Type II radio bursts are observed in the Sun in association with many coronal mass ejections (CME's). In view of this association, there has been an expectation that, by scaling from solar flares to the flares which are observed on M dwarfs, radio emission analogous to solar Type II bursts should be detectable in association with M dwarf flares. However, several surveys have revealed that this expectation does not seem to be fulfilled. Here we hypothesize that the presence of larger global field strengths in low-mass stars, suggested by recent magneto--convective modeling, gives rise to such large Alfven speeds in the corona that it becomes difficult to satisfy the conditions for the generation of Type II radio bursts. As a result, CME's propagating in the corona/wind of a flare stars are expected to be "radio--quiet" as regards Type II bursts. In view of this, we suggest that, in the context of Type II bursts, scaling from solar to stellar flares is of limited effectiveness.Keywords: stars------flare; stars-radio; stars-magnetic fields flare energies can exceed the largest solar flare energies by factors of up to100--1000, there should be a strong correlation between the physical parameters of flare events and those of CME's.However, the expectation has not turned out so well when observers have searched for CME's using two distinct observational approaches: Balmer line profiles, and Type II radio observations. First, in the context of Balmer lines, Leitzinger et al (2014) searched for flares and flare--related CME's in 28 dK--dM stars in a young cluster. Their technique was based on the following statement in their paper: "Pronounced Balmer line asymmetries are likely to be related to CME's as no other sporadic phenomenon is known to produce velocities of several hundred km/sec". They cited Houdebine et al (1990) who had reported observations of a large flare on AD Leo in the Hγ line where a blue--shifted feature was observed at 5800 km/sec with an estimated mass of 8 x 10 17 gm. Leitzinger et al also cited other previous searches of Balmer lines, none of which had produced any convincing evidence of a CME. But in view of the Houdebine et al success with Hγ, Leitzinger et al (2014) obtained spectra in the vicinity of another Balmer line (Hα) and searched for a Doppler--shifted feature in the blue wing of the line profile.Their spectral resolution was such that they could detect CME's only if the projected velocity exceeded their resolution limit, i.e. 135 km/sec. Moreover, in view of their finite S/N ratios, they could detect a CME with a confidence of >3σ against the noise background only if the energy flux of the CME in Hα exceeded 1.4 x 10 --16 ergs/cm 2 /sec. In 4 of their target stars, they reported seeing features which were blue--shifted with speeds ranging from ~175 to ~300 km/sec: however, none of the features was large enough to satisfy the >3σ criterion. They admitted that since CME's are ejected from a star at arbitrary angles, observers can measure only the projected velocity relative to the line o...