Revelle’s Beta: The Wait Is Over—Computation Becomes Possible

Over 45 years ago, William Revelle proposed a reliability measure based on the worst split-half of a
test or scale, commonly known as Revelle’s beta, to assess the general factor saturation. However, to
this day, there is no reliable method for computing this measure, as existing approaches are either
computationally infeasible or insufficiently accurate in identifying the worst split-half. This difficulty
arises because the number of candidate splits increases exponentially with the number of items. In
this paper, we show that computing Revelle’s beta is conceptually equivalent to divisive (“top-down”)
hierarchical clustering. This insight allows us to reduce the number of candidate splits to a quadratic
problem, making the computation feasible. We specify theoretical conditions under which this approach
is guaranteed to recover the worst split-half. To validate the efficiency of our approach, we conduct
simulation studies and analyze real-world data. Code implementations accompanying this work are
available online, together with supplementary materials.