A generalization of coefficient alpha

It is well known that coefficient alpha can be used to estimate the reliability of a test even when the test is split into several parts. It is also known that alpha can severely underestimate test reliability when the several parts have an unequal number of items. A gernalization of alpha,β _k, is proposed to correct this defect. Several properties ofβ _k are also presented. The author gratefully acknowledges the assistance of Dr. Leonard Feldt for reviewing an earlier draft of this paper, and Ms. Rita Karwacki Bode and Mr. Dave Mansell for the analysis of the experimental data reported here. The comments of an unknown referee which contributed substantially to the clarity of the presentation are also gratefully acknowledged.