The figure shows the theoretical (top panel) and empirical (bottom panel) relative variance reduction with number of genes used for NORMA-Gene normalization. As the number of genes increases the relative standard deviation for the fitted a is reduced as displayed (see Eq. A8 in Additional file 1, Appendix A for the mathematical rationale). Top panel: The figure shows the theoretical prediction that the standard deviation of the fitted a is more than halved when using five genes. Adding further genes to the analysis only slightly improves the estimate of a. Bottom panel: The figure shows the reduction in the standard deviation of the fitted a when NORMA-Gene is applied to real data. Dark gray, light gray and white bars represent data-sets I, II and III, respectively. As the improvements (reduction) of the standard deviation is a result of adding one more gene to the analysis, the result is dependent on the genes included in each data-set when all genes are not used. Thus, means and error bars represent three different randomly normalizations. These corroborate with the theoretical predictions of stable and robust normalization when five or more genes are used.
Heckmann et al. BMC Bioinformatics 2011 12:250 doi:10.1186/1471-2105-12-250