Table 2 Choice of \({\text{D}}_{\text{k},\text{n}}\)s
Competitor | Construction | Choice |
|---|---|---|
CPM-Exp (Ross 2014) | \({\text{M}}_{\text{k},\text{n}}=-2\text{log}(\frac{{\text{L}}_{0}}{{\text{L}}_{1}})\) | \({\text{D}}_{\text{k},\text{n}}={\text{M}}_{\text{k},\text{n}}\) |
CPM-Adjusted Exp (Ross 2014) | \({\text{M}}_{\text{k},\text{n}}^{\text{c}}=\frac{{\text{M}}_{\text{k},\text{n}}}{\text{E}({\text{M}}_{\text{k},\text{n}})}\) | \({\text{D}}_{\text{k},\text{n}}={\text{M}}_{\text{k},\text{n}}^{\text{c}}\) |
CPM-Mann–Whitney (Hawkins and Deng 2010) | \({\text{U}}_{\text{k},\text{n}}=\sum_{\text{i}=1}^{\text{k}}\sum_{\text{j}=\text{k}+1}^{\text{n}}\text{sgn}({\text{X}}_{\text{i}}-{\text{X}}_{\text{j}})\) | \({\text{D}}_{\text{k},\text{n}}={\text{U}}_{\text{k},\text{n}}\)(scaled) |
CPM-Mood (Ross et al. 2011) | \(\text{M}=\sum_{{\text{X}}_{\text{i}}}((\sum_{\text{i}\ne \text{j}}^{\text{n}}\text{I}({\text{X}}_{\text{i}}\ge {\text{X}}_{\text{j}}))-\frac{\text{n}+1}{2}{)}^{2}\) | \({\text{D}}_{\text{n}}=\text{M}\)(standardized) |
CPM-Lepage (Ross et al. 2011) | \(\text{L}={\text{U}}^{2}+{\text{M}}^{2}\) | \({\text{D}}_{\text{n}}=\text{L}\) |
CPM-Kolmogorov–Smirnov (Ross and Adams 2012) | \({\text{M}}_{\text{k},\text{n}}={\text{sup}}_{\text{x}}|{\hat{\text{F}}}_{{\text{S}}_{1}}(\text{x})-{\hat{\text{F}}}_{{\text{S}}_{2}}(\text{x})|\) | \({\text{D}}_{\text{k},\text{n}}={\text{M}}_{\text{k},\text{n}}\) |
CPM-Cramer-von-Mises (Ross and Adams 2012) | \({\text{M}}_{\text{k},\text{n}}={\int }_{-\infty }^{\infty }|{\hat{\text{F}}}_{{\text{S}}_{1}}-{\hat{\text{F}}}_{{\text{S}}_{2}}|{\text{dF}}_{\text{t}}(\text{x})\) | \({\text{D}}_{\text{k},\text{n}}={\text{M}}_{\text{k},\text{n}}\) |