title: Hypothesis testing for coefficient alpha: an SEM approach.
abstract: We show how to test hypotheses for coefficient alpha in three different situations: (1) hypothesis tests of whether coefficient alpha equals a prespecified value, (2) hypothesis tests involving two statistically independent sample alphas as may arise when testing the equality of coefficient alpha across groups, and (3) hypothesis tests involving two statistically dependent sample alphas as may arise when testing the equality of alpha across time or when testing the equality of alpha for two test scores within the same sample. We illustrate how these hypotheses may be tested in a structural equation-modeling framework under the assumption of normally distributed responses and also under asymptotically distribution free assumptions. The formulas for the hypothesis tests and computer code are given for four different applied examples. Supplemental materials for this article may be downloaded from http://brm.psychonomic-journals.org/content/supplemental.
authors.affiliation: University of Barcelona, Barcelona, Spain. amaydeu@ub.edu
authors.forename: Alberto
authors.initials: A
authors.lastname: Maydeu-Olivares
authors.forename: Donna L
authors.initials: DL
authors.lastname: Coffman
authors.forename: Carlos
authors.initials: C
authors.lastname: García-Forero
authors.forename: David
authors.initials: D
authors.lastname: Gallardo-Pujol
mesh_terms: D003198:Computer Simulation; D015233:Models, Statistical; D015203:Reproducibility of Results; D012107:Research Design / Q000706:statistics & numerical data*; D012984:Software