# Eye Movement Parameters in Children with Reading Difficulties
## 2 Method
### Fixation Stability Evaluation  
The experiment for fixation stability evaluation was generated using the Titta Master toolbox developed by [PERSON] et al. [49]. Before eye-movement recording, a 5-point monocular calibration and 4-point validation procedure was performed. If the calibration accuracy did not reach 0.5 degrees, a repeated calibration and validation process was performed.  
In order to assess fixation stability, a fixation task was generated in which participants were required to maintain their gaze on a fixation stimulus for 10 s. The demonstrated fixation stimulus consisted of a combination of black circles (5 cd/m\({}^{2}\), RGB (0, 0, 0)) and a white cross (180 cd/m\({}^{2}\); RGB * (255, 255, 255)). The stimulus was displayed on a grey background (90 cd/m\({}^{2}\); RGB (180, 180, 180) and had an overall size of 0.6 degrees (see Figure 2). The fixation task stimulus was chosen based on the study by [PERSON] et al. [50], where this stimulus was found to provide a relatively stable fixation. After validation, a black dot appeared in the center of the screen for 3 s, after which a fixation task was presented at the same screen position. The fixation stimulus was displayed for 10 s, but the analysis of fixation included only the middle 9 s, excluding the first and last 0.5 s of the stimulus presentation. The fixation task was performed under binocular viewing conditions, meaning both eyes fixated on the stimulus simultaneously.  
The data from 279 children (140 boys and 139 girls) were included in the analysis of the fixation stability. Children who did not have a valid eye movement recording due to insufficient participation or technical issues, e.g., one eye not being recorded, were excluded from the further data analysis. Of all the children, 75 had reading difficulties (RDs) and 204 were referred as the control group (CG). In order to determine the minimum sample size required for the study, a power analysis (G*Power version 3.1.9.7) was conducted ([PERSON] al., 2007 [45]). The results of the power analysis indicated that the required sample size to achieve 80% power for detecting a medium effect (f = 0.25), at a significance criterion of \(\alpha\) = 0.05, was N = 60 for ANOVA: repeated measures within-between interaction. Thus, the obtained sample size of N = 346 is sufficient to test the study hypothesis. The results of the power analysis indicated that the required sample size to achieve 80% power for detecting a medium effect (f = 0.25), at a significance criterion of \(\alpha\) = 0.05, was N = 279 for [ANOVA: Fixed effects, special, main effects and interactions]. Thus, the obtained sample size of N = 279 is adequate to test the study hypothesis\".  
In order to extract gaze fixations from the eye movement recordings, the I2 MC (identification by two-means clustering) algorithm was applied. This algorithm has been designed for analyzing data with high levels of noise and missing data, making it particularly suitable for analyzing children's data [51]. Fixation stability was expressed by the bivariate contour ellipse area (BCEA), which was calculated using the following equation (Equation (6)). Note that a smaller BCEA value indicates a more stable fixation.  
\[BCEA=2k\pi\sigma_{H}\sigma_{V}\Big{(}1-\rho^{2}\Big{)}^{\frac{1}{2}}, \tag{6}\]  
where \(\sigma_{H}\) represents the standard deviation of fixations in the horizontal meridian; \(\sigma_{V}\) represents the standard deviation of fixations in the vertical meridian; \(\rho\) represents the Pearson product-moment correlation coefficient between two directions; and the \(k\) value is 1.14, as the chosen probability area is 68% [52].  
To compare gaze fixation stability between children with and without reading difficulties, a mixed-model ANOVA was conducted. The analysis included two between-subject factors: reading performance (levels: children with reading difficulties and children without reading difficulties) and age (6 levels: 7-, 8-, 9-, 10-, 11-, and 12-year-old). The within-subject factor was fixation stability.