Assumptions related to multivariate analysis, including normality, linearity, homoscedasticity of residuals, multicollinearity, and the influence of multivariate outliers, were examined and found to be met.
Preliminary assumption testing was conducted before multivariate analyses to check for normality, linearity, univariate and multivariate outliers, and for homogeneity of variance matrices, and no serious violations were noted.
Prior to conducting the multivariate analyses, assumptions of normality, linearity, and collinearity were tested and adjustments were made where necessary.
Preliminary assumption testing was conducted to check normality, linearity, univariate and multivariate outliers, homogeneity of variance-covariance matrices and muticollinearity, with no serious violations noted.
An exploration analysis performed on dependent variables at pre-test and two post-tests to examine preliminary assumption for mixed between-within subject ANOVA on tests of normality, linearity, multi-collinearity, univariate and multivariate outliers and homogeneity of variance revealed no serious violation to test assumptions [ 33].
The multivariate normality assumption was confirmed by normal quantile-quantile plots of residuals.
The linear regression model assumptions of normality, linearity and homoscedasticity were assessed using residual plots.
Multivariate normality was assessed by calculating the normalized estimate of Mardia's multivariate kurtosis coefficient [ 24].
We conducted Mardia's normalized coefficient of multivariate kurtosis to examine multivariate normality.
Most of the existing bulk-density pedotransfer functions (PTFs) are formulated as linear (multiple) regression functions, with the requirements for multivariate normality and homoscedasticity.
