Table 1.

A Short Summary of the Anchor Selection Strategies That Are Investigated in This Article.

Selection	Description
AO	The items are ranked according to the lowest absolute test statistics $\left|t_j(\{1,\dots ,k\}\setminus j)\right|.$
AOP	Beginning with all other items as anchor, DIF items are iteratively excluded from the anchor until the purified anchor set ${\mathcal{A}}_{\mathrm{purified}}$ is reached; the items are ranked according to the lowest absolute test statistics $\left|t_j\left({\mathcal{A}}_{\mathrm{purified}}\right)\right|.$
NST	The items are ranked according to the lowest number of significant test statistics $t_j(\{\ell \}).$
MT	The items are ranked according to the lowest mean absolute test statistics $\frac{1}{k-1}{\displaystyle \sum _{\ell \in \{1,\dots ,k\}\setminus j}}|t_j(\{\ell \})|.$
MP	The items are ranked according to the largest mean p-values $\frac{1}{k-1}{\displaystyle \sum _{\ell \in \{1,\dots ,k\}\setminus j}}{p}_j(\{\ell \}).$
MTT	The items are ranked according to the smallest number of test statistics $|t_j(\{\ell \})|$ exceeding the $\left(\lceil 0.5\cdot k\rceil \right)$-th ordered absolute mean test statistic $\left|\frac{1}{k-1}{\displaystyle \sum _{\ell \in \{1,\dots ,k\}\setminus j}}{t}_j\left(\left\{\ell \right\}\right)\right|.$
MPT	The items are ranked according to the largest number of p-values $p_j(\{\ell \})$ exceeding the $\left(\lceil 0.5\cdot k\rceil \right)$-th ordered mean p-value $\frac{1}{k-1}{\displaystyle \sum _{\ell \in \{1,\dots ,k\}\setminus j}}{p}_j\left(\left\{\ell \right\}\right).$
perfect	The perfect ranking consists of randomly permuted DIF-free items followed by randomly permuted DIF items.