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#### Mean shifted Z values may lead to incorrect statistical inferences

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Lee, J., Stelzer, J., Scheffler, K., & Lohmann, G. (2018). *Mean
shifted Z values may lead to incorrect statistical inferences*. Poster presented at 24th Annual Meeting of the Organization
for Human Brain Mapping (OHBM 2018), Singapore.

Cite as: http://hdl.handle.net/21.11116/0000-0001-7DA7-7

##### Abstract

Introduction:
Task-based fMRI data collected from Human Connectome Project were analyzed using the general linear model. The acquired Z values were plotted as a histogram. Theoretically, the null distribution of Z values should resemble a standard Gaussian distribution. However, we found that the histogram of Z values is often not centered around zero [mean shifted]. In fact, 12 percent of over 3000 Z maps showed a systematic shift bigger than 0.2 standard deviation.This is problematic because statistical inference based on mean shifted Z values can lead to incorrect results.
Conclusions:
Head motion parameters showed small but significant correlation with the mode of the Z value distribution. Furthermore, shift of the Z value distribution was not dependent on subject based on comparison between motor tfMRI and language tfMRI. Lastly, voxels within white matter region also showed systematically shifted Z values which implies that neuronal alone is not causing the shift. Further investigation is required to pinpoint the cause of the Z score distribution shift.
Methods:
Material
Task-evoked fMRI and motion parameters were acquired from Human Connectome Project WU-Minn HCP 1200 Subjects Data (HCP S1200)[4]. Motor tfMRI and language tfMRI were used in this study. In motor tfMRI (N=1049), the design consisted of five motor tasks including left finger tapping, right finger tapping, left toe squeezing, right toe squeezing and tongue moving blocks. In language tfMRI (N=1048), the design included story block where subjects were presented auditory stories and math block where subjects were presented math task aurally. Acquired images were preprocessed by minimal HCP preprocessing pipeline[2]. Head motion data included estimated rotation in three coordinates, estimated translation in three coordinates and derivative of each parameter for each acquired slices.
Method
Acquired HCP fMRI images were further processed with high-pass filter discarding temporal frequency below 1/100Hz[3]. Then analysis was performed using general linear model (GLM)[1]. With results from GLM analysis, statistical inference was performed. With motor tfMRI, two Z maps were produced for each subjects contrasting left finger tapping blocks to right finger tapping blocks and contrasting left toe squeezing blocks to right toe squeezing blocks. With language tfMRI, story block and math block was contrasted to create another Z map for each subjects. Shift of the Z score distributions were represented as three values; mean, median and mode. Mode of the distribution was estimated; (mode) = 3*(median) - 2*(mean)
Head motion was represented as four variables; maximum head rotation, maximum head translation, summed root mean square (RMS) of head rotation and summed root mean square (RMS) of head translation
Results:
Among 3146 Z maps, about 12 were shifted more than 0.2 standard deviation. An example of shifted Z value distribution is shown in figure 1.
Analysis 1: Correlation between mode of the Z value distribution and head motion variables were very small (Table 1). Biggest correlation was shown between language tfMRI Z map and maximum head translation (Pearson's r = 0.217, p< 0.01).
Analysis 2: Z map shift in finger tapping contrast and toe tapping contrast were highly correlated (Pearson's r = 0.696, p < 0.01). However, Z map shift in language tfMRI was not correlated with neither that of finger tapping contrast (Pearson's r = -0.012, p = 0.70) nor toe squeezing contrast (Pearson's r = -0.073, p = 0.02).
Analysis 3: Z score distribution for voxels within the white matter was shifted as well. Range of the Z distribution shift within white matter was similar to range of the Z distribution shift within the whole brain.