Reliability of test battery

Abstract

After a brief review of methods for assessing the reliability of individual test, the article presents a method of obtaining reliability of a battery of tests where battery score could be defined as sum of weighted or unweighted scores of the component tests. Such battery reliability can be influenced significantly by method of selection of weights to arrive at the battery scores and methods of estimating reliability of component tests. Test reliability as per theoretical definition in terms of length of score vectors of two parallel tests and angle between such vectors in N-dimensional space also helps to find values of error score variance of the test fits well in estimation of battery reliability. Relationship between theoretically defined reliability rtt and split-half correlation rgh was established. For weighted battery score, a Lagrange multiplier-based solution for determination of weights is recommended with the use of reliability as per the theoretical definition. Weights found as above have the advantage that the battery score (Y) has minimum variance. Also, covariance between the battery score and the score of an individual test is a constant. Condition of battery score being equi-correlated with the standardized score of each constituent test was derived.