The general use of the Spearman-Brown formula for calculating the reliability of parallel tests with different lengths is reviewed. The importance of the assumption that the component tests be parallel is noted and the property that parallel tests must be non-negatively correlated is derived. It is concluded that one should pay close attention to the theory underlying an analysis.
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Lord, F. M. and Novick, M. R.Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.
