Finite-size effects in transcript sequencing count distribution: its power-law correction necessarily precedes downstream normalization and comparative analysis

Table 3 The average signal-to-noise characteristics of the comparative dilution analysis (AGS versus NUGC3) before and after power-law correction

	Original data			Power-law corrected data
Mapping method	Median residual (μ ± σ)_noise	Median residual (μ ± σ)_signal	Median signal-to-noise ratio \( \frac{E\left({x}_{signal}^2\right)}{\sigma_{noise}^2} \)	Median residual (μ ± σ)_noise	Median residual (μ ± σ)_signal	Median signal-to-noise ratio \( \frac{E\left({x}_{signal}^2\right)}{\sigma_{noise}^2} \)
Bowtie1	0.018 ± 0.649	−0.192 ± 2.229	11.3	0.002 ± 0.261	0.006 ± 1.021	15.4
Bowtie2 (global)	0.019 ± 0.642	−0.169 ± 2.200	11.3	0.002 ± 0.244	0.003 ± 1.022	17.6
Novoalign	0.017 ± 0.641	−0.153 ± 2.189	11.3	0.001 ± 0.238	−0.001 ± 1.017	18.2
BWA	0.017 ± 0.648	−0.159 ± 2.193	11.1	0.001 ± 0.242	0.001 ± 1.019	17.8

This table complements the MA-plots in Fig. 6A to D. It summarizes the characteristics of the signal and noise comparisons before and after power-law correction for each aligner across 6 normalization methods. The bias and variance of each normalization method, in terms of signal and noise, are computed from the difference between the comparisons and the fitted noise model and with the summary statistics taken. The signal-to-noise ratio, before and after power-law correction, are also given. The average signal-to-noise ratio improvement is about 1.5 times after the correction

ISSN: 1745-6150