# Parameters of Optokinetic Nystagmus Are Influenced by the Nature of a Visual Stimulus
## 2 Materials and Methods
### Data Analysis  
The data of the tested (right) eye of all participants were treated manually in an offline way with the following steps. First, we sought the trials in which a robust OKN response was visible (at least two OKN patterns) [14,25] that occurred in the correct direction, respectively to the direction of the stimulus drift. An example of such a sequence containing a robust OKN response is depicted in Figure 3. These filtered sequences of gaze data were labeled by a combination of a subject, spatial frequency, grating type, and the contrast level, separately for the ten repetitions of every contrast level. Prior to the gaze data analysis, blinks (epochs of the missing pupil) were discarded with a buffer of 50 ms to protect our analysis from potential blink-related artifacts. From every data sequence we derived the onset and offset time of the OKN, the gain, and amplitude as follows. The starting time of the first OKN-QP was considered as the OKN onset time, as done in a previous study [24]. Here the OKN gain was calculated as the average ratio of the OKN-SP and the velocity of the stimulus of the two consequent OKN patterns. Next, the amplitude of the OKN was calculated as the average distance the eye had traveled in the two OKN-SPs of the two consequent OKN patterns. Next, the OKN offset time was determined as the ending time point of the third OKN-QP. Finally, we calculated the average value of the respective parameter for every combination of a participant, spatial frequency, grating type, and contrast level across the ten repetitions of the contrast-specific stimulus. For the analysis of the OKN parameters, we used the first two OKN events as depicted in Figure 3, first in order to have a comparable amount of data across conditions and second to provide the two limits for the robust OKN response, since this has been considered in the past [14,25]. The statistical analysis was conducted using linear mixed-effects models with the statistics software JMP (JMP\({}^{\otimes}\), Version 16. SAS Institute Inc., Cary, NC, USA, 1989-2022) in order to analyze the significance of the effects of the visual stimulus parameters on the OKN onset, offset, amplitude, and gain. We run a single model for every of the tested OKN parameter, where the corresponding parameter acted as a dependent variable, with the participant as a random effect and three fixed effects: spatial frequency, grating type, and the contrast level. The selected method of all these models was the standard least squares. The variables of subject number, spatial frequency, grating type, and the contrast level were set as nominal with the respective OKN parameter (onset, offset, gain, amplitude) as a  
Figure 3: (**A**) OKN pattern for one typical subject for the 2 s grating presentation. Please note that we analyzed the data of the first two OKN patterns (up to the 3 rd OKN-QP). Here the numbers 1 to 6 represent the following time points. (1) onset time of the OKN, (2) start time of the 1 st OKN-SP (end time of the 1 st OKN-QP), (3) start time of the 2 nd OKN-QP (end time of the 1 st OKN-SP), (4) start time of the 2 nd OKN-SP (end time of the 2 nd OKN-QP), (5) start time of the 3 rd OKN-QP (end time of the 2 nd OKN-SP), and (6) end time of the 3 rd OKN-QP. The green area represents the gaze data used for the analysis (first two OKN events). (**B**) The derived horizontal eye velocity. continuous variable. Prior to utilizing the results of the models, we verified the model by visual inspection of the normality of the distribution of the residuals, as well as by statistical testing the homoscedasticity of the variances of residuals using the Brown-Forsythe test and reported in cases of violation. The significance level was set to \(\alpha=5\%\).