We present free-space microwave measurements on composite metamaterials (CMMs) consisting of split ring resonators (SRRs) and wires either on the same dielectric board or on alternating boards. Our experimental results disprove the widely held belief that the occurrence of a CMM transmission peak within the stop bands of the SRRs alone and wires alone constitutes a clear demonstration of left-handed (LH) behavior. This belief is based on the assumption that the stop bands of SRRs alone and wires alone are not affected by the simultaneous presence of both. We show here that this assumption is wrong: The effective plasma frequency, ω′p, of the CMM is actually substantially lower than the wires-only plasma frequency, ωp; furthermore, the in-plane wires, as opposed to the off-plane case, push the magnetic resonance frequency of the SRRs, ωm, to a higher value, ω′m, for the CMM. We conclude that the criterion for deciding whether a peak in the transmission spectrum through a CMM is really left-handed is for the peak to be located above ω′m and below ω′p. Our results provide a definite way for experimentally identifying ω′p.