Determination of optimal test length to maximize the multiple correlation

If the lengths of the tests in a battery are altered, their intercorrelations and their validities or correlations with a criterion are also altered. Consequently, the multiple correlation of the battery with the criterion will also be altered. These changes are a function of the reliabilities of the tests. Suppose we have given from a set of experimental data (1) the time allowed for each test in the battery, (2) the reliability of each test, (3) the intercorrelations, and (4) the validities of all the tests. If we specify the over-all testing time we are willing to allow for the test in the future, we can determine the amount by which each test must be altered in order to give the maximum multiple correlation with the criterion. The method is presented, together with numerical examples and the mathematical proof.