The assumption of normality of residual and BLUP distributions was checked through quantile-quantile plots comparing the observed distributions to a theoretical normal distribution.
This means that the z-scores of the functional TM-helices satisfy the normality assumption reasonably well for the range of thresholds studied, although the tails of the empirical distribution extend slightly more than in the theoretical normal distribution.
The mixed model assumption of normality of residual and BLUPs was checked after model fitting by quantile-quantile plot comparing the distribution of residual and random effect predictors to a theoretical normal distribution (Additional file 2).
The counter-examples validate the fact that the expected-compliance, as a statistical abstraction based on more or less theoretical assumption about normality, not a general applicable measure of robustness.
In addition, these schemas were not value free but leaders have a clear body of theoretical knowledge about normality and how abnormality needs to be addressed [4].
This would represent an improvement over current standards which rely heavily on theoretical assumptions (eg., normality of birth weight at any given gestational age) and insufficiently on relevant empirical information (namely, perinatal morbidity and mortality related to growth restriction).
First, for many statistically less well trained users it is hard to verify to which extent statistical procedures for comparing means are based on theoretical assumptions such as normality or homoscedasticity, i.e. homogeneous or equal variances among all groups.
From a theoretical point of view, this normality assumption may be dropped in favour of other symmetric but heavier-tailed densities, such as the Student t-distribution which allows to identify and accommodate for outliers both on the level of the within-group errors but also at the level of random effects [ 76].
Additionally, plots of sorted residuals versus theoretical quantiles of the normal distribution revealed evidence of non-normality for all four exposures.
Normality was determined by plotting the theoretical quantiles versus standardised residuals (Q-Q plots), while homogeneity of variance was evaluated by plotting residuals versus fitted values [44].
Further characterization of others hemogram components could significantly contribute to design a theoretical model to predict whether hemogram series evolve towards normality or in the opposite sense.
