Note on use of extreme criterion groups in item discrimination analysis

The purpose of this note is to reconsider the Kelley-Cureton definition of optimal extreme groups for estimating item-criterion correlations. Optimal tail per cents are derived, using the criterion of minimum sampling variance of the tetrachoric correlation coefficient, and the findings are related to earlier work of Mosteller. It is shown that upper and lower 27 per cent groups yield the most precise estimate of the tetrachoric coefficient only when the population correlation is close to zero. When the population value is .4, extreme 20 per cent groups provide estimates with the smallest sampling error variance. It is further shown, however, that 27 per cent extremes yield highly efficient estimates. Thus no change is recommended in traditional item analysis procedures.