Partial Scoring of Reordering Tasks Revisited: Linearity Matrix by Excel

Abstract

Estimating a partial score of item reordering tasks has long been neglected in language testing and education sciences. A psychologically valid means of scoring, MRS (Maximal Relative Sequence) was proposed by the author and transplanted to Excel. As the protocol simply picks up elements in relative ascending order, it made easier the non-specialists’ access to and analysis of the calculation process resulting in educational as well as practical significance. However, since the Excel enumeration replicated each step of MRS precisely, the number of columns consumed explodes as the number of elements increases. Moreover, MRS merely counts the number of elements to be relocated; it fails to consider the distance of relocation for recovery. This paper proposes an alternative solution LM (Linearity Matrix), also executable with Excel’s basic functions, with far fewer columns to consume. Further, LM is advantageous over MRS in that it is a general protocol of estimating relative similarity of two sequences of which Kendall’s tau is a special case; LM is adjustable as to the degree of adjacency constraint by changing the distance weight for all combinations of elements.