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Abstract: In educational and psychological tests, there are many methods forestimating reliability based on a single test such as: splithalf correctionformula, Rulon's formula, Flanagan's formula, K-R_(20) formula, Hoyt'sformula, coefficient α and formula β, and so on. Are there any relationsamong these formulas? Which is more superior? These are problems thatrefers to how to use and explain them correctly. These problems are stu-died in this papers and some results are obtained: 1. In estimating reliability of internal consistency, Coefficient α ismore superior, and other formulas of estimation are either its equivalentform or its special example in some cases; 2. In estimating reliability coefficient D(T)/D(X), formula β is moresuperior to coefficient α; Finally, another new formula β_1, of estimating reliability coefficient isgiven and the relation of β and β_1 is discussed.

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