Matlab 2018a statistics and machine learning toolbox

All statistical analyses were performed using R 3.5.0³⁰ or MATLAB 2018a Statistics and Machine Learning Toolbox (Mathworks, Natick, MA, US). There were three groups (saline, 1 h after soman, and 18–24 h after soman), each imaged twice before and after saline or soman exposure. A general linear model was performed evaluating the changes in T₂ after exposure. Group (saline, soman 1 h, soman 18–24 h), treatment (before, after exposure), and brain regions were entered as fixed effects. This was followed by Tukey’s honestly significant difference post-hoc test. For the linear regression, the relaxation rate (R₂) was calculated using $R_2=1/T_2$ . The relationship between changes in R₂ vs. percentage of neurodegeneration was determined through linear regression to calculate the correlation coefficient (r), and equation of the line. We excluded one rat from the linear regression because tissues did not adhere to the slides and FJC staining could not be assessed. Statistical significance was determined a priori using α = 0.05.

To assess the independent and combined effects of the walking speeds and various methods or modes, we tried to use two-way ANOVAs. However, the hypothesis of homogeneity of variances among methods or modes was rejected with Levene’s test, thus Friedman tests were performed for comparison among methods or modes. We used Wilcoxon’s sign rank test to compare the variables within the factor where a significant effect in Friedman test was found. The effect size was estimated using Kendall’s W for Friedman test and $r=z/\sqrt{N}$ for Wilcoxon’s sign rank test, where z is z-statistic estimated by Matlab function signrank. m and N is the number of samples. For all statistical calculations, p < 0.05 was considered significant. All statistical analyses were performed using the MATLAB 2018a Statistics and Machine Learning Toolbox (The MathWorks, Inc., MA, USA) and R-software package version 3.5.2.