A Comparison of the Spearman-Brown and Flanagan-Rulon Formulas for Split Half Reliability under Various Variance Parameter Conditions

Abstract

Differences between the Spearman-Brown and Flanagan-Rulon formulas are examined when the variance parameters for two halves of a test had the following ratios: 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0 and also had a correlation between the two halves of a test at 1.00, .95, .90, .80, .70, .60, .50, .40, .30, .20, .10, .05. It was found that use of the Spearman-Brown formula to estimate the population ρ when the ratio between the standard deviations on two halves of a test is disparate, or beyond .9 to 1.1, was not warranted. Applied and theoretical examples are employed, as well as syntax for user application.