Although both SAM (Significance Analysis of Microarray, [ 8]) and LIMMA (Linear Models for Microarray Data, [ 9]) utilize moderated t-statistic and do not need the assumption of rigorous normality, their sensitivity is generally affected by a non-normal distribution.
By construction, the Kalman-EM filter (cf. Elliott et al. [1]) is not able to capture all stylised characteristics of the data governed by a non-normal distribution.
This choice is justified by the fact that (i) there was no obvious transformation that improved the normality of residuals and (ii) the experimental design was almost perfectly balanced and included large sample sizes, two features known to mitigate the effects caused by a non-normal distribution and/or the heterocedasticity of variances (Ananda and Weerahandi 1997).
However, we adjusted the sample by 20%% expecting a non-normal distribution of this variable.
If by chance a sample from a non-normal distribution happens to look normal, the researcher could falsely assume that the normality assumption holds.
The G6PD values exhibited a normal distribution in the study by Boo et al. but a non-normal distribution in the study by Fok et al. [ 7, 8].
Thus it follows by (1.1) that P is a non-normal cone.
Treatment effects on any secondary outcomes will be assessed in the same way, allowing for any deviations from a non-normal data by generalisations of the LMM.
Correlation to the N-addition microarray data set was determined by Pearson Product-Moment Correlation while correlations to the P-addition data set were determined by Spearman's Rho, due to a non-normal data distribution, using JMP version 5.1.2 (SAS Institute, Cary, NC).
Continuous variables demonstrated a non-normal distribution, as assessed by the Kolmogorov-Smirnov test, and group differences were explored by the Mann-Whitney U-test.
