caa a22 4500 606241795 CHVBK 20210128101315.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11336-013-9393-6 doi (NATIONALLICENCE)springer-10.1007/s11336-013-9393-6 Quantile Lower Bounds to Reliability Based on Locally Optimal Splits [Elektronische Daten] [Tyler Hunt, Peter Bentler] Extending the theory of lower bounds to reliability based on splits given by Guttman (in Psychometrika 53, 63-70,1945), this paper introduces quantile lower bound coefficients λ 4(Q) that refer to cumulative proportions of potential locally optimal "split-half” coefficients that are below a particular point Q in the distribution of split-halves based on different partitions of variables into two sets. Interesting quantile values are Q=0.05,0.50,0.95,1.00 with λ 4(0.05)≤λ 4(0.50)≤λ 4(0.95)≤λ 4(1.0). Only the global optimum λ 4(1.0), Guttman's maximal λ 4, has previously been considered to be interesting, but in small samples it substantially overestimates population reliability ρ. The three coefficients λ 4(0.05), λ 4(0.50), and λ 4(0.95) provide new lower bounds to reliability. The smallest, λ 4(0.05), provides the most protection against capitalizing on chance associations, and thus overestimation, λ 4(0.50) is the median of these coefficients, while λ 4(0.95) tends to overestimate reliability, but also exhibits less bias than previous estimators. Computational theory, algorithm, and publicly available code based in R are provided to compute these coefficients. Simulation studies evaluate the performance of these coefficients and compare them to coefficient alpha and the greatest lower bound under several population reliability structures. The Psychometric Society, 2013 reliability nationallicence split half nationallicence lower bounds nationallicence lambda 4 nationallicence Hunt Tyler University of Utah, Salt Lake City, USA aut Bentler Peter University of California, Los Angeles, Los Angeles, USA aut Psychometrika Springer US; http://www.springer-ny.com 80/1(2015-03-01), 182-195 0033-3123 80:1<182 2015 80 11336 https://doi.org/10.1007/s11336-013-9393-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11336-013-9393-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hunt Tyler University of Utah, Salt Lake City, USA aut NATIONALLICENCE 700 1- Bentler Peter University of California, Los Angeles, Los Angeles, USA aut NATIONALLICENCE 773 0- Psychometrika Springer US; http://www.springer-ny.com 80/1(2015-03-01), 182-195 0033-3123 80:1<182 2015 80 11336