A critique of the expectancy formula approach: Beating a dead horse?

Abstract

The expectancy and severe discrepancy formulas, like those originally considered by the US. Office of Education (1976), provide the oldest but least defensible method of quantifying academic discrepancy. A logical and mathematical analysis reveals that all variations of this approach have several major weaknesses. First, the expectancy formulas themselves are predicated upon the very questionable assumption that achievement follows a straight line growth pattern, which raises questions about the accuracy of the resulting severe discrepancy values. Second, when discrepancy values are obtained by multiplying the expected values by a fractional constant, the approach is necessarily biased in the direction of applying a more stringent underachievement criterion for older and brighter children. Third, the formulas employ a grade equivalent scale that results in inconsistencies, one being that fewer arithmetic problems are identified. Finally, the expectancy approach does not consider errors in measurement or regression effects, and consequently produces serious identification errors. A variation of the expectancy approach involving a discrepancy ratio between obtained and expected achievement has the previously mentioned limitations, except the bias, and it produces scores that cannot be easily interpreted.