A comparison of reliability coefficients for psychometric tests that consist of two parts

If a test consists of two parts the Spearman-Brown formula and Flanagan's coefficient (Cronbach's alpha) are standard tools for estimating the reliability. However, the coefficients may be inappropriate if their associated measurement models fail to hold. We study the robustness of reliability estimation in the two-part case to coefficient misspecification. We compare five reliability coefficients and study various conditions on the standard deviations and lengths of the parts. Various conditional upper bounds of the differences between the coefficients are derived. It is shown that the difference between the Spearman-Brown formula and Horst's formula is negligible in many cases. We conclude that all five reliability coefficients can be used if there are only small or moderate differences between the standard deviations and the lengths of the parts.