Table 2 Description of ranking metrics sorted from the most parametric, through non-parametric to data mining methods

T-test

\(\frac {\overline {x_{1}} - \overline {x_{2}} }{\sqrt {\frac {{s_{1}^{2}}}{n_{1}}+ \frac {{s_{2}^{2}}}{n_{2}}}} \)

[9]

MWT

\(\frac {\overline {x_{1}} - \overline {x_{2}} }{se_{m}}\); \( {se_{m}^{2}}=\frac {d_{0}{s_{0}^{2}+d_{w}{s_{w}^{2}}}}{d_{0}+d_{w}}\)

and absolute value

[35]

MSD

\(\left \{\begin {array}{ll} {CI}_{left} & log(FC)>0 \\ -{CI}_{right} & log(FC)<0 \end {array}\right.\)

[41]

S2N

\(\frac {\overline {x_{1}} - \overline {x_{2}} }{s_{1}+s_{2}}\)

and absolute value

[9]

WAD

AD∗w; \(AD=\overline {x_{1}} - \overline {x_{2}} \)

and absolute value

[39]

\(w=\frac {\overline {x}-min}{max-min} \); \(\overline {x}=\frac {\overline {x_{1}} + \overline {x_{2}} }{2} \)

Difference

\(\overline {x_{1}} - \overline {x_{2}}\)

[9]

Ratio

\(\frac {\overline {x_{1}}}{ \overline {x_{2}}}\)

and log₂

[9]

FCROS

\({Mean}_{(truncated,10\%)}\left |\begin {array}{ccc}{FC}_{1,1}&...&{FC}_{1,k}\\.&&.\\.&...&.\\.&&.\\FC_{N,1}&...&{FC}_{N,k}\end {array}\right | \)

[40]

k - pairwise comparison; FC - fold change, N - no. of genes

SoR

\(\sum \limits _{i=1}^{N_{1}}R_{i}\) ; N ₁ - size of group 1; R - ranks of elements from group 1

[31]

BWS

\(\frac {B_{1}+B_{2}}{2}\); \( B_{1}=\frac {1}{n_{1}}\sum \limits _{j=1}^{n_{1}}\frac {\left (R_{1}^{j}-\frac {n_{2}+n_{1}}{n_{1}}j\right)^{2}}{\frac {j}{(n_{1}+1)} \left (1-\frac {j}{(n_{1}+1)}\right) \left (\frac {n_{2}(n_{2}+n_{1})}{n_{1}}\right) }\)

[31, 36]

\(B_{2}=\frac {1}{n_{2}}\sum \limits _{i=1}^{n_{2}}\frac {\left (R_{2}^{i}-\frac {n_{2}+n_{1}}{n_{2}}i\right)^{2}}{\frac {i}{\left (n_{2}+1\right)} \left (1-\frac {i}{(n_{2}+1)}\right) \left (\frac {n_{1}(n_{2}+n_{1})}{n_{2}}\right) }\)

ReliefF

\(W-\frac {\sum _{k=1}^{K}D(x,h_{k})}{tK}+\sum \limits _{c\neq class(x)}^{} \frac {P(c)}{1-P(class(x))}\frac {\sum _{k=1}^{K}D(x,m_{k})}{tK}\)

and tied rank

[38]