Speed and Power Indices of tests and items

Abstract

A simple index is proposed to measure speed or power components of a test. The index is independent of position of the items and provides necessary and sufficient condition for pure speed test and pure power test and enables testing of statistical hypothesis to infer that the test can be taken as a speed test or a power test. Similar index of an item is also proposed to reflect whether the item is a speed item or a power item. The proposed index C is a ratio such that C = 0 ⟺Pure power test and C = 1⟺Pure speed test facilitating computation of similar index of each item and statistical test of significance. Properties of the index discussed. Operational method outlined to modify a test to speed or power test. Items can be ranked with respect to such item-wise index. Identification of power items and speed items help to modify the test to a speed or power test by deleting items in stages, if speediness (or power) is not intended. Relationship between index for the test and item-wise indices derived.