The discrimination of an item can be calculated as:
$$D = \frac {K_h-K_l}{N}$$
Where $K_h$ is the number of correct responses from the high scoring group, $K_l$ from the lowest scoring group (top and bottom 27% usually) and $N$ the number of individuals in either group.
This is a measure of the item's ability to discriminate.
Another measure of the ability of an item to differentiate scores is the corrected item-scale correlation (correlation of the item with the score after removing the item from the scale).
Are this measures equivalent? When should you use one method over another? What is the best cutoff (standard is 27%) for discrimination analysis, why?
