# Eye Movement Parameters in Children with Reading Difficulties
## 2 Method
### Smooth Pursuit Evaluation  
Prior to the smooth pursuit evaluation, repeated calibration (5 points) and validation (4 points) was performed. If the calibration accuracy did not reach 0.5 degrees, a repeated calibration and validation process was performed. The stimulus color remained black (5 cd/m\({}^{2}\); RGB (0, 0, 0)), and the background color of the calibration and validation stimuli was grey (33 cd/m\({}^{2}\); RGB (114, 114, 114)), adjusted to the experimental settings in smooth pursuit evaluation. The experiment started with a fixation cross demonstrated at the center of the screen. After 3 s the fixation cross disappeared, and a black stimulus (circle, 0.7 degrees) was presented at the same position and started moving to the right at a speed of 6 degrees per second. Once the stimulus position reached 10.8 degrees from the initial position, the object motion reversed coming to 10.8 degrees to the left from the initial fixation and returned to the center of the screen. After completing three cycles of movement (moving to the right, left and returning to the initial position), the stimulus disappeared and a fixation cross was once again presented at the center of the screen. A similar procedure was performed in the vertical direction, with 3 cycles of movement up (10.8 degrees) and down (10.8 degrees) from the initial position. Eye movement data were extracted and analyzed in Tobii Pro Lab software, working in accordance with the Tobii Pro Fusion eye tracker. The data for smooth pursuit eye movement analysis included 348 (horizontal movement) and 346 (vertical movement) children who managed to record at least one smooth pursuit movement in one direction with the Tobii Pro Fusion device. Of all participants whose smooth pursuit eye movements were analyzed, 92 (horizontal) and 91 (vertical) had reading difficulties (RD), and 256 (horizontal) and 255 (vertical) children were included in the control group (CD). In order to determine the minimum sample size required for the study, power analysis (G*Power version 3.1.9.7) was conducted ([PERSON] et 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. Data analysis was performed on Microsoft Excel and SPSS programs. Data analysis was performed based on the raw data file provided by Tobii Pro Lab. The following data were excluded from the data analysis: (1) the latency period and the first 100 ms of the smooth pursuit corresponding to the open-loop phase of smooth pursuit eye movements; (2) blinks detected by the Tobii Pro Fusion and classified as \"_EyesNotFound_\"; (3) saccades (eye movements reaching velocity > 100 degrees/second); and (4) fixations corresponding to a relative stable gaze position. From the filtered data, eye movement velocity (degrees/second) and velocity gain were calculated, and the number of saccades performed during the smooth pursuit task was recorded. The smooth pursuit eye movement velocity was calculated based on raw data analysis in Microsoft Excel using the following equation (Equation (4)):  
\[v_{eye}=\frac{(x_{n}-x_{n-1})*1000}{(t_{n}-t_{n-1})}*dpp*1000, \tag{4}\]where \(v_{eye}\) is eye tracking velocity (deg/s), (\(x_{n}-x_{n-1}\)) are the difference of two adjacent \(x\)-axis coordinates (px), (\(t_{n}-t_{n-1}\)) are the difference of two adjacent time (us), and dpp represents degrees per pixel (deg/px). Equation (4) represents the velocity calculations for horizontal smooth pursuit eye movements. Velocity in the vertical direction was calculated using the same equation by applying the vertical coordinates (y instead of x). Smooth pursuit velocity gain refers to the ratio of eye velocity to the stimulus velocity.