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A measurement technique for the phase and group birefringence of an optical fiber is thoroughly investigated. It is based on differential group delay measurements of twisted fibers and is capable of giving in a simple and elegant way the intrinsic birefringence values in the absence of twist. Analyzing various fibers with this method, we find that phase and group birefringence can be quite different for certain fiber types. Consequently, the commonly used assumption that in an optical fiber, phase and group birefringence are equal-and the resulting carelessness in distinguishing between these two a priori separate physical effects-is to be employed cautiously.