the saccade (\(\overset{\rightarrow}{b}\)--the actual amplitude of saccadic eye movements) and the coordinates of the center of the saccadic target (\(\overset{\rightarrow}{a}\)--representing the distance from the fixation point to the center of the target). Therefore, the magnitude of the landing error depends on the location of the saccadic target, including the direction and distance. The following equation based on the Euclidean distance was applied to calculate the landing error (Equation (3)):  
\[S_{e}=\sqrt{\left(a-b\right)^{2}}, \tag{3}\]  
where \(a\) represents the distance between the center of the fixation point and the center of the target (px) and \(b\) represents the amplitude of saccadic eye movements (px). Since the experiment for each participant was performed only once (without replications), a portion of the data (saccades at specific directions) were not obtained due to blinking, distractions, or other factors. These data were referred as \"_Untclassifide_\" or \"_Eye-sNotFound_\" by Tobii Pro Fusion. In order to ensure a successful data analysis without excluding the already obtained results from children who had some of the data missing, missing data replacement was performed. In order to evaluate the amount and the possible source of missing data, a _missing value analysis_ was performed in SPSS. The results of the missing value analysis were not statistically significant (\(p\) = 0.386), therefore enabling the substitution of missing values [46]. [PERSON] [47] concluded that mean value or median substitution can be only applied if less than 10% of the data is missing, and if more than 10% is missing, the regression or ML algorithm should be applied. In order to include all of the children in the further data analysis, the K-Nearest Neighbors Algorithm (KNN) with k = 10 was applied for handling the missing data. KNN is a simple classification method or algorithm that determines the class of a target object based on the class most frequently found in its nearest neighbors [48]. In order to compare the saccadic eye movement performance in children with and without reading difficulties, mixed-model ANOVA was performed. The study employed a between-subjects design with three factors--reading performance (two levels: with and without reading difficulties), age (six levels: 7, 8, 9, 10, 11 and 12 years), and direction--that was analyzed separately for horizontal directions (two levels: right and left) and vertical directions (with two levels: up and down). A Bonferroni post hoc analysis was applied for pairwise comparisons. Horizontal saccades were analyzed separately from the vertical saccades, since the distance between the fixation point and the saccade target was different.