Table utilities / Normalisation / scaling
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CPM divides each sample’s counts by its total and multiplies by one million, removing differences in sequencing depth; TPM first corrects for gene length (kb) and then rescales, so genes within a sample are comparable. Both are often followed by log2(x + 1) for plotting.
Median of ratios (DESeq2 size factors) estimates one scaling factor per sample from genes expressed in every sample and is robust to a few highly expressed genes changing; quantile normalisation makes every sample’s distribution identical and is common for microarrays.
z-score, min–max, centring and Pareto scaling are used for heatmaps, clustering and metabolomics: “by row” compares one gene across samples, “by column” rescales within each sample.
The box plot shows each sample after normalisation; with a sensible method the medians should roughly line up. For differential expression, use raw counts with a dedicated statistical method rather than testing CPM/TPM directly.
TPM: Wagner et al. 2012 (Theory Biosci 131:281); median of ratios: Anders & Huber 2010 (Genome Biol 11:R106); quantile normalisation: Bolstad et al. 2003 (Bioinformatics 19:185); Pareto scaling: van den Berg et al. 2006 (BMC Genomics 7:142).
Up to 200,000 rows; the chart samples about 3,000 values per sample.
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