Extending the theory of lower bounds to reliability based on splits given by Guttman (in Psychometrika 53, 63–70, <CitationRef CitationID="CR10">1945</CitationRef>), this paper introduces quantile lower bound coefficients λ <Subscript>4(Q)</Subscript> that refer to cumulative proportions of potential locally optimal “split-half” coefficients that are...</subscript></citationref>