Computational protocol: Magnitude processing of symbolic and non-symbolic proportions: an fMRI study

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[…] fMRI data analysis was performed using SPM12 ( Images were slice-time corrected, motion corrected, and realigned to each participant’s mean image. Motion parameters did not exceed 2.5 mm translation in total (i.e., they did not exceed voxel size) and a head rotation of 1.5 degree in pitch, roll, and yaw in total. Therefore, none of the participants had to be excluded from the analyses because of head movements. The mean image was co-registered with the whole-brain volume. Imaging data was then normalized into standard stereotaxic MNI space (Montreal Neurological Institute, McGill University, Montreal, Canada). Images were resampled every 2.5 mm using 4th degree spline interpolation to obtain isovoxel and then smoothed with a 8 mm full-width half-maximum (FWHM) Gaussian kernel to accommodate inter-subject variation in brain anatomy and to increase signal-to-noise ratio in the images. The data were high-pass filtered (128 s) to remove low-frequency noise components and corrected for autocorrelation assuming an AR(1) process.The onsets of the four presentation formats (i.e., fractions, decimals, pie charts, dot patterns) were entered as separate conditions in the GLM. As regressors of interest, logarithmic overall distance as first and reaction times as second parametric modulation of the conditions were added on the single-participant level. We decided to use overall distance (instead of reaction times) as the first parametric modulator due to its specific numerical features. Parametric modulators are serially orthogonalised in SPM. Therefore, only variance not explained by the first modulator can be explained by the second modulator. Consequently, logarithmic distance entered the model first, because its inherent numerical quality was of particular interest. Generally, no supra-threshold activation was found for the parametric modulation of RT unless stated otherwise. Movement parameters estimated at the realignment stage of preprocessing were included as covariates of no interest. Brain activation was convolved over all experimental trials with the canonical haemodynamic response function (HRF) as implemented in SPM12 and its time and dispersion derivatives.We performed a three-stage analysis. First, we evaluated activation associated with the distance effect in all four presentation formats, respectively, to examine specific magnitude-related brain activation in proportion processing. Second, in an exploratory analysis, we examined format-specific activations of both symbolic and non-symbolic relative magnitudes. Third, analogous to previous studies on proportion processing [, ], a conjunction analysis was calculated as implemented in SPM12 (conjunction null, see []) to identify brain activation common in all four presentation formats during magnitude processing.The SPM Anatomy Toolbox [], available for all published cytoarchitectonic maps (, was used for anatomical localization of effects where applicable. In areas not yet implemented, the anatomical automatic labelling tool (AAL) in SPM12 ( was used.If not stated otherwise, thresholds for statistical inference were set at FWE-corrected p < .05 at the voxel level, corrected for multiple comparisons at the cluster level to FWE-corrected p < .05 with a cluster size of k = 10 voxels.An uncorrected statistical threshold of p < .001 was chosen for the conjunction analysis because four conditions of interest needed to significantly modulate the fMRI signal in a given region in the conjunction analysis. The effective p value for a conjunction analysis is the square of the p values for each component. Therefore, a more liberal threshold for such a conservative statistical procedure is justified []. […]

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